Motivated Cognitive Limitations

Transcription

1 Motivated Cognitive Limitations Christine L. Exley and Judd B. Kessler May 3, 2018 Abstract Behavioral biases are often blamed on agents inherent cognitive limitations. We show that biases can also arise, or be exacerbated, because agents are motivated to display cognitive limitations. In a series of experiments involving nearly 3200 participants, agents motivated to avoid being generous make simple computational errors and respond to the salience of information known to them, and agents motivated to believe they are smart update on entirely uninformative signals of ability. When we remove self-serving motives, agents appear completely (or much more) rational. Biases that are due to motivated cognitive limitations survive standard debiasing interventions including simplifying the decision environment, giving agents experience, and making sure agents are attentive. Exley: clexley@hbs.edu, Harvard Business School; Kessler: judd.kessler@wharton.upenn.edu, The Wharton School, University of Pennsylvania.

2 1 Introduction Over the past 40 years, psychologists and economists have documented various behavioral biases and other inconsistencies in human decision making. These 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). 1 A vast literature in behavioral economics has aimed to understand and explain these biases. The standard explanation is that these biases 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. Complementary 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 Much of the empirical evidence in support of these 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). However, one confound that may be of interest to explore rather than eliminate is the motive to hold particular beliefs or to achieve particular outcomes. In many settings outside of the lab, agents are motivated to hold beliefs that favor their intelligence, their preferred political party, or their in-group. In addition, agents are often motivated to avoid costly actions associated with future or social benefits, such as saving for 1 In addition to these biases, research has also uncovered a number of non-standard preferences, including loss aversion and inequity aversion. As noted by DellaVigna (2009), however, these non-standard preferences only lead to framing effects and preference reversals due to narrow bracketing. For example, agents might be loss averse, but without narrow bracketing, they could not be made to view the same decision in a loss frame or a gain frame (e.g., without narrow bracketing, saving 200 out of 600 lives or losing 400 out of 600 lives would be interpreted in the same way, on a base of the entire relevant population). 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). 1

3 retirement, dieting, exercising, investing in education, learning a new technology, or being prosocial. In this paper, we explore environments in which agents are motivated. We find that agents display behavioral biases not only because of inherent limitations of their cognitive ability but also because they are motivated to display cognitive limitations. 4 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 by being included in a list of potential recipient charities. 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 behavioral biases look like limitations of cognitive ability, and one could imagine developing a behavioral theory based on cognitive constraints 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 believe an uninformative signal is good news, participants look rational (in the first and third studies) or much more rational (in the second study). We say that the behavioral biases we observe are due to motivated cognitive limitations because the biases look like they derive from true limitations of cognitive ability (which we call unmotivated cognitive limitations ), but the limitations are motivated in nature. 5 The first main contribution of our paper is to document how cognitive limitations operate when agents are motivated. We show that behavioral biases can arise entirely from motivated cognitive limitations (as in our first and third studies) and that unmotivated cognitive limitations and motivated cognitive limitations can simultaneously cause a behavioral bias (as in our second study). Together, these results suggest that motivated cognitive limitations may cause or contribute to behavioral biases in many environments. 6 Absent jointly considering unmotivated and motivated 4 Throughout this paper, we call any systematic response to irrelevant information or to a decision frame a behavioral bias, even if arises due to agents being motivated. Our definition contrasts with a potential definition of behavioral bias that requires a behavioral bias be due to an inherent limitation of cognitive ability. However, 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, the latter potential definition would not allow us to call biased behavior a behavioral bias until we had ruled out that agents motivations might be a contributing cause. See further discussion in footnote 9. 5 The distinction between motivated and unmotivated cognitive limitations seeks to distinguish motives from the various ways true limitations on humans cognitive ability might affect decisions. In particular, we define unmotivated cognitive limitations to include the work on deliberate or rational inattention, in which agents may be unwilling to fully process information in an attempt to save on cognition costs; see, e.g., Taubinsky and Rees-Jones (Forthcoming). As we will show, our results depart from this work in two important ways. First, in our settings, agents systematically exploit their failure to process information correctly in a self-serving direction. Second, when we keep stakes comparable but remove self-serving motives, agents appear better at processing information, suggesting that the extent to which they engage in processing itself depends on whether or not they are motivated. 6 While not examples we will focus on in this paper, one could imagine motivated cognitive limitations contributing 2

4 cognitive limitations 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 an unmotivated cognitive limitation, a motivated cognitive limitation, or both. We test whether debiasing techniques traditionally used to overcome unmotivated cognitive limitations can also mitigate motivated cognitive limitations. Biases due to unmotivated 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. 7 A recent example can be found in Enke and Zimmermann (Forthcoming), in which unmotivated 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 cognitive limitations are motivated, however, then agents may not want to make the correct calculations and these strategies need not be effective. Indeed, we find thats these techniques do not debias participants displaying motivated cognitive limitations. Our motivated cognitive limitations arise in exceedingly simple environments and survive making the environments simpler. Giving participants experience with the decision task does not mitigate motivated cognitive limitations. Finally, participants who choose to pay attention are, if anything, more likely to display a motivated cognitive limitation. 8 Consequently, determining how to debias behavior in practice likely requires identifying whether a behavioral bias is driven by an unmotivated cognitive limitation, a motivated cognitive limitation, or both. Identifying the driver of a behavioral bias is also relevant for determining whether debiasing agents will be good for them. Unmotivated cognitive limitations may cause agents to make mistakes and so debiasing is likely to make them better off; see, e.g., the discussion in Chetty (2015). Motivated cognitive limitations, on the other hand, may help agents avoid taking actions they to a number of well-documented behavior biases. 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 their house to maintain the belief that they made a good investment; 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. 7 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. 8 That attention does not mitigate motivated cognitive limitations 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. 3

5 prefer not to take, and so debiasing may make them worse off. 9 This observation suggests an important role for new theory on motivated cognitive limitations, including work exploring their value or cost for agents, which we discuss further in Section 5.1. More generally, our results suggest the need to explore motivated cognitive limitations alongside, and in conjunction with, the robust literature on unmotivated cognitive limitations. 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. Prior work on motivated reasoning has suggested that it requires some form of flexibility to be present (Gino, Norton and Weber, 2016). 10 Prior literature has documented self-serving behavior arising when payoffs are ambiguous (Haisley and Weber, 2010) or risky (Exley, 2015), or when individuals maintain uncertainty by avoiding payoff information (Dana, Weber and Kuang, 2007). In our first two studies, we document that uncertainty is not necessary for self-serving behavior to arise in response to payoff information; entirely certain payoffs result in self-serving behavior. Similarly, prior literature has documented self-serving beliefs arising when agents update in response to signals that are informative but noisy, and thus offer flexibility to non-bayesian agents (Eil and Rao, 2011; Mobius et al., 2014; Schwardman and van der Weele, 2017; Zimmermann, 2018). In our third study, we document that a degree of informativeness is not necessary for self-serving beliefs to arise in response to signals; entirely uninformative signals generate self-serving beliefs. In all our studies, motivated cognitive limitations arise when information is certain, unavoidable, and simple that is, absent any flexibility. These new findings suggest the broad relevance of self-serving behavior and self-serving beliefs. They also highlight the potential difficulty in mitigating them, 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 For example, if an agent is donating money to maintain a good self-image, and if a motivated cognitive limitation allows the agent to maintain that self-image without donating, then the agent may value the motivated cognitive limitation. Note that in this paper, we call any systematic response to irrelevant information or to a decision frame a behavioral bias, regardless of whether or not displaying the bias is beneficial to the agent. See further discussion in footnote Flexibility is also known to arise from subjectivity around which set of actions is fair, appropriate, or plausibly justified (Snyder et al., 1979; Kunda, 1990; 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) and 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). That individuals desire to exploit excuses to avoid giving may also contribute to individuals being 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). 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 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 could imagine blaming this error on a behavioral bias driven by an unmotivated cognitive limitation. We show that this behavior is instead due to a motivated cognitive limitation. 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 avoid accurate calculations when they are motivated. In additional analysis, we show that the motivated cognitive limitation survives attempts to debias participants by giving them experience or by further simplifying the (already simple) decision environment, and we show that the motivated cognitive limitation is 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 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. 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 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 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. 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). Each non-zero amount within a bundle equals d. Thus, the total amount going to charity if 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). 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 To

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. 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 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, 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 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 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, the price list contains 31 rows. On each row, the participant must decide between 150 cents being 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 (and screenshots where appropriate) 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 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 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 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 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 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 non-zero amount to a baseline n/4-bundle. In particular, we report results from the following linear 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. 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). Column 4 and Column 5 of Table 2 examine whether our effect persists with more restricted samples 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 it is a motivated cognitive limitation In the previous subsection, we document a clear behavioral bias. 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 an unmotivated 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) 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 A key feature of these explanations is that something about the additional zero makes participants unable to do the calculation of the sum correctly. We explore an alternative explanation for this behavioral bias. We posit that participants are motivated to estimate the sum incorrectly 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 inability to add 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. 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. 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). That participants do not respond to the addition of a zero in the absence of self-serving motives means that participants are capable of correctly adding a zero. This implies that participants in the Self/Charity version were not unable to correctly add a zero to a bundle but rather they were motivated to add it 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 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. 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 a motivated cognitive limitation. 2.4 Attempting to debias the motivated cognitive limitation We have documented evidence of a motivated cognitive limitation. In this subsection, we explore whether common de-biasing strategies mitigate the motivated cognitive limitation, drawing from a vast related literature. We specifically consider experience, inattention, and complexity. The role of experience We identify our motivated cognitive limitation as it arises within an individual, so we can ask whether it is 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 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, 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 De Quidt, Haushofer and Roth (2017)). 27 The difference across versions is also readily apparent at the individual level. 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 (statistically significantly less than the 50% observed in the Self/Charity version, p < 0.01). In addition, participants in the Charity/Charity version are just as likely to do the opposite: 31% of participants in the Charity/Charity version at least once reject an n/4-bundle but choose the n/5-bundle constructed from it (this is similar to the 26% of participants who do this at least once in the Self/Charity version). Finally, we find evidence that participants in the Self/Charity version are more likely to be inconsistent than participants in the Charity/Charity version. We call a participant inconsistent if, for one or more pairs of an n/4-bundle and its corresponding n/5-bundle, the participant chooses the outside option in one decision and the bundle in the other. 42% of participants are inconsistent in the Charity/Charity version, while 58% are inconsistent in the Self/Charity version (p < 0.01). 15

17 Column 3) or late in each set (from the second half of each set, decisions and 37-48, Column 4). Rather than mitigating our motivated cognitive limitation, 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 cognitive limitation. To assess whether inattention is driving our motivated cognitive limitation, 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 cognitive limitation is driven by individuals who choose not pay attention to the information in a bundle, then it 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 cognitive limitation is 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 cognitive limitation is prevalent in attentive decisions directly implies that it persists in decisions where participants are particularly inclined to choose the bundle. The role of complexity While our environment is exceedingly simple it only requires participants to add a few twodigit 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 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 16

18 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 cognitive limitation persists 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 cognitive limitation. That the motivated cognitive limitation persists in the Self/Charity-Sum version, that it is not eliminated by experience, and that it persists among decisions in which participants choose to be attentive, all suggest that motivated cognitive limitations may be particularly difficult to overcome. Next, we explore the robustness of our result and test whether motivated cognitive limitations 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 a motivated cognitive limitation. When self-serving motives are present, over 50% of the response to salience is due to a motivated cognitive limitation. 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 cognitive limitations and demonstrates that a motivated cognitive limitation can be active alongside 17

19 an unmotivated cognitive limitation that also leads to biased behavior. In Study 2, we again show that the motivated cognitive limitation survives attempts to debias participants by giving them experience and that the motivated cognitive limitation is present even when participants are attentive. Unlike Study 1, however, in Study 2 we find that the motivated cognitive limitation is 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). 29 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. 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. 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 28 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. 29 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. 18