Motivated Errors. Christine L. Exley and Judd B. Kessler. May 31, Abstract

Transcription

1 Motivated Errors Christine L. Exley and Judd B. Kessler May 31, 2018 Abstract Behavioral biases that cause errors in decision making are often blamed on cognitive limitations. We show that biases can also arise, or be exacerbated, because agents are motivated to make errors. In three experiments involving nearly 3200 participants, agents motivated to be selfish make simple computational errors and respond to the salience of information known to them, and agents motivated to believe they are high ability update on entirely uninformative signals. When we remove self-serving motives, agents appear completely (or much more) rational. Biases due to motivated errors survive standard debiasing interventions including providing experience, ensuring attention, and simplifying decisions. Exley: Harvard Business School; Kessler: The Wharton School, University of Pennsylvania.

2 1 Introduction A rich literature in behavioral economics has documented various behavioral biases that cause errors in decision making. 1 Additional work has attempted to develop debiasing techniques to help agents overcome these biases; it has shown that biases are prevalent in many domains and are often quite hard for agents to overcome. The standard explanation for the presence and persistence of these biases is that they arise due to humans inherent cognitive limitations. Some of the earliest work in behavioral economics suggested that agents lacked the cognitive capacity to process all relevant information when making decisions and thus relied on heuristics, which led to behavioral biases (Simon, 1955; Conlisk, 1996). Similarly, when describing the causes of behavioral biases in their work, Kahneman and Tversky suggested humans cognitive limitations were at play. They blamed imperfections of human perception and decision and drew analogies to the limits of humans visual perception (Tversky and Kahneman, 1981, 1986; Kahneman, 2011). 2 More recently, a rich empirical literature documents, and a rich behavioral theory literature formalizes how specific cognitive limitations distort decisions, including work on saliency effects, proportional thinking, focusing, and relative thinking. Additional work shows that certain biases can be explained by assuming agents optimize under cognitive constraints, such as the work on inattention; for a review, see Caplin, Dean and Leahy (2016). 3 In this paper, we provide a complementary explanation for the presence and persistence of behavioral biases that cause errors in decision making. We focus on the vast array of domains where agents may be motivated to achieve particular outcomes or to hold particular beliefs. We find that in these settings, agents display behavioral biases not only because of inherent limitations of their cognitive ability but also because they are motivated to make errors. 4 1 Throughout this paper, we define as a behavioral bias any systematic response to information or a decision frame that causes errors in decision making. Our definition contrasts with a less restrictive definition in which a behavioral bias need not reflect errors in decision making, and for reasons that will become obvious throughout the paper our definition also contrasts with a more restrictive definition in which a behavioral bias must also be caused by a cognitive limitation (see further discussion in footnote 8). Such biases include anchoring bias, availability bias, contrast effects, correlation and selection neglect, base-rate neglect, projection bias, responses to saliency, as well as mental accounting and other forms of narrow bracketing; for reviews, see Rabin (1998) and DellaVigna (2009). 2 The full quote reads: [R]ational choice requires that the preference between options should not reverse with changes of frame. Because of imperfections of human perception and decision, however, changes of perspective often reverse the relative apparent size of objects and the relative desirability of options (Tversky and Kahneman, 1981). 3 For empirical and theoretical work on these biases and their explanations, see, e.g., Tversky (1972); Tversky and Kahneman (1973); Thaler (1985); Ariely, Loewenstein and Prelec (2003); List (2003); Loewenstein, O Donoghue and Rabin (2003); Sims (2003); Simonsohn and Loewenstein (2006); Chetty, Looney and Kroft (2009); Finkelstein (2009); Caplin, Dean and Martin (2011); Bordalo, Gennaioli and Shleifer (2012, 2013); Cunningham (2013); Kőszegi and Szeidl (2013); Brocas et al. (2014); Gabaix (2014); Hanna, Mullainathan and Schwartzstein (2014); Schwartzstein (2014); Busse et al. (2015); Taubinsky and Rees-Jones (Forthcoming); Bushong, Rabin and Schwartzstein (2017); Dean, Kıbrıs and Masatlioglu (2017); Enke and Zimmermann (Forthcoming); Enke (2017); Gabaix (2017); Haggag and Pope (Forthcoming); Handel and Schwartzstein (2018). An additional, related line of work shows that individuals cognitive limitations are predictive of their risk and time preferences (Benjamin, Brown and Shapiro, 2006; Dohmen et al., 2010; Frederick, 2005). 4 Much of the empirical evidence in support of the cognitive limitations explanation of behavioral biases comes from controlled laboratory environments that take care to eliminate potential confounds (i.e., so agents respond only to the financial incentives offered in the experiment). These potential confounds include motives to achieve particular 1

3 In three studies, including a total of nearly 3200 participants, we show that individuals who have preferences to act or think in a certain way display behavioral biases in which they: (1) make computational errors, (2) respond to the saliency of something that is known to them, and (3) update their beliefs based on uninformative signals. In the first study, participants who want an excuse not to donate money look like they cannot properly add a zero (i.e., they act as if 4 d 4 d + 0). In the second study, participants in a similar setting look like they care about whether or not a charity that is known to receive a donation of $0 is made salient. In the third study, participants incentivized to correctly guess a measure of their cognitive ability update favorably on a signal of ability that is known to be entirely uninformative. These systematic responses to irrelevant information look like limitations of cognitive ability, and one could imagine developing a behavioral theory based on cognitive constraints to attempt to rationalize them. However, in a series of experimental treatments, we document that once we remove the motivation to be selfish or the motivation to hold favorable beliefs about one s own ability, participants look rational (in the first and third studies) or much more rational (in the second study). We say that the biased behavior we observe are due to motivated errors since they look like the kind of errors that arise from cognitive limitations but are motivated in nature. As we show throughout this paper, motivated errors differ from behavior observed in prior work on deliberate or rational inattention in which agents are unwilling to fully process information in an attempt to save on cognition costs, as in Taubinsky and Rees-Jones (Forthcoming) since participants displaying motivated errors systematically exploit their failure to process information in a self-serving direction. That biased behavior is either reduced or eliminated when agents are no longer motivated also demonstrates that our results are not driven by social desirability bias or an experimenter demand effect. The first main contribution of our paper is to document that motivated errors can cause or contribute to behavioral biases. These biases can arise entirely from motivated errors (as in our first and third studies) and jointly from cognitive limitations and motivated errors (as in our second study). Together, these results suggest that motivated errors may cause or contribute to behavioral biases in many environments. 5 Absent jointly considering cognitive limitations and motivated outcomes and motives to hold particular beliefs. However, given the myriad opportunities individuals have to be motivated in decision-making environments of interest, we see these motives as worth exploring. In line with motives faced by agents outside of the lab, we explore environments in which agents are motivated to choose a selfish outcome (in our Study 1 and Study 2) or are motivated to hold favorable beliefs about their intelligence (in our Study 3). Of course, the array of possible motives is extensive. Agent are often motivated to avoid costly actions associated with future or social benefits, such as saving for retirement, dieting, exercising, investing in education, or learning a new technology. Agents are also motivated to hold beliefs that favor their preferred political party or their in-group. 5 We focus on motives to be selfish and motives to hold favorable beliefs about one s own ability because these are commonly studied motives in the literature, influence decisions in an array of contexts, and can be cleanly manipulated in a laboratory paradigm. However, one could also easily imagine motivated errors contributing to a number of well-documented behavior biases that have been observed in settings where agents may be motivated. For examples, agents may engage in projection bias on a sunny day because they want to buy a convertible, even if it is not a prudent purchase; agents may fail to properly calculate a tax-inclusive price as an excuse to buy a product that they might otherwise deem too expensive; agents may anchor the sale price of their house to the purchase price of 2

4 errors a combination largely overlooked, since the cognitive limitation and motivated reasoning literatures have evolved rather separately one could easily misdiagnose the underlying driver of biased behavior. The second main contribution of our paper is highlighting why it is important to diagnose whether a behavioral bias is caused by cognitive limitations, motivated errors, or both. We test whether debiasing techniques traditionally used to overcome cognitive limitations can also mitigate motivated errors. Biases due to cognitive limitations are expected to become less pronounced as decision environments are made simpler, as agents are made to pay more attention to a decision, or as agents gain experience with a decision. 6 A recent example can be found in Enke and Zimmermann (Forthcoming), in which cognitive limitations prevent agents from making accurate calculations due to correlation neglect. In that setting where motivations are not relevant making sure that agents pay attention to the correlated nature of signals or simplifying the underlying correlation structure help agents make fewer mistakes. If a behavioral bias is due to motivated errors, however, then agents may not want to make correct calculations and these strategies need not be effective. Indeed, we find that these techniques do not debias participants displaying motivated errors. Our motivated errors arise in exceedingly simple environments and survive making the environments simpler. Giving participants experience with the decision task does not mitigate motivated errors. Finally, participants who choose to pay attention are, if anything, more likely to display motivated errors. 7 Consequently, determining how to debias behavior in practice likely requires identifying whether a behavioral bias is driven by cognitive limitations, motivated errors, or both. Cognitive limitations may cause suboptimal outcomes due to mistakes, and so debiasing is likely to make agents displaying cognitive limitations better off; see, e.g., the discussion in Chetty (2015). Motivated errors, on the other hand, may favorably alter the implications of an outcome, and so debiasing may make agents displaying motivated errors worse off. 8 This observation suggests an their house to maintain the belief that they made a good investment; agents may display confirmation bias because they are motivated to hold their preexisting beliefs or theories; and agents may engage in correlation neglect in their consumption of news to allow them to update too much on favorable information from multiple, correlated sources. 6 For reviews, see Conlisk (1996); DellaVigna (2009); Madrian (2014); Gabaix (2017); for related examples, see List (2003); Chetty, Looney and Kroft (2009); Finkelstein (2009); Brocas et al. (2014); Hanna, Mullainathan and Schwartzstein (2014); Schwartzstein (2014); Taubinsky and Rees-Jones (Forthcoming); Enke and Zimmermann (Forthcoming). DellaVigna (2009) highlights an exception where failure to Bayesian update can cause experience to exacerbate a bias. 7 That attention does not mitigate motivated errors underscores that our findings are distinct from the work on motivated information avoidance as in Dana, Weber and Kuang (2007). However, we do find evidence that supports and extends the work on motivated information avoidance. As described in Section 5.2, we test whether self-serving motives affect information acquisition and find that individuals acquire less information when self-serving motives are present. We know of no prior literature that facilitates such a direct test. 8 For example, if an agent is donating money to maintain a good self-image, and if a motivated error allows the agent to maintain that self-image without donating, then the agent may value the motivated error. As noted in footnote 1, we call any systematic response to information or to a decision frame a behavioral bias, so our definition is agnostic to whether the behavior is caused by cognitive limitations, motivated errors, or both, and it is agnostic to whether the behavior is harmful or beneficial for the agent. As we show in our experiments, biased behavior can look identical regardless of whether or not it is motivated in nature. Consequently, in settings where agents may be motivated, a definition that required behavioral biases to be due to a cognitive limitation would not allow us to call 3

5 important role for new theory on motivated errors, including work exploring whether they impose a cost or have value for agents, which we discuss further in Section 5.1. The third main contribution of our paper is documenting that the scope for self-serving behavior and the scope for self-serving beliefs are both much larger than previously thought. Unlike prior literature that documents motivated reasoning arising from the ability to avoid information and thus maintain moral wiggle room (Dana, Weber and Kuang, 2007), we document self-serving responses to unavoidable information. 9 Unlike prior literature that documents motivated reasoning arising from uncertainty in payoff information and thus the ability to distort how one responds to ambiguity (Haisley and Weber, 2010) or to risk (Exley, 2015), we document self-serving responses to information that is free of any uncertainty. More generally, unlike prior work on motivated reasoning that highlights the importance of seemingly reasonable justification (Kunda, 1990) or sufficient flexibility to allow plausible justification (Gino, Norton and Weber, 2016), we document self-serving responses to irrelevant information and thus information that does not permit flexibility in terms of how much it should influence behavior or beliefs: it shouldn t at all. 10 Our findings thus suggest a broader relevance of self-serving behavior and self-serving beliefs. The persistence of our findings to standard de-biasing approaches also highlights the difficulty in mitigating motivated reasoning, although there has been some success on that front see Gneezy et al. (2017) for an example of how self-serving assessments are reduced when preceded by unbiased assessments. 11 The rest of the paper proceeds as follows. Section 2 describes the design and results of Study 1. Section 3 describes design and results of Study 2. Section 4 describes design and results of Study 3. Section 5 summarizes our results and discusses their implications. Section 6 concludes. 2 Study 1: Computational Errors In Study 1, we present results of an experiment in which participants make computational errors. Their choices suggest that they believe adding a zero to a sum decreases its value. One biased behavior a behavioral bias until we had ruled out that agents motivations might be a contributing cause. 9 A substantial body of work shows that individuals are less likely to give when a donation request is expected or avoidable (Broberg, Ellingsen and Johannesson, 2007; Oberholzer-Gee and Eichenberger, 2008; Jacobsen et al., 2011; DellaVigna, List and Malmendier, 2012; Lazear, Malmendier and Weber, 2012; Kamdar et al., 2015; Trachtman et al., 2015; Andreoni, Rao and Trachtman, 2016; Lin, Schaumberg and Reich, 2016; Exley and Petrie, 2018). 10 Flexibility is known to arise from subjectivity around which set of actions is fair, appropriate, or plausibly justified (Snyder et al., 1979; Babcock et al., 1995; Hsee, 1996; Konow, 2000; Shalvi et al., 2011; Shalvi, Eldar and Bereby-Meyer, 2012; Gino and Ariely, 2012; Gino, Ayal and Ariely, 2013; Di Tella et al., 2015; Pittarello et al., 2015; Danilov and Saccardo, 2016; Exley, 2018; Schwardman and van der Weele, 2017; Zimmermann, 2018; Gneezy, Saccardo and van Veldhuizen, Forthcoming), to arise due to the existence of intermediaries, others, or nature who are seemingly responsible (Hamman, Loewenstein and Weber, 2010; Linardi and McConnell, 2011; Coffman, 2011; Bartling and Fischbacher, 2012; Andreoni and Bernheim, 2009; Falk and Szech, 2013), and to arise when signals are informative but noisy and thus offer flexibility to non-bayesian agents in terms of how much they should update (Eil and Rao, 2011; Mobius et al., 2014; Schwardman and van der Weele, 2017; Zimmermann, 2018). 11 Relatedly, see also Babcock et al. (1995), Konow (2000), Haisley and Weber (2010), and Gneezy, Saccardo and van Veldhuizen (Forthcoming). Lin, Zlatev and Miller (2016) further show that the removal of an excuse causes individuals to subsequently engage in more prosocial behavior, and findings in Cialdini (1984), Bazerman, Loewenstein and White (1992), Falk and Zimmermann (2016), Bohnet and Bazerman (2016), and Falk and Zimmermann (Forthcoming) document how a desire for consistency can constrain decisions. 4

6 could imagine blaming these systematic mistakes on a cognitive limitation. Instead, we show that the biased behavior is due to motivated errors. In particular, when we remove the possibility that computational errors could be used as an excuse to make a selfish choice, participants no longer make these computational errors. This pattern reveals that participants are neither unable nor unwilling to make accurate calculations they instead appear to avoid accurate calculations when they are motivated. In additional analysis, we show that the motivated errors survive attempts to debias participants by giving them experience or by further simplifying the (already simple) decision environment, and we show that the motivated errors are present even among participants who choose to pay full attention to the decision. 2.1 Experimental Design Study 1 included 1000 participants in one of five versions. 12 In all versions, each participant received $4 for completing the 25-minute study. In addition, one randomly selected decision for each participant was implemented for bonus payment and resulted in an additional payment for the participant or a donation to charity. In all versions, participants make 48 binary choices in which they choose between a bundle, which changes from decision to decision, and an outside option, which is fixed for all 48 decisions. In each decision, the value of the bundle is equal to the sum of 4 or 5 summands. For simplicity, each summand in a bundle is either 0 or a single positive number that (usually) appears multiple times. Consequently, the sum of a bundle can always be calculated as n d (where n is the number of times the positive number d appears in the bundle, with all remaining summands being 0). The five versions of Study 1 Self/Charity, Charity/Charity, Self(150)/Self, Self/Charity- Choice, and Self/Charity-Sum vary along three dimensions: (1) the recipient and level of the outside option, (2) the recipient of the bundle, and (3) what information about the bundle participants have to learn before making each choice. The differences across the five versions of Study 1 are best visualized in Table 1. We begin by describing the Self/Charity version in depth, since the other four versions are easily explained as slight variations off of this version. 13 In the Self/Charity version, the recipient of the outside option is the participant and the level of the outside option is calibrated on the participant 12 From January 16-17, 2018, we recruited and randomized 600 participants from Amazon s Mechanical Turk (MTurk) into one of three study versions: Self/Charity, Charity/Charity, Self(150)/Self, and 599 participants completed the study. On January 18, 2017, we recruited and randomized 401 participants from MTurk into one of two study versions: Self/Charity-Choice, Self/Charity-Sum, and all 401 participants completed the study. Overall, 51% of participants are female, the median age is 33 years old, and the median educational attainment is an Associate s Degree. Across these demographic variables, there is only one significant difference across the Self/Charity, Charity/Charity, and Self(150)/Self versions and there are no significant differences across the Self/Charity-Choice and Self/Charity-Sum versions, demonstrating successful randomization. Full instructions for Study 1 can be found in Appendix Section C. 13 The naming of the versions indicates the recipient of the outside option followed by the recipient of the bundle. For example, in the Self/Charity version, the outside option benefits the participant (thus Self/ ) and the bundle benefits a charity (thus Charity). Information after a hyphen indicates a difference in information structure. For example, as will be described in detail below, in the Self/Charity-Choice version, participants have a choice about what information to learn about the bundle (thus -Choice). 5

7 Table 1: Study 1 Versions Outside Option to......charity...self Information is Optional Self/Charity-Choice (n = 195) Required Charity/Charity Self/Charity Self(150)/Self (n = 199) (n = 198) (n = 202) Required and Sum Shown Self/Charity-Sum (n = 206) Bundle to......charity...self level; the recipient of the bundle is the national chapter of the Make-A-Wish Foundation, a charity; and participants must learn about each summand in the bundle before making their choice. In the remainder of this section, we explain how the bundles are constructed, we explain how and why we calibrated the outside option at the participant level, and then we describe how the other four versions differ from the Self/Charity version. Bundles in the Self/Charity version Each bundle in the Self/Charity version of Study 1 includes four or five summands (called amounts to participants) that are either zero or the same non-zero number. Participants are informed that if the bundle is chosen, the sum of these four or five amounts will be donated (in cents) to the Make-A-Wish Foundation national chapter. The first amount in a bundle is always revealed by default (see Figure 1 for an example). Participants are then required to reveal the remaining three or four amounts in a bundle by clicking on the header above each amount. 14 ensure participants comprehend this structure, we require participants to correctly answer questions about how much money would be given to charity in several example bundles before they make choices in the study. To facilitate comparisons across each participant s decisions, we carefully structured the 48 bundles (importantly, however, participants are not informed of this structure). In particular, we started with 12 baseline bundles, which we call n/4-bundles, since they include four amounts of which n amounts are non-zero (so, if n < 4, then 4 n amounts are zero). amount within a bundle equals d. To Each non-zero Thus, the total amount going to charity if a baseline n/4- bundle is chosen is n d cents. The n and d parameters for the baseline bundles are chosen such that n d varies systematically around 150 cents. We have four baseline bundles with n = 2, four baseline bundles with n = 3, and four baseline bundles with n = 4. We randomly select d {51, 52, 53, 54, 55, 56, 57, 58, 59} at the bundle level, so that n d is substantially below 150 cents for the bundles with n = 2, slightly above 150 cents for bundles with n = 3, and substantially 14 We present the bundles to participants in this interactive manner for two reasons. First, we believed this design would be more engaging for participants whose task is to view and make decisions about 48 bundles. Second, the design facilitates a clean comparison with a version of the study, detailed later in this section, in which participants are not required to become fully informed and can selectively view information (i.e., the Self/Charity-Choice version). 6

8 Figure 1: Example of how a bundle initially appears in Study 1 Clicking on each header reveals the number of cents associated with that amount. above 150 cents for the bundles with n = 4. Since each of the four or five amounts in a bundle appear in a designated order, in addition to the amount d and the number of times that amount appears in a bundle, we also vary where the zeros and the non-zeros are in the bundle, as shown in Appendix Table A From each of 12 baseline bundles, we construct an n/5-bundle by adding a zero to it. Each n/5-bundle mirrors the payoff structure of an n/4-bundle except for the addition of a fifth amount that is zero. From each of these 12 baseline bundles, we additionally construct a (n+1)/5-bundle by improving it. Each (n+1)/5-bundle mirrors the payoffs structure of an n/4-bundle except for the addition of a fifth amount that is d. We call the 12 baseline bundles and the 24 bundles constructed from them our main bundles. In addition to our main bundles, we have 12 non-main bundles with four amounts each. We included these bundles both to balance the number of bundles of each size (i.e., to have 24 bundles with four amounts along with the 24 bundles with five amounts) and to provide additional data to perform secondary analyses conducted in Section Until then, decisions involving these non-main bundles are excluded from our analysis. The order in which participants make their 48 binary decisions varies. Half of participants make their 24 decisions involving bundles with four amounts first and the other half make their 24 decisions involving bundles with five amounts first. In addition, within each block of 24 decisions, the order in which each bundle is shown randomly varies for each participant. Outside options in the Self/Charity version We calibrate the outside option for each participant in the Self/Charity version for two reasons. First, we want each participant to be close to indifferent between the outside option and the bundle for at least some of the decisions and to be further from indifferent for other decisions, so that 15 Appendix Table A.1 describes the twelve baseline bundles by indicating whether the first, second, third and/or fourth amount was d cents (i.e., a non-zero amount). Note that while the four-amount bundles with n = 4 only vary in terms of which value for d is randomly selected (since there are no zeros in those bundles), the four bundles with n = 2 and the four bundles with n = 3 also vary in terms of which amounts (i.e., the 1st, 2nd, 3rd, and/or 4th amount shown on the decision screen) are zero. 16 These bundles are described in Appendix Table A.2. 7

9 we have a well-controlled measure of how likely the participant is to select the bundle absent any computational errors. 17 Second, the outside option has to be set to something, and the calibration allows us to keep the value of the outside option similar across study versions with and without self-serving motives, which we discuss further in Section 2.3 and Section While the previous paragraph highlights the value of the calibration, it is also worth emphasizing that the main results of Study 1 and of Study 2 which also utilizes the calibration do not rely on the calibration or on how well it matches the value of the outside option across study versions. The lack of reliance on the calibration is clear from our within-participant identification strategy: adding a zero to a bundle should not influence the extent to which a participant prefers it relative to the outside option, regardless of the value of the outside option. In addition, as discussed in footnote 17, our results persist in a version of Study 2 in which the calibration is not used to set the outside option. How do we implement the participant-level calibration? Before facing the 48 binary decisions, each participant completes a multiple price list that aims to elicit an X value that makes the participant indifferent between X cents for themselves and 150 cents for the national chapter of the Make-A-Wish Foundation. Once we identify the X value, we set each individual participant s outside option to this X cents for themselves since, as detailed above, the amount donated by the main bundles varies systematically around 150 cents. The multiple price list generates an indifference range for X. We assign participants an X value equal to the lower bound of their indifference range, unless the lower bound of the indifference range is 0, in which case we assign X = 5 cents. 19 The distribution of X values are displayed in Panel A 17 A behavioral bias in response to how a bundle is constructed would be difficult to observe if participants always preferred the outside option benefiting themselves to the bundle benefiting charity. This constant preference for the outside option might arise in our experiment if we had set the nominal amounts of money in the outside option and the bundle to be similar, since most individuals value money for themselves more than money for others in a meta-study on the dictator game, Engel (2011) finds that individuals choose to give nothing approximately 36% of the time. In Study 2, we run an additional study version that does not use this calibration and instead assigns an outside option of 150 cents (i.e., close to the nominal value of donations made by the average bundle) for all participants. These results are presented in Section 3.4, after we describe the main results from Study 2. We find that our main results from Study 2 persist in the absence of the calibration. As expected, however, in this 150-cent version, the rates of choosing the bundle are significantly lower and twice as many participants choose the outside option for themselves in all 48 choices than in its calibrated counterpart (51% always choose the outside option in the 150-cent version as compared to 25% in its calibrated counterpart), which underscores the value of the calibration exercise. 18 We see the calibration procedure as a valuable methodological contribution to laboratory experiments that aim to make treatments with different outside options comparable, and we have used variants of it in our other work (Exley, 2015, 2018; Exley and Kessler, 2017). 19 In particular, as shown in Appendix Figure C.3, the price list contains 31 rows. On each row, the participant must decide between 150 cents being given to the Make-A-Wish Foundation national chapter and an amount of money for themselves that varies from 0 cents to 150 cents in five-cent increments (i.e., the price list gives 5 (r 1) cents to the participant on the r th row). If a participant switches from choosing the first payment option on the r th to the second payment option on the (r + 1) th row, then that participant is indifferent between 150 cents for the national chapter and X cents for themselves, where 5 (r 1) X 5 r. As noted in the main text, a participant s X value is set at the lower bound of a participant s possible X range (i.e., we set X = 5(r 1) cents), unless this would set X = 0 cents, in which case we set X = 5 cents. Setting X to the lower bound ensures that, if anything, participants should prefer bundles over their outside option more when the outside option is X cents for 8

10 of Appendix Figure B Additional versions of Study 1 Each of the four other versions of Study 1 have a slight variation off of the Self/Charity version, and they are described here. Additional details are shown in the corresponding sections where we discuss the results from these versions. The Charity/Charity version is like the Self/Charity version, except that the outside option for all the decisions is 150 cents going to the national chapter of the Make-A-Wish Foundation. Since the national chapter of the Make-A-Wish Foundation is the recipient of both the bundle and the outside option, participants who want to maximize donations to the charity should choose the bundle whenever its sum is greater than 150 cents. This study version allows us to examine decisions in a setting where stakes are comparable to the Self/Charity version (due to the calibration procedure) but where self-serving motives are absent. The results of this version are reported in Section 2.3. The Self(150)/Self version is like the Self/Charity version, except for two changes. First, the recipient of the bundle is the participant (i.e., self) and the outside option for all the decisions is 150 cents going to the participant (i.e., self). Since the participant is the recipient of both the bundle and the outside option, participants who want to maximize earnings in the experiment should choose the bundle whenever its sum is greater than 150 cents. This study version allows us to consider how the absence of self-serving motives influences decisions in a setting where participants own money is still at stake. The results of this version are reported in Section 2.3. The Self/Charity-Choice version is like the Self/Charity version, except for what participants must learn about each bundle. In particular, in Self/Charity-Choice, participants are shown the first amount in each bundle by default but do not need to reveal the other three or four amounts before making a choice about the bundle. This version allows us to examine whether our results persist among decisions in which participants are known to pay attention to the information in a bundle. The results of this version are reported in Section 2.4. The Self/Charity-Sum version is like the Self/Charity version, except for what participants must learn about each bundle. In particular, in Self/Charity-Sum, participants must view all of the amounts in the bundle before making a choice, just like in the Self/Charity version, but they are also shown the sum of the amounts in the bundle on the decision screen (i.e., the computer sums the amounts for them and displays this sum). This version allows us to examine participants decisions when the already simple decision environment is simplified further. The results of this version are reported in Section 2.4. themselves than when it is 150 cents for the national chapter of the Make-A-Wish Foundation. 20 As will be shown throughout the paper, our results are robust to a restricted sample that excludes the 12% of participants whose lower bound implies X = 0 and for whom we assign X = 5 cents. 9

11 2.2 Documenting the behavioral bias In the Self/Charity version, we find clear evidence that participants make systematic computational errors, demonstrating a behavioral bias. In particular, participants are less likely to choose a bundle when a zero is added to it, even though the donation made by the bundle (i.e., the sum of the amounts in the bundle) has not changed. Figure 2 shows our results graphically, collapsing across all our main bundles. The shading of the bars indicates the number of non-zero amounts in the bundle, which determines the sum of the bundle and whether the sum is above or below 150 cents. 21 It is clear that participants willingness to choose a bundle is not solely driven by the number of non-zero amounts. For each of the four-amount bundles (i.e., the 4/4-bundles, the 3/4-bundles, and the 2/4-bundles), there are corresponding five-amount bundles that involve the same number of non-zero donation amounts (i.e., the 4/5-bundles, the 3/5-bundles, and the 2/5-bundles). The fact that these five-amount bundles contain an additional zero is payoff irrelevant, but adding a zero causes a substantial drop in participants willingness to choose a bundle. Figure 2: In the Self/Charity version of Study 1, fraction choosing a main bundle Fraction choosing bundles /5 4/4 4/5 3/4 3/5 2/4 2/5 Description of bundles Data include all participants decisions in all main bundles in the Self/Charity version of Study 1. Table 2 presents the results from the main bundles in a regression framework that includes additional controls and carefully isolates the impact of adding a zero and the impact of adding a non-zero amount to a baseline n/4-bundle. In particular, we report results from the following linear 21 In the 5/5-bundles, 5 of the donation amounts are non-zero, so the sum is 255 to 295 cents. In the 4/4- and 4/5-bundles, 4 of the donation amounts are non-zero, so the sum is 204 to 236 cents. In the 3/4- and 3/5-bundles, 3 of the donation amounts are non-zero, so the sum is 153 to 177 cents. Finally in the 2/4- and 2/5-bundles, 2 of the donation amounts are non-zero, so the sum is 102 to 118 cents. 10

12 probability model: P(choose bundle) = β 1 ( + 0) + β 2 ( + 1) n=2 d=51 k n l d + ɛ (1) where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) is an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle (averaging the effect over the possible d values), k n are dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1), and l d are dummies for the value of the non-zero amounts in the bundle, which range from 51 to 59 cents. The coefficient estimate on ( + 0) in Column 1 of Table 2 shows that adding a zero significantly decreases participants willingness to choose a bundle by 6 percentage points. This effect is large. It is 10% of the likelihood of choosing a baseline bundle, which is It is more than half the magnitude of the 10 percentage point increase observed from adding a non-zero amount to a bundle (see the coefficient estimate on ( + 1)), which on average increases the total amount donated in a main bundle by 33%. In addition, the 6 percentage point average effect reflects a large fraction of participants responding to the addition of the zero in this biased way. In particular, 50% of our participants engage in behavior consistent with this bias by at least once choosing an n/4-bundle but not the n/5-bundle constructed by adding a zero to it. What can we say about why participants respond to the addition of the zero? First, participants do not solely interpret five-amount bundles more negatively than four-amount bundles, since adding a non-zero amount to a bundle increases participants willingness to choose it. More is not less. 22 Our effect is instead driven by participants responding to the addition of a zero to a bundle. Adding a zero makes a bundle less attractive, even though it does not change the sum of donations to charity. Second, our results are not solely about the presence of a zero in a bundle. 23 Column 2 of Table 2 examines the impact of adding a zero to a baseline bundle absent any zeros (i.e., to 4/4-bundles) while Column 3 of Table 2 examines the impact of adding a zero to a baseline bundle with one or two zeros (i.e., to 2/4-bundles or 3/4-bundles). The negative effect of adding a zero persists in both cases: adding a zero decreases participants willingness to choose a bundle by 4 percentage points when a zero is not already present and by 7 percentage points when a zero is already present. Our findings are also robust to different restrictions on the set of participants we consider. Column 4 and Column 5 of Table 2 examine whether our effect persists with more restricted samples 22 This is not surprising. The donation from choosing a bundle in our experiment is known with certainty, and so our setting differs from prior literature that has documented a more is less phenomenon in environments in which underlying uncertainty about the value of a bundle allows agents to update about the bundle s overall quality when a good is added (Hsee, 1998; List, 2002; Leszczyc, Pracejus and Shen, 2008). 23 This result helps us to differentiate from effects related to the presence of a zero, such as those observed in Magen, Dweck and Gross (2008) and Read, Olivola and Hardisty (2016), which show that decision-makers choosing between money now and money later can be made more patient by reminding them that taking money now means receiving $0 later. 11

13 Table 2: In the Self/Charity version of Study 1, regression of choosing a main bundle Sample: full choice varies X is lower bound main if 4/4 if 2/4 or 3/4 main main bundles baseline baseline bundles bundles (1) (2) (3) (4) (5) ( + 0) (0.01) (0.02) (0.01) (0.01) (0.01) ( + 1) (0.01) (0.02) (0.02) (0.02) (0.01) N k n l d FEs yes yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self/Charity version of Study 1, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) is an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-3 analyze all participants decisions: in all main bundles in Column 1, involving the baseline 4/4-bundles in Column 2, and involving the baseline 2/4- and 3/4-bundles in Column 3. Column 4 analyzes all main bundles but among a restricted sample of participants who choose the bundle at least once and choose their outside option at least once across all 48 decisions. Column 5 analyzes all main bundles but among a restricted sample of participants with outside option X set to the lower bound of their indifference range (and thus excludes participants with a zero lower bound). of participants. The restricted sample in Column 4 only includes participants who choose the bundle at least once and choose their outside option at least once. 24 Not surprisingly, the impact of adding a zero is even larger (i.e., it is 8 percentage points) for this restricted sample. The restricted sample in Column 5 shows that our results are robust to excluding participants for whom we assigned an outside option of 5 cents because the lower bound of their indifference range was 0 cents. 2.3 Showing that the bias is due to motivated errors In the previous subsection, we document a behavioral bias that is clearly indicative of errors in decision making. When a zero is added to a bundle, participants are less likely to choose that bundle, even though the additional zero does not change the donation made by the bundle. Put differently, participants act as though (n d) + 0 < (n d). A natural inclination for behaviorally minded researchers is to attempt to identify a cognitive limitation that might explain this effect. For example, one might hypothesize that participants systematically miscalculate the amount in the bundle when a zero is added because they think in terms of the average amount (which is mechanically lower when there are more zeros) or because they overweight the last amount in the bundle (which is zero when a zero is added). 25 A key feature of these explanations is that something 24 Across all 48 decisions, 10% of participants never choose the outside option, and 11% of participants always choose the outside option. 25 As evidence against this latter hypothesis, we do not observe any differences in behavior due to the location of zeros within a bundle in the Self/Charity version. 12

14 about the additional zero hinders participants ability to do the calculation of the sum correctly. We explore an alternative explanation for this behavioral bias. We posit that participants are motivated to incorrectly respond to the amounts in a bundle due to self-serving motives. To examine this explanation, we introduce two additional versions of Study 1 that eliminate self-serving motives to see if agents still display the same response to the addition of a zero. As described above, participants in the Self/Charity version made binary decisions between a bundle of money for a charity and an outside option of money for themselves and so had a potentially motivated reason to choose the outside option. In the Charity/Charity version, we eliminate the self-serving motive by having participants chose between the bundle for charity an an outside option of 150 cents for the same charity. Similarly, participants in the Self(150)/Self version chose between the bundle for themselves an an outside option of 150 cents for themselves. In these two versions, there is no self-serving motive to choose the outside option. Panel A of Figure 3 reproduces Figure 2 for the Charity/Charity version. As expected, whether there are 3 or more non-zero amounts in a bundle (and thus the sum of the bundle is more than 150 cents) is the key determinant in whether the bundle is selected. Notably however, adding a zero to a bundle does not influence whether the bundle is selected. Participants unresponsiveness to the addition of a zero is confirmed by the near-zero coefficient estimates on ( + 0) in Panel A of Table 3. Similarly, Panel B of Figure 3 reproduces the figure for the Self(150)/Self version. The pattern looks almost identical to Panel A and participants unresponsiveness to the addition of a zero is again confirmed by the near-zero coefficient estimates on ( + 0) in Panel B of Table 3. Figure 3: In the Charity/Charity and Self(150)/Self versions of Study 1, fraction choosing a main bundle Panel A: Charity/Charity version Panel B: Self(150)/Self version Fraction choosing bundles /5 4/4 4/5 3/4 3/5 2/4 2/5 Description of bundles Fraction choosing bundles /5 4/4 4/5 3/4 3/5 2/4 2/5 Description of bundles Data include all participants decisions in all main bundles: in the Charity/Charity version of Study 1 in Panel A and in the Self(150)/Self version of Study 1 in Panel B. That participants do not respond to the addition of a zero in the absence of self-serving motives means that participants are capable of recognizing that the addition of a zero should not change 13

15 Table 3: In the Charity/Charity and Self(150)/Self versions of Study 1, regression of choosing a main bundle Sample: full choice varies X is lower bound main if 4/4 if 2/4 or 3/4 main main bundles baseline baseline bundles bundles (1) (2) (3) (4) (5) Panel A: Charity/Charity version ( + 0) (0.01) (0.01) (0.01) (0.01) (0.01) ( + 1) (0.01) (0.01) (0.02) (0.01) (0.01) N k n l d FEs yes yes yes yes yes Panel B: Self(150)/Self version ( + 0) (0.01) (0.01) (0.01) (0.01) (0.01) ( + 1) (0.01) (0.01) (0.01) (0.01) (0.01) N k n l d FEs yes yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Charity/Charity version of Study 1 in Panel A and in the Self(150)/Self version of Study 1 in Panel B, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) is an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-3 analyze all participants decisions: in all main bundles in Column 1, involving the baseline 4/4-bundles in Column 2, and involving the baseline 2/4- and 3/4-bundles in Column 3. Column 4 analyzes all main bundles but among a restricted sample of participants who choose the bundle at least once and choose their outside option at least once across all 48 decisions. Column 5 analyzes all main bundles but among a restricted sample of participants with outside option X set to the lower bound of their indifference range (and thus excludes participants with a zero lower bound). their decision. This implies that participants in the Self/Charity version were not unable to respond correctly to the addition of a zero but rather that they were motivated to respond incorrectly. To statistically confirm that the effect of adding a zero is different when self-serving motives are present and absent, we compare results from the Self/Charity and Charity/Charity versions. In both versions, participants face the same bundles going to the Make-A-Wish Foundation national chapter, and the only difference is the outside option to choosing a bundle, which is X for participants in Self/Charity and 150 cents for the national chapter in Charity/Charity. 26 Since we estimate each 26 This comparison between the Self/Charity version and the Charity/Charity version keeps all other features of the experimental design constant, and so our results also rule out any potential explanations for the response to adding a zero that are related to the experimental design itself, including experimenter demand effects; see, e.g., De Quidt, Haushofer and Roth (2017). 14

16 participant s X value to make them indifferent between X for themselves and 150 cents for national chapter, the comparison between these versions isolates the impact of removing self-serving motives without changing stakes. Appendix Table B.1 directly compares the results from these two versions. The coefficients on ( + 0) and ( + 1) show the effects in Self/Charity version (which are mechanically the same as in Table 2). The coefficient on Charity/Charity and the associated interactions show how these effects differ in the Charity/Charity version. In particular, the coefficient on Charity/Charity*( + 0) shows that the effect of adding a zero is fully eliminated when self-serving motives are removed. The difference across versions is also readily apparent at the individual level. 27 That the systematic inability to add a zero to a bundle is eliminated when self-serving motives are removed reveals that we have documented motivated errors Attempting to debias the motivated errors We have documented evidence of motivated errors. In this subsection, we explore whether common de-biasing strategies mitigate the motivated errors, drawing from a vast related literature. We specifically consider experience, inattention, and complexity. The role of experience We identify our motivated errors as they arise within an individual, so we can ask whether errors are mitigated as a participant gains experience over the 48 decisions in our study. Put differently, we can ask whether the negative response to adding a zero lessens or disappears with experience. We answer this question in two ways. First, we exploit that participants either make all 24 decisions involving four-amount bundles and then make all 24 decisions involving five-amount bundles or vice versa. Second, we exploit that the order of bundles randomly varies within the set of 24 four-amount bundles and within the set of 24 five-amount bundles. Appendix Table B.2 examines whether our results differ as participants gain experience. For simplicity, only the results related to adding a zero are shown. Columns 1 and 2 split participants based on whether they faced the four-amount bundles first (and so the zeros were added in the 27 The fraction of participants who engage in our observed biased behavior at least once choosing an n/4-bundle but not the n/5-bundle constructed from it is only 26% in the Charity/Charity version but significantly increases to 50% in the Self/Charity version (p < 0.01). 28 Our data also rule out potential alternative hypotheses for the differential effects across our Self/Charity and Charity/Charity versions. For example, while one might be concerned that individuals use an additional zero as a way to break an indifference between the bundle and the outside option, we have two reasons to believe that such an explanation is not contributing to our differential results across study versions. First, a general intuition is that subjects are more likely to be indifferent between a bundle and the outside option in the Charity/Charity version when their own money is not at stake, which would work against us finding more biased behavior in the Self/Charity version than in the Charity/Charity version. Second, we observe that many participants in the Self/Charity version exhibit biased behavior in two or more bundles with different total donation amounts. Since the outside option is constant across bundles, however, participants can only be indifferent for at most one of these bundles. In particular, in the Self/Charity version, 29% of participants (i.e., roughly 60% of the subjects who display biased behavior at all) are less likely to choose a bundle when a zero is added to it for two or more bundles with different total donation amounts, which is both substantial and significantly greater than the 14% of participants who do so in the Charity/Charity version. See also a thorough discussion that rules out other alternative hypotheses in Section

17 second half of the study, Column 1) or the five-amount bundles first (so the zeros were added in the first half of the study, Column 2). Columns 3 and 4 show the results from decisions involving main bundles that occur early in each set (from the first half of each set, decisions 1-12 and 25-36, Column 3) or late in each set (from the second half of each set, decisions and 37-48, Column 4). Rather than mitigating motivated errors, experience, if anything, makes the behavioral bias larger (i.e., the estimated magnitude is larger in Column 4 than in Column 3). The role of inattention Even though participants must reveal all of the amounts in the Self/Charity version, they may fail to carefully attend to the amounts in the bundle, which might drive the motivated errors. For instance, while they clearly notice an additional 0 in a bundle, they may fail to pay attention to the other amounts in a bundle. To assess whether inattention is driving our motivated errors, we ran the Self/Charity-Choice version in which participants have the option to avoid information about a bundle. While participants must still view the first amount in a bundle (as it is revealed by default), they can choose whether to click to reveal each of the remaining amounts in the bundle before making their choice. If our motivated errors are driven by individuals who choose not pay attention to the information in a bundle, then they will not persist among decisions in which participants self-select into acquiring all of the information about a bundle before making their choice. Decisions in which all information is revealed we call attentive decisions. Column 1 of Appendix Table B.3 presents results from all decisions involving the main bundles in the Self/Charity version and the 44% of decisions involving the main bundles in the Self/Charity- Choice version that we classify as attentive because the participant chooses to reveal all the information about the bundle. Our motivated errors are present even when restricting to attentive decisions. The coefficient on ( + 0) applies to the attentive decisions in the Self/Charity-Choice version and shows that adding a zero significantly decreases participants willingness to choose a bundle by 11 percentage points. The statistically significant positive coefficient on Self/Charity*( + 0) shows that the negative effect of adding a zero is larger among attentive decisions in the Self/Charity- Choice version than across all the decisions in the Self/Charity version. That is, restricting to the attentive decisions makes the behavioral bias worse. In addition, the statistically significant negative coefficient on Self/Charity shows that the baseline four-amount bundles are more likely to be chosen in attentive decisions in the Self/Charity-Choice version than in the Self/Charity version. Consequently, that our motivated errors are prevalent in attentive decisions directly implies that they persist in decisions where participants are particularly inclined to choose the bundle. The role of complexity While our environment is exceedingly simple the relevant calculation for the participant s binary decision involves adding a few two-digit numbers in a manner that can also be achieved with basic multiplication one could theoretically imagine making it even simpler. In particular, an extreme intervention to debias participants would be to do the requisite math for them by directly 16

18 showing them the sum of the amounts in the bundle. Such an intervention reveals that a bundle generates the same donation to charity whether or not the zero is added to the bundle. In the Self/Charity-Sum version, we provide this information on the sum. In particular, in addition to being required to reveal each amount in a bundle, participants are directly informed of the sum of the amounts in the bundle when making the choice, as shown in Panel B of Figure 4 (Panel A of Figure 4 shows how the corresponding decision appears in the Self/Charity version). Figure 4: Example question faced by participants in the Self/Charity version versus the Self/Charity-Sum versions (a) Self/Charity version (b) Self/Charity-Sum version The only difference between the two study versions is a sentence stating the sum of the amounts in the bundle on each decision screen. In these examples, X is 100 cents. Column 2 of Appendix Table B.3 presents results from decisions involving the main bundles in the Self/Charity-Sum and Self/Charity versions. The coefficient on ( + 0) applies to the decisions in the Self/Charity-Sum version and its statistically significant negative coefficient demonstrates that our motivated errors persist when we further simplify the decision environment by presenting the sum of donations made by the bundle. Even telling participants how much money is donated if the bundle is chosen does not completely eliminate the bias. However, the statistically significant negative coefficient on Self/Charity*( + 0) reveals that participants are less biased in the Self/Charity-Sum version than in the Self/Charity version. Presenting the sum does somewhat mitigate the motivated errors. That motivated errors persist in the Self/Charity-Sum version, that they are not eliminated by experience, and that they persist among decisions in which participants choose to be attentive, all suggest that motivated errors may be particularly difficult to overcome. Next, we explore the robustness of our result and test whether motivated errors can cause another behavioral bias by presenting the design and results of Study 2. 3 Study 2: Salience In Study 2, participants respond to the salience of information that is known to them. Choices suggest that participants dislike when a charity that is known not to receive a donation is made salient by being included on rather than excluded from a list of potential recipient charities. We show that this effect is primarily driven by motivated errors. When self-serving motives are 17

19 present, over 50% of the response to salience is due to motivated errors. When we remove the self-serving motive to respond to salience, participants are significantly less likely to engage in the biased behavior. Study 2 both highlights the robustness of motivated errors and demonstrates that motivated errors can be active alongside a cognitive limitation that also leads to biased behavior. In Study 2, we again show that the motivated errors survive attempts to debias participants by giving them experience and that the motivated errors are present even when participants are attentive. Unlike Study 1, however, in Study 2 we find that the motivated errors are not mitigated by further simplifying the decision environment. 3.1 Experimental Design A total of 1596 individuals participated in one of eight versions of Study As in Study 1, each participant received $4 for completing the 25-minute study. In addition, one randomly selected decision for each participant was implemented for bonus payment and resulted in an additional payment for the participant or a donation to charity. Participants in Study 2 face the same 48 binary decisions as participants in Study 1, except for one difference. In Study 2, each amount in a bundle is given to a different Make-A-Wish Foundation state chapter (rather than the sum of the amounts going to the national chapter). 30 Which state chapters receive which amounts in a bundle is displayed on the decision screen for participants (see Figure 5 for an example). Participants are informed that any state chapter not included in a bundle receives no donation, and understanding questions ensure comprehension of this structure. The eight versions of Study 2 Self/Charity, Charity/Charity, Self/Charity-Choice, Charity/Charity- Choice, Self/Charity-Sum, Charity/Charity-Sum, Self(150)/Charity, and Charity(ARC)/Charity vary along two dimensions: (1) the recipient and level of the outside option and (2) what information about the bundle participants must learn before making each choice. 31 The differences across the eight versions of Study 2 are best visualized in Table 4. The versions that do not mirror versions from Study 1 are discussed in more detail as they become relevant in the analysis that follows. 29 From October 10-13, 2016, we recruited and randomized 1200 participants into one of six study versions in a 2 3 design: {Self/, Charity/ } {Charity, Charity-Choice, Charity-Sum}, and 1196 participants completed the study. On March 13, 2017, we recruited and randomized 400 participants into one of two study versions: Self(150)/Charity and Charity(ARC)/Charity, and all 400 participants completed the study. Overall, 50% of participants are female, the median age is 33 years old, and the median educational attainment is an Associate s Degree. There are not significant differences across the Self/ version and the Charity/ version for any of {Charity, Charity-Choice, Charity-Sum} or between Self(150)/Charity and Charity(ARC)/Charity, demonstrating successful randomization. Full instructions for Study 2 can be found in Appendix Section D. 30 Due to constraints (related to which chapters were IRB approved and to how some states shared chapters), we randomly drew states from a list of 28 states that we matched with corresponding Make-A-Wish Foundation chapters. This list of states was: Alaska, California, Colorado, Connecticut, Florida, Georgia, Illinois, Indiana, Iowa, Kentucky, Louisiana, Maine, Michigan, Missouri, Nebraska, Nevada, New Hampshire, New York, North Carolina, Ohio, Oklahoma, South Carolina, Tennessee, Texas, Utah, Virginia, Washington, and Wisconsin. 31 Unlike Study 1, the recipients of the bundles in Study 2 (i.e., included state chapters) vary across decisions. 18

20 Figure 5: Example of how a bundle initially appears in Study 2 Clicking on each header reveals the number of cents donated to that state chapter. Table 4: Study 2 Versions Outside Option to......charity...self Optional Charity/ Charity-Choice Self / Charity-Choice Information (n = 215) (n = 190) Bundle to... Required Required and Sum Shown Charity(ARC)/ Charity (n = 200) Charity/ Charity (n = 191) Charity/ Charity-Sum (n = 202)...Charity Self / Charity (n = 203) Self / Charity-Sum (n = 195) Self(150)/ Charity (n = 200) 19

21 3.2 Another bias due to motivated errors Figure 6 shows the main results from the Self/Charity and Charity/Charity versions of Study 2. Panel A shows that making salient a charity that does not receive a donation (i.e., including it in the bundle rather than excluding it from the bundle) decreases participants willingness to choose the bundle in the Self/Charity version, even though the charity is known to receive no donation regardless of whether or not it is included in the bundle. Panel B shows that the effect is attenuated, but still present, when self-serving motives are removed in the Charity/Charity version. 32 Figure 6: In the Self/Charity version and the Charity/Charity version of Study 2, fraction choosing a main bundle Panel A: Self/Charity Panel B: Charity/Charity Fraction choosing bundles /5 4/4 4/5 3/4 3/5 2/4 2/5 Description of bundles Fraction choosing bundles /5 4/4 4/5 3/4 3/5 2/4 2/5 Description of bundles Data include all participants decisions in all main bundles: in the Self/Charity version of Study 2 in Panel A and the Charity/Charity version of Study 2 in Panel B. Table 5 presents results from regressions that include data from the Self/Charity version in Panel A and from the Charity/Charity version in Panel B. The coefficient on ( + 0) in Column 1 of Panel A shows that making salient a charity that does not receive a donation significantly decreases participants willingness to choose a bundle by 9 percentage points in the Self/Charity version. This effect is large. It is 21% of the likelihood of choosing a baseline bundle, which is It is the same size as the increase observed from adding a state chapter that receives a donation (see the coefficient estimate on ( + 1)), which increases a bundle s total donations by 33% on average. The coefficient on ( + 0) in Column 1 of Panel B shows that making salient a charity that does not receive a donation also statistically significantly decreases participants willingness to choose a bundle in the Charity/Charity version. Comparing the magnitudes of the impact of adding a 32 That this effect persists absent self-serving motives may relate to how salience influences narrow framing; see, e.g., Barberis, Huang and Thaler (2006), Rabin and Weizsäcker (2009), and Imas (2016). For example, participants may only consider how a decision affects state chapters in a bundle which can be influenced by salience rather than all state chapters. Indeed, Exley and Kessler (2017) suggests narrow framing may establish the domain over which inequity preferences are applied. 20

22 Table 5: In the Self/Charity and Charity/Charity versions of Study 2, regression of choosing a main bundle Sample: full choice varies X is lower bound main if 4/4 if 2/4 or 3/4 main main bundles baseline baseline bundles bundles (1) (2) (3) (4) (5) Panel A: Self/Charity version ( + 0) (0.01) (0.02) (0.01) (0.02) (0.01) ( + 1) (0.01) (0.01) (0.02) (0.02) (0.01) N k n l d FEs yes yes yes yes yes Panel B: Charity/Charity version ( + 0) (0.01) (0.02) (0.01) (0.01) (0.01) ( + 1) (0.02) (0.02) (0.02) (0.02) (0.02) N k n l d FEs yes yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self/Charity version of Study 2 in Panel A and in the Charity/Charity version of Study 2 in Panel B, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) is an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-3 analyze all participants decisions: in all main bundles in Column 1, involving the baseline 4/4-bundles in Column 2, and involving the baseline 2/4- and 3/4-bundles in Column 3. Column 4 analyzes all main bundles but among a restricted sample of participants who choose the bundle at least once and choose their outside option at least once across all 48 decisions. Column 5 analyzes all main bundles but among a restricted sample of participants with outside option X set to the lower bound of their indifference range (and thus excludes participants with a zero lower bound). zero across these two versions, however, reveals the role of motivated errors. The magnitude of the coefficient on ( + 0) is reduced by 56% (from 0.09 to 0.04) when self-serving motives are removed. As shown in Column 1 of Appendix Table B.4, this difference is statistically significant. 33 These results persist when restricting to the type of bundles or restricting the sample of participants as shown in Columns 2-5 of Table 5 (and of Appendix Table B.4). 33 In Appendix Table B.4, the positive coefficient on Charity/Charity also shows a level-effect of choosing the bundle that is itself reflective of self-serving motives. Even though we calibrated the outside option to be weakly less desirable in the Self/Charity version (by choosing the lower bound of a participant s X range), participants are on average more likely to choose the outside option in the Self/Charity version than in the Charity/Charity version of Study 2. This result may reflect the development of uniform excuses to keep money for oneself, such as participants overweighting a dislike of state chapters or overweighting a dislike of the inequity in bundles given that only a subset of state chapters receive a donation. 21

23 3.3 Attempting to debias the motivated errors We have again documented evidence of motivated errors. In this subsection, we follow the approach we took for Study 1 and explore the role of experience, inattention, and complexity in potentially mitigating these motivated errors. The role of experience Following the analysis we performed for Study 1, we investigate whether experience mitigates the motivated errors identified in Study 2. Appendix Table B.5 shows regressions exploring the role of experience. Panel A presents the results from the Self/Charity version of Study 2. Looking across Columns 1-4, we see that experience does not mitigate our motivated errors. 34 Like the motivated errors that caused computational errors in Study 1, the motivated errors that cause a response to salience in Study 2 are not mitigated by experience. The role of inattention Following our analysis from Study 1, Column 1 of Panel A of Appendix Table B.6 presents results from the 30% of decisions involving main bundles in the Self/Charity-Choice version in which participants fully revealed all the information about the bundle which we again call attentive decisions and all decisions involving main bundles in the Self/Charity version. The coefficient on ( + 0) shows that restricting to the attentive decisions in the Self/Charity-Choice version generates a large, 16 percentage point effect of salience. The statistically significant positive coefficient on Self/Charity*( + 0) shows that the effect of salience is indeed larger among these attentive decisions than among decisions in the Self/Charity version. 35 Thus, like the motivated errors in Study 1, the motivated errors in Study 2 are not mitigated by attention. The role of complexity In Study 1, further simplifying the (already simple) decision environment by summing the donations made to charity in the bundle mitigated the motivated errors. We explore whether the same intervention mitigates the motivated errors in Study In the Self/Charity-Sum version of Study 2, participants are directly informed of the total amount donated to state chapters in the bundle. Column 2 of Panel A of Appendix Table B.6 presents results from the Self/Charity-Sum 34 Panel B of Appendix Table B.5 presents the results from the Charity/Charity version of Study 2. The extent of the bias caused by the motivated errors is best captured by the difference between the coefficient on ( + 0) in the Self/Charity version and the coefficient on ( + 0) in the Charity/Charity version. This difference is consistently 4 to 6 percentage points, and thus the motivated part of the bias is not mitigated. For a discussion of why the bias persists in the Charity/Charity version, see footnote Column 1 of Panel B of Appendix Table B.6 shows the equivalent results for the Charity/Charity-Choice version, although it is harder to compare coefficients across these study versions because of selection into a decision being attentive. 50% of decisions are attentive in the Charity/Charity-Choice version, which is statistically significantly greater than the 30% of decisions that are attentive in the Self/Charity-Choice version, a difference we highlight in greater depth in Section 5.2. For a discussion of why the bias persists in the Charity/Charity-Choice version, see footnote To the extent that participants care about the distribution of donations made to various state chapters, the sum of donations is not a sufficient statistic about the bundle, so this intervention may not simplify the decision as much as it did in Study 1. 22

24 and Self/Charity versions. The coefficient on ( + 0) applies to the decisions in the Self/Charity-Sum version and shows that our result persists even when the sum of donations is provided on the decision screen. The near-zero coefficient on Self/Charity*( + 0) suggests that the salience effect we observe is just as big in the Self/Charity-Sum version as in the Self/Charity version, demonstrating that the motivated errors are not mitigated by simplifying the decision environment in Study Robustness of our motivated errors In this subsection, we present results from the final two versions of Study 2 to show robustness of our results and to further confirm that observed differences between the Self/ and Charity/ versions of each study are due to self-serving motives. We first present results from the Self(150)/Charity version and show that our results are not driven by the calibration procedure. We then present results from the Charity(ARC)/Charity version and show that our results are not driven by the recipient of the bundle and the recipient of the outside option being more different in the Self/Charity versions than in the Charity/Charity versions. The role of the calibration procedure The calibration procedure described in Section 2.1 ensures that each participant in Study 1 and Study 2 values their outside options roughly equivalently regardless of whether they are randomized into a Self/ or Charity/ version of the study. While the calibration has a number of important advantages, one might harbor concerns that a feature of the calibration might cause differential behavior across the Self/ and Charity/ versions. For example, for many participants, the calibration sets the nominal level of the outside option far from the sum of the donations in the bundle, which might make the amounts harder to compare. 38 Note that for a feature of the calibration to drive the differences across the versions it would have to explain why adding a zero would become harder (in Study 1), and why the salience of a charity that does not receive a donation would become more relevant (in Study 2), in the presence of the calibrated outside option. 39 That is, for a feature of the calibration to drive the differences across our versions it could not simply be that the calibration makes decisions harder in general in the Self/Charity versions, but rather that this difficulty interacts with adding a zero or changing the salience of a state chapter. However, rather than speculate about the existence of such features of the calibration or debate how unlikely they might be, we ran the Self(150)/Charity version of Study 2 to help assuage any potential concerns. In the Self(150)/Charity version, we still ask participants 37 Column 2 of Panel B of Appendix Table B.6 replicates the results for the Charity/Charity-Sum and Charity/Charity versions of Study 2. The extent of the bias caused by the motivated errors in the Sum versions is best captured by the difference between the coefficient on ( + 0) in Panel A and the coefficient on ( + 0) in Panel B. This difference is 5 percentage points, the same difference as we saw in the main versions of Study 2 without the sum shown. For a discussion of why the bias persists in the Charity/Charity-Sum version, see footnote We are grateful to George Loewenstein for raising this potential critique to us and inspiring the final two versions of the study, which are presented in this subsection. 39 Note also that we observe our results among participants with various X values, including participants with X that are close to or exactly 150 cents. 23

25 the calibration question (to keep procedures identical to the other treatments), but all participants make all decisions with 150 cents for themselves as the outside option. In this Self(150)/Charity version, the rate of choosing a baseline n/4-bundle is only This is substantially and statistically significantly lower than the 0.42 rate of choosing a baseline n/4-bundle in the Self/Charity version of Study 2. This difference suggests the need for the calibration in order to avoid censoring concerns from participants being too far from indifferent between the outside option and the bundles. Indeed, while only 25% of participants in the Self/Charity version of Study 2 choose their outside option in all 48 decisions, this rate doubles to 51% in the Self(150)/Charity version. In spite of the lower rate of selecting bundles mechanically shrinking the effect in percentage point terms, Appendix Table B.7 shows that the response to making salient a charity that does not receive a donation is robust to the 150-cent outside option. Column 1 shows that participants are 5 percentage points less likely to choose a bundle when we add to it a charity that does not receive a donation. Given the lower rate of choosing the bundles in this version, the 5 percentage point reduction is the same percent effect (21%) as the percent effect in the Self/Charity version of Study 2 (21%). Columns 2-5 confirm the robustness of this result. Notably, in Column 4, when we focus on the restricted sample of participants who choose the bundle in at least one of the 48 decisions and choose the outside option in at least one of the 48 decisions, we see a coefficient that is similarly sized as in the Self/Charity version (10 percentage points here as compared to 9 percentage points in the Self/Charity version of Study 2). Thus, these results indicate that self-serving motives rather than something about the calibration are driving the larger effects we observe the Self/ versions than in the Charity/ versions. The role of difficulty in making decisions involving different recipients In Study 1, in the Charity/Charity version (and also in the Self(150)/Self version), money goes to the same recipient regardless of whether the outside option or bundle is selected. In Study 2, the recipients of the outside option and of the bundle are similar in the Charity/Charity versions (i.e., the Make-A-Wish Foundation national chapter for the outside option and Make-A-Wish Foundation state chapters for the bundle). In contrast, the recipient of the outside option and the recipient of the bundle must be different in the Self/Charity versions of each study so that a self-other trade-off can be established. That the recipient of the outside option and the bundle are more similar in the Charity/Charity versions than in the Self/Charity versions may contribute to our results if comparisons between less similar recipients are somehow harder to make in a way that interacts with a zero being added in Study 1 or with salience being manipulated in Study 2. As before, rather than speculate about whether the similarity of the recipients might contribute to differential responses across our versions, we ran the Charity(ARC)/Charity version of Study 2. In this version, the bundle continues to go to Make-A-Wish Foundation state chapters, but the outside option is now 150 cents for the American Red Cross, a charity that differs from the Make- A-Wish Foundation in both its mission and the types of people that it serves. If similarity between the recipients is relevant in generating the effects we see, then this difference should exacerbate the 24

26 effect of making salient a charity that does not receive a donation (relative to the Charity/Charity version of Study 2 in which the recipients are more similar). As shown in Appendix Table B.7, the magnitude of the behavioral bias does not increase in the Charity(ARC)/Charity and instead becomes statistically indistinguishable from 0. In fact, the estimated coefficient estimated on ( + 0) in Charity(ARC)/Charity is statistically significantly smaller than that observed in the Charity/Charity version. This evidence directly counters the hypothesis that the difference between the recipient of the outside option and the recipient of the bundle is a key driver of the size of the bias Study 3: Uninformative Signal The first two studies provided evidence for the existence of motivated errors that induce computational errors (in Study 1) and lead to large responses to salience (in Study 2). The structure of those studies allowed us to observe participants making repeated decisions and allowed us to run a variety of additional versions to test debiasing strategies and evaluate the robustness of our results. However, both of the two previous studies were in the domain of prosocial behavior. In the third study, we show that motivated errors extend to a completely different setting in which individuals are motivated to hold high beliefs about their ability. This third study also allows us to document a motivated error in a more classic setting where cognitive limitations have often been considered: when individuals are asked to make inferences after receiving signals. 4.1 Experimental Design Study 3 included 600 participants randomized into one of four study versions arising from a 2 2 design of {Self, Other} {Two-Robots, Three-Robots}. 41 All versions consisted of two rounds, and each participant received $3 for completing the 20-minute study. In addition, one randomly selected round for each participant was implemented for bonus payment and determined the additional payment, if any, for the participant. In the first round, participants in all versions have 10 minutes to answer a series of questions from practice tests of the Armed Services Vocational Aptitude Battery (ASVAB). They are presented with a total of 20 questions, four of which are selected from each of the following five categories: General Science, Arithmetic Reasoning, Math Knowledge, Mechanical Comprehension, and Assembling Objects. Participants are informed that: In addition to being used by the military to 40 Note that any variant of this difference-in-recipient argument that claims the differential effects across our Self/ and Charity/ versions arise due to particular difficulties associated with making self-other trade-offs will be isomorphic to our argument that self-serving motives (arising from a desire to keep money for oneself) are at play. We are happy to call any response particular to a self-other trade-off a result of self-serving motives. 41 From January 22-24, 2018, we recruited and randomized 600 participants into one of these four versions. Our randomization was weighted such that approximately twice as many participants would be randomized into one of the Three-Robots versions, since the third robot is equally likely to provide a good signal or a bad signal. All 600 participants completed the study. Overall, 51% of participants are female, the median age is 33 years old, and the median educational attainment is an Associate s Degree. There are no significant differences on these observable characteristics across any of the pairs of study versions. Full instructions for Study 3 can be found in Appendix Section E. 25

27 determine which jobs armed service members are qualified for, performance on the ASVAB is often used as a measure of cognitive ability by academic researchers. Participants are told that if the first round is randomly selected to count for payment, they will receive 10 cents for each question they answer correctly. In the second round, participants in all versions learn that they will be ranked against other study participants based on the number of questions they answered correctly in Round 1 (with ties being broken by giving better rankings to participants who answered the questions more quickly in Round 1). Participants also learn that this ranking determines whether they place in the bottom group (those ranked in the lowest third), the middle group (those ranked in the middle third), or the top group (those ranked in the highest third). Participants are then informed that they will be asked to predict whether a specific study participant will place in the bottom group, middle group, or top group. Participants are told that if the second round is randomly selected to count for payment, they will receive 50 cents if their prediction is correct. Participants randomly assigned to the Self versions are asked to make this prediction about themselves. Participants randomly assigned to the Other versions are asked to make this prediction about a randomly selected other subject in the study. To help with their prediction, all participants are provided with messages from two honest robots. The honest robots each pick a different, unnamed, randomly selected question out of the 20 questions asked in Round 1 and report whether the participant (in the Self versions) or the randomly selected other subject (in the Other versions) answered it correctly or incorrectly. This is all the information participants randomly assigned to the Two-Robot versions receive prior to making their predictions. Participants assigned to the Three- Robot versions also receive a message from a third random robot. This third robot randomly selects a third, unnamed, different question but is equally likely to say that the answer is correct or incorrect. Participants must answer an understanding question to ensure that they comprehend that the third robot is equally likely to tell a lie or the truth. Thus, participants in both the Two-Robot version and the Three-Robot versions are provided with exactly the same number of informative signals. All that differs between these two versions is that participants in the Three- Robot versions are provided with a third, entirely uninformative signal (about themselves in the Self version and about the randomly selected other subject in the Other version). Obviously, in either case the participant should ignore the message from the third robot. However, participants in the Self versions may be motivated to use the message from the third robot to inflate beliefs about how well they scored in Round 1, while this motive will be absent for participants in the Other versions. 4.2 A third bias due to motivated errors Table 6 presents the results from ordinary least squares regressions of the performance prediction, which equals 1, 2, or 3 if the performance is predicted to fall into the bottom group, the middle group, or the top group, respectively. All regressions include fixed effects for the messages sent by the first two robots and fixed effects for the number of questions a participant correctly answered in Round 1. All regressions include an indicator for whether the third (entirely uninformative) robot 26

28 provided a message that the third randomly selected answer was correct (see the coefficients on uninformative good signal). 42 Table 6: Regression of predicted performance Excluding uninformative bad Including all decisions signals when prediction is about... when prediction is about......self...other...self or other...self...other...self or other (1) (2) (3) (4) (5) (6) uninformative good signal (0.08) (0.07) (0.08) (0.08) (0.07) (0.08) other prediction (0.10) (0.08) other prediction* uninformative good signal (0.11) (0.11) uninformative bad signal (0.09) (0.08) (0.09) other prediction* uninformative bad signal (0.12) N Robot 1 and 2 FEs yes yes yes yes yes yes Performance FEs yes yes yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are robust and shown in parentheses. The results are from an ordinary least squares regression of the prediction, which equals 1 if participants predict the bottom third, 2 if participants predict the middle third, and 3 if participants predict the top third. uninformative good signal is an indicator for the third robot s message being good, uninformative bad signal is an indicator for the third robot s message being bad, other prediction is an indicator for participants making predictions about another randomly selected subject rather than themselves. Robot 1 and 2 FEs include fixed effects for all combination of messages sent by robot 1 and 2 as well as interactions of those fixed effects with the other prediction indicator. Performance FEs include fixed effects for each potential performance level as well as interactions of those fixed effects with the other prediction indicator. Columns 1 and 4 include participants asked to make predictions about their own performance, Columns 2 and 5 include participants asked to make predictions about another randomly selected subject s performance, and Columns 3 and 6 include all participants. In Column 1, the coefficient on uninformative good signal shows that participants make significantly more favorable predictions about their own performance when the third robot tells them that their third randomly selected answer was correct even though participants know this third robot is equally likely to tell a lie or the truth. The estimated average increase of 0.24 corresponds 42 Columns 4-6 include an indicator for whether the third randomly selected answer was reported as incorrect (see the coefficients on uninformative bad signal). Columns 3 and 6 include an indicator for whether participants are asked to make a prediction about another subject (see the coefficients on other prediction) as well as interactions of this indicator with uninformative good signal (in Columns 3 and 6) and uninformative bad signal (in Column 6) to capture how participants update differently to an uninformative signal when asked to make predictions about others instead of themselves. 27

29 to a 12% increase in the predicted performance (i.e., the average predicted performance in the Self- Two-Robot version is 1.99, almost exactly a prediction of being in the middle group). By contrast, the coefficient on uninformative good signal in Column 2 shows that participants making a prediction about another subject do not update off of the uninformative good signal sent from the third robot. The coefficient on other prediction*uninformative good signal in Column 3 confirms that this differential response when participants make predictions about themselves versus others is statistically significant. Consequently, our results document another example of motivated errors. Participants update based on an entirely irrelevant signal, but only when it allows them to formulate better beliefs about their own performance. Columns 4-6 show that our results are robust to also including in the analysis the participants who are provided with an uninformative bad signal. Results show that participants do not respond significantly to an uninformative bad signal about themselves or others Discussion Section Across our three studies, participants are provided with relevant information (positive donations to charity in Study 1 and 2 and informative signals about performance in Study 3) and irrelevant information (donations to charity of zero cents in Study 1 and 2 and irrelevant signals about performance in Study 3). Rather than only responding to the relevant information, participants display behavioral biases by systematically responding to the irrelevant information. In addition, the extent to which participants display such biases depends on whether there are self-serving motives to do so. When self-serving motives are present, participants engage in biased behavior that results in keeping money for themselves (in Study 1 and Study 2) and reporting that they are of higher ability (in Study 3). Absent self-serving motives, participants decisions are not at all reflective of a behavioral bias (in Study 1 and Study 3) or substantially less reflective of a behavioral bias (in Study 2). Thus, in all three settings, we find evidence of motivated errors causing or exacerbating a behavioral bias. Table 7 summarizes our findings across all versions of our three studies. In this section, we interpret our findings and present new results to make two additional contributions. In Section 5.1, we highlight the likely role of signaling in generating the behavior we observe and provide results that may be of particular interest to those aiming to model motivated errors. In Section 5.2, we show how our findings relate to the literature on information avoidance and provide new results for that literature. 43 The extent to which participants make accurate predictions is not significantly different across our study versions. In the Self versions, participants make accurate predictions 41% of the time if they only view messages from two robots, 42% of the time if they view a good message from the third robot, and 51% of the time if they view a bad message from the third robot. In the Other versions, participants make accurate predictions 42% of the time if they only view messages from two robots, 35% of the time if they view a good message from the third robot, and 44% of the time if they view a bad message from the third robot. 28

30 Table 7: The impact of irrelevant information in each study version N Self-serving motives? Baseline Average Impact of irrelevant information Change in Percent Average Change Study 1 Self/Charity 198 Yes % Self/Charity-Choice 195 Yes % Self/Charity-Sum 206 Yes % Charity/Charity 199 No % Self(150)/Self 202 No % Study 2 Self/Charity 203 Yes % Self/Charity-Choice 190 Yes % Self/Charity-Sum 195 Yes % Self(150)/Charity 200 Yes % Charity/Charity 191 No % Charity/Charity-Choice 215 No % Charity/Charity-Sum 202 No % Charity(ARC)/Charity 200 No % Study 3 Self 197 Yes % Other 212 No % p < 0.10, p < 0.05, p < For Study 1 and Study 2, the baseline average is the fraction of baseline n/4-bundles chosen, and the change in average is the estimated coefficient on ( + 0) from the regression specification detailed for Column 1 of Table 2, run separately for each study version. For Study 3, the baseline average is the average predicted performance in the Two-Robot version, and the change in average is the estimated coefficient on uninformative good signal in Column 1 (for the Self version) and in Column 2 (for the Other version) of Table The role of signaling and results on non-monotonic behavior Participants use of irrelevant information to avoid choosing the bundle in the first two studies and to rate themselves as more able in the third study suggests that participants want to keep money for themselves and want to rate themselves as high ability. If participants are motivated to behave in this way, why should participants display the behavioral bias in response to the irrelevant information? Why not just keep the money for themselves in the first two studies, regardless of the information about the bundle? Why not just report the favorable beliefs in the third study, regardless of the information provided? One potential answer relates to signaling for a related review, see Bénabou and Tirole (2016). 44 Since participants may wish to believe that they are not selfish and that they are a high ability 44 See also Bénabou and Tirole (2002), Köszegi (2006), Bénabou and Tirole (2006), Mijović-Prelec and Prelec (2010), Grossman (2015), Grossman and van der Weele (2017), Bénabou, Falk and Tirole (2018), and Foerster and van der Weele (2018). Related to the idea that individuals need some justification to engage in self-serving behavior, see a discussion of the vast literature in psychology in Kunda (1990). See also a discussion of a desire to manage self-image in Cialdini and Trost (1998). 29

31 type, they may exploit irrelevant information that, if not processed as irrelevant, could facilitate these beliefs. 45 In other words, motivated errors may allow individuals to think of themselves more favorably. For example, when participants choose money for themselves over a bundle with an additional zero, they may view themselves as less selfish by thinking of the additional zero as indicative of the bundle generating less in charitable donations. Similarly, when provided with an irrelevant good signal about their performance, participants may form more optimistic beliefs about their own ability by thinking the good signal is somehow relevant. With this latter scenario in particular, since participants are also incentivized for the accuracy of their beliefs, participants face a trade-off between between the extent to which they value such image concerns and financial incentives (e.g., see Bénabou and Tirole (2002) and Zimmermann (2018)). 46 To the extent the irrelevant information facilitates these self-image concerns, we note that participants are able to use the irrelevant information to achieve a more favorable view of themselves in an arguably more subtle way in our studies than in the prior literature. The use of irrelevant information requires a distorted response to information that is not avoided, that is not conflicting or ambiguous, and that participants are (largely) capably of processing accurately. As detailed below, the use of irrelevant information also appears to come at a cost of failing to process relevant information correctly. In particular, to assess whether using this irrelevant information comes at a cost of failing to process relevant information correctly, we construct a measure that captures whether participants choices in Study 1 display a particular form of non-monotonic behavior with regard to the sum of donations made by a bundle (focusing on a set of 16 decisions with bundles that have similar sums). 47 We additionally construct a measure of whether participants process irrelevant information by looking at whether they are less likely to choose a bundle when a zero is added to it (focusing on 45 Participants may additionally, or alternatively, be engaged in a form of social signaling to the experimenter. The discussion in this section could apply to both types of signaling. Also, that participants are not fully aware of the irrelevance of the irrelevant information is likely important for such a signaling channel to arise. That being said, such a signaling channel can still arise if participants are, to some degree, choosing to be ignorant by not carefully processing the information (e.g., see Grossman and van der Weele (2017)). Moreover, self-serving but unconscious motives can also influence how we make decisions (e.g., see Simler and Hanson (2018)). 46 One could even imagine a trade-off between the extent to which they value thinking of smart because they performed well on the cognitive assessment test in Study 3 versus thinking of themselves as smart because they can accurately predict their performance. Relatedly, Ashraf, Bandiera and Lee (2014) document results that are consistent with individuals putting forth less effort on a test of their ability so that the corresponding feedback from that test is less informative, allowing them to maintain a more favorable view about their own ability. 47 To dos so, we consider evidence from choices of some non-main bundles from Study 1 that were not analyzed in the previous sections. We use decisions from four bundles that are denoted as 4 L /4-bundles because all four amounts are non-zero, but each amount is smaller than the amounts in the main bundles. The non-zero amounts in these bundles are randomly selected to be d L cents, where d L {30, 31, 32, 33, 34, 35, 36, 37, 38} (for more details about these bundles, see Appendix Table A.2). These bundles were constructed so that the sum of each bundle was close to, but lower than, the sum of each 3/4-bundle and each 3/5-bundle (i.e., 3 d > 4 d L for all d and d L ). Thus, we can ask whether each participant chooses one or more 4 L /4-bundles and fails to choose all of the 3/4-bundles and 3/5-bundles. While we could construct other measures of non-monotonic behavior, even among this set of 16 bundles, this measure seems particularly natural since it utilizes bundles designed to be close in sum to our main bundles but with significantly lower donation amounts. 30

32 a distinct set of 16 bundles from among our main bundles). 48 In the Self/Charity version of Study 1, 37% of participants are non-monotonic and 38% of participants respond to irrelevant information by our measures. The correlation between these two is statistically significant (ρ = 0.37, p < 0.01), suggesting that responding to irrelevant information (i.e., responding to the zero) is associated with failing to respond perfectly to relevant information (i.e., failing to be monotonic with respect to donation amounts). In addition, along with being less likely to display biased behavior in the Charity/Charity and Self(150)/Self versions, participants are also much less likely to be classified as non-monotonic in the Charity/Charity version (only 25% of participants, p < 0.01 when compared to Self/Charity) and in the Self(150)/Self version (only 18% of participants, p < 0.01 when compared to Self/Charity). Thus, our main results suggest that agents may be engaged in self-signaling in their use of motivated errors, and our additional analysis suggests that agents experience a trade-off in taking advantage of irrelevant information and carefully processing relevant information. These findings may serve useful in modeling behavioral biases driven by motivated errors, which we view as a fruitful avenue for future work. 5.2 Results on information avoidance Our results in the prior subsection suggest that individuals maintain a positive self-image by failing to fully process the information presented to them in our studies. This insight is related to mechanisms at play in the literature on information avoidance, which shows that individuals often avoid information in order to maintain moral wiggle room about the extent to which a decision is selfish (Dana, Weber and Kuang, 2007). 49 However, the motivated errors we document are not driven by individuals who would simply avoid information if given an opportunity. As noted in Sections 2.4 and 3.3, the motivated erros documented in our studies arise when individuals cannot avoid information (in the Self/Charity versions of Study 1 and Study 2), and even when individuals can avoid information but choose to fully reveal it (in the Self/Charity-Choice versions of Study 1 and Study 2). Despite our main results not being driven by motivated information avoidance, four of our versions in Study 2 the Self/Charity, Charity/Charity, Self/Charity-Choice, and Charity/Charity-Choice versions generate rich data that allow us to speak directly to the related literature on information avoidance. Before describing our new contributions, we show that we can replicate a common finding in the information avoidance literature: participants who avoid information make more selfish decisions. First, we note that looking across all 48 bundles in the Self/Charity-Choice version, participants 48 In particular, we look at whether participants respond negatively to a zero by at least once choosing a baseline 2/4-bundle or 4/4-bundle but not the corresponding 2/5-bundle or 4/5-bundle constructed from it. Note that we exclude the 3/4-bundles and 3/5-bundles from this measure since we use those bundles to construct the measure of non-monotonicity, and we want to avoid introducing a mechanical relationship between the measures. 49 For more work related to motivated information avoidance, see Larson and Capra (2009); Nyborg (2011); Conrads and Irlenbusch (2013); Bartling, Engl and Weber (2014); Feiler (2014); Grossman (2014); van der Weele et al. (2014); Grossman and van der Weele (2017); Bartoš et al. (2016); Exley and Petrie (2018); Golman, Hagmann and Loewenstein (2017). 31

33 avoid revealing all information on a bundle in 70% of decisions. Consistent with the previous literature, when we look at settings where information is likely to encourage giving (i.e., decisions where the sum of donations in the bundle is greater than 150 cents), participants who can avoid information are significantly less likely to choose the bundle than participants who are forced to fully reveal information in the Self/Charity version (these bundles are chosen 49% of the time in the Self/Charity-Choice version vs. 41% in the Self/Charity version, p < 0.05 with standard errors clustered at the participant level). This finding is similar to moral wiggle room studies, where the ability to avoid information leads to less generous behavior (Dana, Weber and Kuang, 2007). In addition to replicating this common finding, our results allow us to make two additional contributions to the literature on information avoidance. First, unlike most of the prior literature, our experiments additionally include decisions in which information is likely to discourage giving (i.e., decisions where the sum of donations in the bundle is less than 150 cents). 50 In these settings, and perhaps not surprisingly given the nature of the information, we no longer find that the ability to avoid information results in reduced giving. Participants who can avoid the information in the Self/Charity-Choice version are, if anything, more likely to choose bundles than participants who are forced to fully reveal information in the Self/Charity version (these bundles are chosen 23% of the time in Self/Charity-Choice version vs. 28% in the Self/Charity version, p = 0.16 with standard errors clustered at the participant level). This finding suggests that in settings where there is uncertainty about whether revealing information is going to encourage or discourage giving, information avoidance may backfire as a strategy to behave selfishly. 51 Second, our results provide the first test, to our knowledge, of whether individuals avoid information more when they have a self-serving motive than when they do not. This test is worth performing because there may be other, unmotivated reasons to avoid information in decision environments, including the implicit costs of collecting and processing information. We observe significant unmotivated information avoidance: participants avoid fully revealing information about the bundles in 50% of decisions in the Charity/Charity-Choice version when self-serving motives are not relevant. However, we also observe evidence of motivated information avoidance. The rate at which participants avoid fully revealing information about the bundles statistically significantly increases to 70% 50 In Dana, Weber and Kuang (2007), revealing information either eliminates the possibility to engage in costly prosocial behavior (i.e., when subjects find themselves in an aligned state where the option that is most beneficial to them is also most beneficial to another subject) or encourages costly prosocial behavior (i.e., when subjects find themselves in an unaligned state and thus learn that sacrificing some of their own payoff would be very beneficial to another subject). In our study, while revealing information may also encourage costly prosocial behavior (e.g., if participants learn that sacrificing the outside option that benefits themselves would be very beneficial to charity, resulting in a large donation of more than 150 cents), it may also discourage costly prosocial behavior (e.g., if participants learn that sacrificing the outside option would be only somewhat beneficial to charity, resulting in a small donation of less than 150 cents). 51 Because we have only slightly more bundles with sums greater than 150 cents than bundles with sums less than 150 cents, the overall rate at which participants choose bundles is approximately the same in the Self/Charity-Choice version (when they choose 35% of all bundles) as in the Self/Charity version (when they choose 38% of all bundles), a difference that is not statistically significant. 32

34 in the Self/Charity-Choice version when self-serving motives are relevant. 52 Thus, our estimates suggest that 71% (i.e., 0.50/0.70) of the information avoidance we observe in the Self/Charity- Choice version is unmotivated in nature and 29% (i.e., 0.20/0.70) is due to self-serving motives. Given the high rates of unmotivated information avoidance, future work on motivated information avoidance may seek to net out possible unmotivated information avoidance by considering settings where self-serving motives are and are not relevant. 6 Conclusion Behavioral biases that cause errors in decision making have historically been attributed to cognitive limitations, and a robust empirical and theoretical literature in behavioral economics has been devoted to exploring and explaining these biases. In this paper, we document that behavioral biases can also be attributed to motivated errors, which look like limitations of cognitive ability but are motivated in nature. We show that these motivated errors can cause behavioral biases on their own or in conjunction with cognitive limitations. We additionally show that traditional interventions aimed at debiasing agents making environments simpler, giving agents experience, making agents attentive may not succeed in mitigating motivated errors. Our experiments investigate motivated errors arising from a desire to make selfish decisions and from a desire to hold more favorable beliefs about one s own ability. In addition, many other selfserving motives arise regularly in daily life. Agents may be motivated to avoid costly investments that would benefit their future selves they may desire to avoid saving, to avoid exercising, to avoid investing in their education, and to indulge in temptation goods such as junk food. 53 Agents may also desire to view news, events, and other information in a manner that aligns with their own worldview or allows them to hold more favorable beliefs about themselves or their in-group. 54 Biases arising in these domains may be driven (at least in part) by motivated errors. Our results suggest significant value in exploring an observed bias to determine whether motivated errors are contributing to it or causing it. How to debias agents and whether doing so will be good for them may depend on whether the bias is driven by motivated errors, cognitive limitations, or both. 52 The likelihood that participants choose a bundle (or a main bundle) is 20 percentage points lower in the Self/Charity-Choice version than in Charity/Charity-Choice version in Study 2 (p < 0.01 with standard errors clustered at the participant level). As discussed in Section 2.1, the individual-level calibration allows us to compare information avoidance across decision environments that differ in whether self-serving motives are present but in which participants face similar stakes. 53 Handel and Schwartzstein (2018) document biases arising in health care, financial decision making, and in other domains that often persist in the presence of relevant available information. Our results suggest another reason why these biases may persist: they may be driven by agents displaying motivated errors. 54 As discussed in Schwardmann (2018), motivated beliefs may be particularly prevalent in settings where the agent is limited in their ability to alter the outcome, such as with certain health outcomes. 33

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43 A Appendixes Additional Information on Experimental Design Table A.1: The 36 main bundles i = 4 i = 3 i = 2 n/4-bundles 1st amount d d d d 0 d d d 0 d d 0 2nd amount d d d d d 0 d d 0 0 d d 3rd amount d d d d d d 0 d d 0 0 d 4th amount d d d d d d d 0 d d 0 0 Total amount 4d 4d 4d 4d 3d 3d 3d 3d 2d 2d 2d 2d n/5-bundles 1st-4th amount same as in n/4-bundles 5th amount Total amount 4d 4d 4d 4d 3d 3d 3d 3d 2d 2d 2d 2d (n+1)/5-bundles 1st-4th amount same as in n/4-bundles 5th amount d d d d d d d d d d d d Total amount 5d 5d 5d 5d 4d 4d 4d 4d 3d 3d 3d 3d Each column within the top, middle, or bottom panel indicates the amounts associated with each bundle. In the n/5-bundles and (n+1)/5-bundles, the payoff structure for the first four amounts is the same as in the corresponding n/4-bundle. 0 indicates a zero-amount, and d indicates a non-zero of d that is randomly selected on the participant-bundle level such that d {51, 52, 53, 54, 55, 56, 57, 58, 59}. Table A.2: The 12 non-main bundles i = 4 L i = 3 L i = 1 n/4-bundles 1st amount d L d L d L d L 0 d L d L d L d nd amount d L d L d L d L d L 0 d L d L 0 d 0 0 3rd amount d L d L d L d L d L d L 0 d L 0 0 d 0 4th amount d L d L d L d L d L d L d L d Total amount 4d L 4d L 4d L 4d L 3d L 3d L 3d L 3d L d d d d Each column indicates the amounts associated with each bundle. 0 indicates a zero-amount, d L indicates a non-zero of d L that is randomly selected on the participant-bundle level such that d L {30, 31, 32, 33, 34, 35, 36, 37, 38} and d indicates a non-zero of d that is randomly selected on the participant-bundle level such that d {51, 52, 53, 54, 55, 56, 57, 58, 59}. 42

44 B Additional Results Figure B.1: Distribution of X values (a) Study 1 (b) Study 2 Percent Outside option X Percent Outside option X Data include all participants decisions in the calibration procedure across all versions of Study 1 in Panel A and across all versions of Study 2 in Panel B. X is set to the lower bound of participants implied indifference range from the calibration procedure except for when there is a zero lower bound and so X is set to 5 cents. There is a zero lower bound for 12% of the 1000 participants in Study 1 and for 13% of the 1596 participants in Study 2. 43

45 Table B.1: In the Self/Charity and the Charity/Charity version of Study 1, regression of choosing a main bundle Sample: full choice varies X is lower bound main if 4/4 if 2/4 or 3/4 main main bundles baseline baseline bundles bundles (1) (2) (3) (4) (5) ( + 0) (0.01) (0.02) (0.01) (0.01) (0.01) ( + 1) (0.01) (0.02) (0.02) (0.02) (0.01) Charity/Charity*( + 0) (0.02) (0.02) (0.02) (0.02) (0.02) Charity/Charity*( + 1) (0.02) (0.02) (0.02) (0.02) (0.02) Charity/Charity (0.03) (0.03) (0.03) (0.02) (0.03) N k n l d FEs yes yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self/Charity version or in the Charity/Charity version of of Study 1, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) is an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, Charity is an indicator for the Charity/Charity version, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-3 analyze all participants decisions: in all main bundles in Column 1, involving the baseline 4/4-bundles in Column 2, and involving the baseline 2/4- and 3/4-bundles in Column 3. Column 4 analyzes all main bundles but among a restricted sample of participants who choose the bundle at least once and choose their outside option at least once across all 48 decisions. Column 5 analyzes all main bundles but among a restricted sample of participants with outside option X set to the lower bound of their indifference range (and thus excludes participants with a zero lower bound). 44

46 Table B.2: Considering the role of experience in the Self/Charity version of Study 1, regression of choosing a main bundle 5-bundles first 4-bundles first early bundles late bundles (1) (2) (3) (4) ( + 0) (0.02) (0.02) (0.02) (0.02) N ( + 1) controls yes yes yes yes k n l d FEs yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self/Charity version of Study 1, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) controls involve an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-2 analyze decisions in all main bundles by participants who first view the set of five-amount bundles than the set of four-amount bundles in Column 1 and instead by participants who first view the set of four-amount bundles than the set of five-amount in Column 2. Columns 3-4 analyze all participants decisions in main bundles that occur early within each set of bundles (i.e., decisions 1-12 and 25-36) in Column 3 and that instead occur late within the set of bundles (i.e., decisions and 37-48) in Column 4. 45

47 Table B.3: Considering the role of inattention and simplifying the decision environment in Study 1, regression of choosing a main bundle Self/Charity and attentive decisions from Self/Charity-Sum Self/Charity-Choice (1) (2) ( + 0) (0.02) (0.01) Self/Charity*( + 0) (0.02) (0.02) Self/Charity (0.03) (0.03) N ( + 1) controls yes yes k n l d FEs yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self/Charity or Self/Charity-Choice versions of Study 1 in Column 1 and in the Self/Charity or Self/Charity- Sum versions of Study 1 in Column 2, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, Self/Charity is an indicator for being in the Self/Charity version, ( + 1) controls involve an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle as well as an interaction of that indicator with the Self/Charity indicator, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Column 1 analyzes all participants decisions in all main bundles in the Self/Charity version of Study 1 and all participants decisions that are attentive (as indicated by them fully revealing information in that decision) in all main bundles in the Self/Charity-Choice version of Study 1. Column 2 analyzes all participants decisions in all main bundles in the Self/Charity version of Study 1 and all participants decisions in all main bundles in the Self/Charity-Sum version of Study 1. 46

48 Table B.4: In the Self/Charity and the Charity/Charity version of Study 2, regression of choosing a main bundle Sample: full choice varies X is lower bound main if 4/4 if 2/4 or 3/4 main main bundles baseline baseline bundles bundles (1) (2) (3) (4) (5) ( + 0) (0.01) (0.02) (0.01) (0.02) (0.01) ( + 1) (0.01) (0.01) (0.02) (0.02) (0.01) Charity/Charity*( + 0) (0.02) (0.03) (0.02) (0.02) (0.02) Charity/Charity*( + 1) (0.02) (0.02) (0.03) (0.02) (0.02) Charity/Charity (0.03) (0.04) (0.03) (0.03) (0.03) N k n l d FEs yes yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self/Charity version or in the Charity/Charity version, of Study 1, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) is an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, Charity/Charity is an indicator for the Charity/Charity version, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-3 analyze all participants decisions: in all main bundles in Column 1, involving the baseline 4/4-bundles in Column 2, and involving the baseline 2/4- and 3/4-bundles in Column 3. Column 4 analyzes all main bundles but among a restricted sample of participants who choose the bundle at least once and choose their outside option at least once across all 48 decisions. Column 5 analyzes all main bundles but among a restricted sample of participants with outside option X set to the lower bound of their indifference range (and thus excludes participants with a zero lower bound). 47

49 Table B.5: Considering the role of inexperience in the Self/Charity and Charity/Charity versions of Study 2, regression of choosing a main bundle 5-bundles first 4-bundles first early bundles late bundles (1) (2) (3) (4) Panel A: Self/Charity ( + 0) (0.02) (0.02) (0.02) (0.02) N ( + 1) controls yes yes yes yes k n l d FEs yes yes yes yes Panel B: Charity/Charity ( + 0) (0.02) (0.02) (0.02) (0.02) N ( + 1) controls yes yes yes yes k n l d FEs yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in in the Self/Charity version of Study 2 in Panel A and in the Charity/Charity version of Study 2 in Panel B, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) controls involve an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-2 analyze decisions in all main bundles by participants who first view the set of five-amount bundles than the set of four-amount bundles in Column 1 and instead by participants who first view the set of four-amount bundles than the set of five-amount in Column 2. Columns 3-4 analyze all participants decisions in main bundles that occur early within each set of bundles (i.e., decisions 1-12 and 25-36) in Column 3 and that instead occur late within the set of bundles (i.e., decisions and 37-48) in Column 4. 48

50 Table B.6: Considering the role of inattention and simplifying the decision environment in Study 2, regression of choosing a main bundle Panel A: Self/Charity versions Self/Charity and attentive decisions from Self/Charity-Sum Self/Charity-Choice (1) (2) ( + 0) (0.03) (0.01) Self/Charity*( + 0) (0.03) (0.02) Self/Charity (0.04) (0.04) N ( + 1) controls yes yes k n l d FEs yes yes Panel B: Charity/Charity versions Charity/Charity and attentive decisions from Charity/Charity-Sum Charity/Charity-Choice (1) (2) ( + 0) (0.01) (0.01) Charity/Charity*( + 0) (0.02) (0.02) Charity/Charity (0.02) (0.02) N ( + 1) controls yes yes k n l d FEs yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self/Charity or Self/Charity-Choice versions of Study 2 in Column 1 and in the Self/Charity or Self/Charity-Sum versions of Study 2 in Column 2, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, Self/Charity is an indicator for being in the Self/Charity version, ( + 1) controls involve an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle as well as an interaction of that indicator with the Self/Charity indicator, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Column 1 analyzes all participants decisions in all main bundles in the Self/Charity version of Study 2 and all participants decisions that are attentive (as indicated by them fully revealing information in that decision) in all main bundles in the Self/Charity-Choice version of Study 2. Column 2 analyzes all participants decisions in all main bundles in the Self/Charity version of Study 2 and all participants decisions in all main bundles in the Self/Charity-Sum version of Study 2. 49

51 Table B.7: In the Self(150)/Charity and Charity(ARC)/Charity versions of Study 2, regression of choosing a main bundle Sample: full choice varies X is lower bound main if 4/4 if 2/4 or 3/4 main main bundles baseline baseline bundles bundles (1) (2) (3) (4) (5) Panel A: Self(150)/Charity version ( + 0) (0.01) (0.02) (0.01) (0.02) (0.01) ( + 1) (0.01) (0.01) (0.01) (0.02) (0.01) N k n l d FEs yes yes yes yes yes Panel B: Charity(ARC)/Charity version ( + 0) (0.01) (0.01) (0.01) (0.01) (0.01) ( + 1) (0.01) (0.01) (0.02) (0.01) (0.01) N k n l d FEs yes yes yes yes yes p < 0.10, p < 0.05, p < Standard errors are clustered at the participant-level and shown in parentheses. The results are from a linear probability model of the likelihood to choose a main bundle in the Self(150)/Charity version of Study 2 in Panel A and in the Charity(ARC)/Charity version of Study 2 in Panel B, where ( + 0) is an indicator for an n/5-bundle that is constructed by adding a fifth amount that is equal to zero to a baseline n/4-bundle, ( + 1) is an indicator for an (n+1)/5-bundle that is constructed by adding a fifth amount that is non-zero to a baseline n/4-bundle, k n l d FEs include all possible interactions of dummies for the number of non-zero amounts within the underlying baseline n/4-bundle (see Table A.1) and dummies for the value of the non-zero amount d in the bundle to fully control for the sum of the amounts in the baseline bundle. Columns 1-3 analyze all participants decisions: in all main bundles in Column 1, involving the baseline 4/4-bundles in Column 2, and involving the baseline 2/4- and 3/4-bundles in Column 3. Column 4 analyzes all main bundles but among a restricted sample of participants who choose the bundle at least once and choose their outside option at least once across all 48 decisions. Column 5 analyzes all main bundles but among a restricted sample of participants with outside option X set to the lower bound of their indifference range (and thus excludes participants with a zero lower bound). 50

52 FOR ONLINE PUBLICATION C Full instructions for Study 1 C.1 Instructions for Self/Charity version of Study 1 After consenting to participate in the study, each participant is informed of the $4 study completion fee and of the opportunity to earn additional payment for themselves or the Make-A-Wish Foundation. Figure C.1 shows how this payment information is explained and the corresponding understanding question that must be answered correctly in order for the participant to proceed. Figure C.1: Payment Information 51

53 In Part 1, each participant completes a multiple price list that allows us to calibrate the outside option used for the decisions in Part 2. In particular, the outside option equals X cents for participants, where we calibrate X to make the participant indifferent between X cents for themselves and 150 cents for the Make-A-Wish Foundation. Figure C.2 presents the instructions for the multiple price list and corresponding understanding questions that the participant must answer correctly to proceed. Figure C.3 shows how the multiple price list appears. Figure C.2: Part 1 Instructions 52

54 Figure C.3: Part 1 Decisions: Multiple Price List Before decisions are indicated After decisions are indicated if X =

55 In Part 2, each participant makes 48 binary decisions between a bundle that changes from decision to decision and an outside option that is fixed for all 48 decisions. Choosing the outside option results in the participants receiving X cents for themselves, where X is calibrated from Part 1 as previously explained. Choosing a bundle results in Make-A-Wish Foundation receiving the sum of the 4 or 5 amounts in the bundle. Appendix Tables A.1 and A.2 in the paper detail the amounts that comprise each bundle. The first amount in a bundle is always revealed by default, and a participant is required to reveal all of the remaining amounts in a bundle by clicking on the header above each amount before proceeding onto the next decision screen. Also, the order of these decision screens varies. It is randomly determined whether a participant first makes the 24 decisions involving bundles with four amounts or instead first makes the 24 decisions involving bundles with five amounts. Within each block of 24 decisions, the order of those decisions is also randomly determined. Prior to making these 48 decisions, participants face extensive instructions and understanding questions. Figure C.4 shows the first and second pages of the instructions for Part 2 along with the corresponding understanding questions that the participant must answer correctly to proceed. These understanding questions ensure that participants understand the payoffs that result from choosing a bundle versus the outside option and that they must reveal all amounts in a bundle before making a decision. Figures C.5 shows the subsequent three example bundles and corresponding understanding questions that the participant must answer correctly to proceed. These understanding questions ensure that participants know how to determine the total donation amount made by a bundle. Figure C.4: Part 2 Instructions First Page (if X = 100) Second Page 54

56 Figure C.5: Part 2 Examples Example 1 Example 2 Example 3 Only after completing all of these understanding questions successfully do participants proceed to make their 48 decisions. Each decision appears on a separate screen, and Figure C.6 shows an example of one such decision. Figure C.6: Part 2: Example Decision Screen After completing all 48 decisions in Part 2, participants answer follow-up questions about their decisions in the study and provide demographic information. We distributed the relevant payments after the study was completed. 55

57 C.2 Instructions for other versions of Study 1 The previous section details the instructions for the Self/Charity version of Study 1. In this section, we describe how these instructions differ for the remaining four versions of Study 1. In the Self/Charity-Choice version, all that differs is that aside from the first amount in a bundle still being revealed by default participants can choose whether or not to reveal the other amounts in a bundle. Thus, how decision screens appear in Part 2 is still as shown in Figure C.6, but the participant can make a decision without clicking on all the headers. In the Self/Charity-Sum version, all that differs is that participants are also shown the sum of amounts in the bundle on the decision screen, as shown in Figure C.7. Figure C.7: Part 2: Example Decision Screen for Charity/Self-Sum version of Study 2 56

58 In the Charity/Charity version, choosing the outside option now results in 150 cents being given to Make-A-Wish Foundation (regardless of the decisions in Part 1), as shown in Figure C.8. Figure C.8: Part 2: Example Decision Screen for Charity/Charity version of Study 2 In the Self(150)/Self version, choosing the outside option now results in 150 cents being given to the participant (regardless of the participant s decisions in Part 1) and choosing a bundle now results in the amount of money in the bundle being given to the participant, as shown in Figure C.9. Figure C.9: Part 2: Example Decision Screen for Self(150)/Self version of Study 2 57

59 D Full instructions for Study 2 D.1 Instructions for Self/Charity version of Study 2 After consenting to participate in the study, each participant is informed of the $4 study completion fee and of the opportunity to earn additional payment for either themselves or the Make- A-Wish Foundation. Figure D.1 shows how this payment information is explained along with the corresponding understanding question that the participant must answer correctly to proceed. Figure D.1: Payment Information 58

60 In Part 1, each participant completes a multiple price list that allows us to calibrate the outside option used for the decisions in Part 2. In particular, the outside option equals X cents for participants, where we calibrate X to make the participant indifferent between X cents for themselves and 150 cents for the national chapter of the Make-A-Wish Foundation. Figure D.2 presents the instructions for the multiple price list and corresponding understanding questions that the participant must answer correctly to proceed. Figure D.3 shows how the multiple price list appears. Figure D.2: Part 1 Instructions 59

61 Figure D.3: Part 1 Decisions: Multiple Price List Before decisions are indicated After decisions are indicated if X =

62 In Part 2, each participant makes 48 binary decisions between a bundle that changes from decision to decision and an outside optionthat is fixed for all 48 decisions. Choosing the outside option results in the participants receiving X cents for themselves, where X is calibrated from Part 1 as previously explained. Choosing a bundle results in various state chapters of the Make-A-Wish Foundation each receiving an amount from the bundle. Appendix Tables A.1 and A.2 in the paper detail the amounts that comprise each bundle. Due to constraints (related to which chapters were IRB approved and to how some states shared Make-A-Wish Foundation chapters), we randomly drew states for each bundle from a list of 28 states that we matched with corresponding Make- A-Wish Foundation chapters. This list of states was: Alaska, California, Colorado, Connecticut, Florida, Georgia, Illinois, Indiana, Iowa, Kentucky, Louisiana, Maine, Michigan, Missouri, Nebraska, Nevada, New Hampshire, New York, North Carolina, Ohio, Oklahoma, South Carolina, Tennessee, Texas, Utah, Virginia, Washington, and Wisconsin. The first amount in a bundle is always revealed by default, and a participant is required to reveal all of the remaining amounts in a bundle by clicking on the header above each amount before proceeding onto the next decision screen. Also, the order of these decision screens varies. It is randomly determined whether a participant first makes the 24 decisions involving bundles with four amounts or instead first makes the 24 decisions involving bundles with five amounts. Within each block of 24 decisions, the order of those decisions is also randomly determined. Prior to making these 48 decisions, participants face extensive instructions and understanding questions. Figure D.4 shows the first and second pages of the instructions for Part 2 along with the corresponding understanding questions that the participant must answer correctly to proceed. These understanding questions ensure that participants understand the payoffs that result from choosing a bundle versus the outside option and that they must reveal all amounts in a bundle before making a decision. Figures D.5 shows the subsequent three example bundles and corresponding understanding questions that the participant must answer correctly to proceed. These understanding questions ensure that participants know the number of state chapters that receive a donation from the bundle and the total donation amount made by a bundle. 61

63 Figure D.4: Part 2 Instructions First Page (if X = 100) Second Page Figure D.5: Part 2 Examples (if X = 100) Example 1 Example 2 Example 3 62

64 Only after completing all of these understanding questions successfully do participants proceed to make their 48 decisions. Each decision appears on a separate screen, and Figure D.6 shows an example of one such decision. Figure D.6: Part 2: Example Decision Screen After completing all 48 decisions in Part 2, participants answer follow-up questions about their decisions in the study and provide demographic information. We distributed the relevant payments after the study was completed. D.2 Instructions for other versions of Study 2 The previous section details the instructions for the Self/Charity version of Study 2. In this section, we describe how these instructions differ for the remaining seven versions of Study 2. In the Self/Charity-Choice version, all that differs is that aside from the first amount in a bundle that is still revealed by default participants can choose whether or not to reveal the other amounts in a bundle. Thus, how decision screens appear in Part 2 is still as shown in Figure D.6, but the participant can make a decision without clicking on all the headers. In the Self/Charity-Sum version, all that differs is that participants are also shown the sum of amounts in the bundle on the decision screen, as shown in Figure D.7. 63

65 Figure D.7: Part 2: Example Decision Screen for Charity/Self-Sum version of Study 2 In the Self(150)/Charity version, choosing a bundle results in the same payoffs, but choosing the outside option now results in results in 150 cents being given to the participant (regardless of the participant s decisions in Part 1), as shown in Figure D.8. Figure D.8: Part 2: Example Decision Screen for Self(150)/Charity version of Study 2 64

66 In the Charity/Charity version, choosing the outside option now results in 150 cents being given to the national chapter of Make-A-Wish Foundation (regardless of the participant s decisions in Part 1), as shown in Figure D.9. Figure D.9: Part 2: Example Decision Screen for Charity/Charity version of Study 2 In the Charity/Charity-Choice version, subjects face the same bundles and outside options as in the Charity/Charity version. All that differs is that aside from the first amount in a bundle that is still revealed by default participants can choose whether or not to reveal the other amounts in a bundle. Thus, how decision screens appear in Part 2 is still as shown in Figure D.9, but the participant can make a decision without clicking on all the headers. In the Charity/Charity-Sum version, subjects face the same bundles and outside options as in the Charity/Charity version. All that differs is that participants are also shown the sum of amounts in the bundle on the decision screen, as shown in Figure D

67 Figure D.10: Part 2: Example Decision Screen for Charity/Charity-Sum version of Study 2 In the Charity(ARC)/Charity version, subjects face the same bundles as in the Charity/Charity version, but choosing the outside option now results in 150 cents being given to the American Red Cross, as shown in Figure D.11. Figure D.11: Part 2: Example Decision Screen for Charity(ARC)/Charity version of Study 2 66

68 E Full instructions for Study 3 E.1 Instructions for Two-Robots, Self version of Study 3 After consenting to participate in the study, each participant is informed of the $3 study completion fee and of the opportunity to earn additional payment. Figure E.1 shows how this payment information is explained along with the corresponding understanding question that the participant must answer correctly to proceed. Figure E.1: Payment Information In Round 1, each participant has 10 minutes to answer a series of questions from practice tests of the Armed Services Vocational Aptitude Battery (ASVAB). Participants are told that if Round 1 is randomly selected to count for payment, they will receive 10 cents for each question they answer correctly. Figure E.2 presents the instructions for Round 1 and the corresponding understanding question that the participant must answer correctly to proceed. Figure E.3 shows how the the top of the screen for Round 1 appears (scrolling down the screen would reveal more questions, and the clock would count down from 10 minutes and 0 seconds). 67

69 Figure E.2: Round 1 Instructions Figure E.3: Round 1 Decisions 68

70 In Round 2, participants learn that they will be ranked against other study participants based on the number of questions they answered correctly in Round 1 and that this ranking will put them into the bottom group, the middle group, or the top group. Participants are told that if Round 2 randomly selected to count for payment, they will receive 50 cents if they correctly predict the group in which they are ranked. To help with their prediction, they are also informed that they will first receive messages from two robots, who each pick a different, randomly selected question out of the 20 questions asked in Round 1 and report whether the participant answered it correctly or incorrectly. Figure E.4 presents the instructions and corresponding understanding questions that the participant must answer correctly to proceed. Figure E.5 shows the decision screen including the messages from both robots. Figure E.4: Round 2 Instructions Top of Screen Bottom of Screen 69

71 Figure E.5: Round 2 Decision (if the first and second randomly selected questions were answered incorrectly) E.2 Instructions for other versions of Study 3 The previous section details the instructions for the Two Robots, Self version of Study 3. In this section, we will detail how these instructions differ for the remaining three versions of the Study 3. Relative to the Two Robots, Self version of Study 3, all that differs in the Three Robots, Self version is that participants also receive a message from a third robot. Participants are informed that this third robot is equally likely to tell the truth or a lie and participants must answer an understanding question that ensures that they are aware of this feature, as shown in Figure E.6. Figure E.7 shows the decision screen including messages from all three robots. 70

72 Figure E.6: Round 2 Instructions for the Three Robots, Self version of Study 3 Top of Screen Bottom of Screen 71

73 Figure E.7: Round 2 Decision (if first and second randomly selected question were answered correctly and incorrectly, respectively, and if third robot truthfully or not reports that answer to third randomly selected question is correct) Relative to the Two Robots, Self version of Study 3, all that differs in the Two Robots, Other version of Study 3 is that each participant makes predictions about your partner, who will be a randomly selected study participant instead of about you (i.e., themselves). Similarly, relative to the Three Robots, Self version of Study 3, all that differs in the Three Robots, Other version of Study 3 is that each participant make predictions about your partner, who will be a randomly selected study participant instead of about you (i.e., themselves). 72