Journal of Economc Behavor & Organzaton 133 (2017) 52 73 Contents lsts avalable at ScenceDrect Journal of Economc Behavor & Organzaton j ourna l ho me pa g e: www.elsever.com/locate/jebo Perceptons, ntentons, and cheatng L Hao a,, Danel Houser b a Department of Economcs, Walton College of Busness, WCOB 421, Unversty of Arkansas, Fayettevlle, AR 72701, Unted States b Interdscplnary Center for Economc Scence, George Mason Unversty, 4400 Unversty Dr, MSN 1B2, Farfax, VA 22030, Unted States a r t c l e n f o Artcle hstory: Receved 6 October 2015 Receved n revsed form 16 October 2016 Accepted 19 October 2016 Avalable onlne 27 October 2016 JEL: C91 D03 Keywords: Cheatng Perceptons Self-mage Honest appearance Expermental desgn a b s t r a c t We report data from a laboratory experment demonstratng that havng to announce one s own future possbly dshonest actons can deter msconduct. Further, results from ndependent evaluators suggest that a possbly dshonest acton taken after t s announced s more lkely to be perceved as dshonest than an equvalent acton absent the announcement. Consequently, requrng announcements promotes honest actons among people who care about mantanng an honest self-mage. Fnally, a type-classfcaton analyss shows that the mxture of maxmum cheatng and honest types best characterze the cheatng behavor, suggestng that ncomplete cheatng reported n the lterature s not an ntrnsc preference for beng honest, but may rather be due to a preference for appearng honest. 2016 Elsever B.V. All rghts reserved. 1. Introducton There s a return to appearng honest, but not to beng honest. Akerlof (1983, p. 57) Ths paper provdes evdence that havng to announce one s own future decsons can deter msconduct, and argues that ths effect can stem from a desre to mantan an honest appearance. 1 The reason s that when the announcement of own future decsons sgnal ntent to cheat, the appearance of honesty s jeopardzed. Indeed, the value people place on mantanng an honest appearance s evdenced by the market for albs and excuses for absences. For example, as the company Alb Network advertses, Poltcans have spn doctors, celebrtes have publcsts, corporatons have lawyers Some of the data and analyses reported n ths paper were prevously reported n the unpublshed workng paper Honest Les, by the same authors. For helpful comments we thank Davd Gll, Glenn Harrson, Ed Karn, R. Lynn Hannan, Cary Deck, Salar Jahed, Roberto Weber, Omar Al-Ubaydl, Marco Castllo, Ragan Petre, Jo Wnter, Larry Whte, Chrs Coyne, our colleagues at ICES, George Mason Unversty and Unversty of Arkansas, semnar partcpants at CEAR, Georga State Unversty (2010), the ESA North-Amercan meetng (2010, 2011), Unversty of Fayettevlle, Arkansas (2011), GSPW at George Mason Unversty (2011), and Southern Economc Assocaton meetngs (2012), Shangha Unversty of Fnance and Economcs (2013), Southwestern Unversty of Fnance and Economcs (2013). The authors are of course responsble for any errors n ths paper. Correspondng author. E-mal addresses: lhao@walton.uark.edu (L. Hao), dhouser@gmu.edu (D. Houser). 1 We argue the preference for appearng honest s an mportant, but not the sole reason for the observed behavoral dfferences between our treatments. There are alternatve (and closely related) mechansms, ncludng that ndvduals mght dslke feelng extra scrutny, or the dscomfort of sendng a dshonest sgnal early and remanng n an awkward stuaton for a longer tme. http://dx.do.org/10.1016/j.jebo.2016.10.010 0167-2681/ 2016 Elsever B.V. All rghts reserved.
L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 53 Fg. 1. Screenshot of Excel spreadsheet for the quadratc scorng rule. and publc relatons departments, nvestment banks have analysts, now regular people have ALIBI NETWORK 2 ; Despte the substantal economcs lterature on decepton (e.g., Gneezy, 2005; and papers we revew n Secton 2) and the extensve lterature on sgnalng to self (see, e.g., Bénabou and Trole, 2004; Mazar et al., 2008) and to others (see e.g., Andreon and Bernhem, 2009; Arely et al., 2009), we are aware of very lttle evdence regardng how announcng one s future behavor may affect subsequent decsons to cheat. 3 Knowng whether announcng one s own future decsons can deter dshonest behavor s mportant (see e.g., Hannan et al., 2006). For example, requrng travelng employees to submt ther estmated travel budgets pror to ther trps may reduce fraudulent travel expenses. Moreover, one may announce one s own future behavor to help address self-control problems (.e., cheatng on oneself). For nstance, to combat procrastnaton ssues, t may be useful to announce to frends or colleagues a self-mposed deadlne for well-specfed tasks (see e.g., www.stckk.com). Smlarly, when tryng to acheve a healthy weght, one mght be able to curb cheatng by announcng plans for det and exercse publcly and subsequently offerng regular publc progress reports. 4 Our nvestgaton s based on a novel game that requres partcpants to announce, n ths case a predcton announcement, the percent chance that each outcome occurs when rollng a 4-sded de. We consder three treatments: CONTROL, PREDICT, and REPORT. In CONTROL there was no opportunty to cheat; subjects rolled a physcal de, and were pad based on the accuracy of ther predctons compared to the actually outcome they rolled. In PREDICT subjects rolled the de prvately and they knew ths would be the case when they made ther predctons. 5 In REPORT subjects kept ther predctons prvate untl after they observed the outcomes. Hence, a proft-maxmzng subject n the PREDICT and REPORT treatments could earn the maxmum amount by placng 100% on the outcome that s/he rolled. It s mportant to note that our desgn attempts to mtgate dfferences n cogntve requrements between PREDICT and REPORT. Frst, both treatments requre retrevng nformaton from memory wthn mnutes: ether recallng the outcomes n PREDICT, or recallng the predctons n REPORT. Second, to elmnate the possblty that t mght be harder to recall from memory four probabltes n REPORT than one outcome n PREDICT, we provded an nteractve decson support tool (a spreadsheet, see Fg. 1) on the computer n front of each subject throughout the entre experment. Ths tool enabled subjects to explore the relatonshp between predctons and potental earnngs: they entered probablstc predctons, and the spreadsheet computed and dsplayed possble payoffs. Subjects were provded suffcent tme to use the spreadsheet. 2 Alb Network (www.albnetwork.com) offers customzed albs to clents. The company provdes fabrcated arlne confrmaton, hotel stay and car rental recepts for any locaton and tme of the clent s choce. For those who want excuses for an upcomng absence, a 2 5 day alb package s offered so that one can pretend he/she s gong to a conference or career tranng. The package s extremely comprehensve and ndvdually talored, ncludng the conference nvtaton, confrmaton emals and/or phone calls, maled conference programs such as tmetable and topc overvew, vrtual ar tcket and hotel stay confrmaton, and even a fake hotel number that s answered by a traned receptonst. 3 Jang (2013), revewed n Secton 2, nvestgates a smlar queston. 4 Ths type of pre-commtment effects may work through, for example, gult averson (Charness and Dufwenberg, 2006), or socal pressure (DellaVgna et al., 2012). The effect s lmted for those who do not experence gult from lyng, or n envronments where the norm s to le. 5 Due to ts senstve nature, the possblty of cheatng was not explctly announced. However, the fact that the de roll would be prvate was emphaszed three tmes n the nstructons. Hard copy nstructons were n front of the subjects durng the entre experment, and were also read aloud by the expermenter.
54 L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 When fnshed, they could leave ther fnal predctons on the screen and smply transcrbe the four probabltes from the screen to ther decson sheet. To understand how potental behavoral dfferences arse between the two cheatng treatments, consder three types of play. 6 Frst, ndvduals who are averse to cheatng per se would always predct the objectve probabltes {25%, 25%, 25%, 25%} and obtan a guaranteed amount regardless the outcomes n both PREDICT and REPORT; second, absolute proft maxmzers n both treatments would predct {100%, 0%, 0%, 0%}, whch they would make sure perfectly match the outcomes to obtan the maxmum earnngs. In contrast, the thrd type, those who would cheat for proft but also prefer mantanng an honest appearance, may change ther cheatng behavor f ther decsons put ther honest appearances n jeopardy. In partcular, ths thrd type mght be more cautous about cheatng n PREDICT f, for example, they worry that they could be perceved as premedtated cheaters. 7 In PREDICT, the ntent to cheat s emboded n submttng predctons that are closer to {100%, 0%, 0%, 0%}, than to {25%, 25%, 25%, 25%}. There are multple reasons, however, that people may submt probablty predctons that depart from the objectve probabltes. For example, those wth rsk-seekng preferences would make predctons that devate from the unform dstrbuton, and ndeed we observed that some predctons n CONTROL were as large as 50% on a sngle outcome. To account for rsk atttudes, hunches and other reasons people may choose not to report objectve probabltes, we use the emprcal dstrbuton of predctons n CONTROL (where cheatng was not possble) as the baselne to evaluate whether predctons n cheatng treatments are honest-lookng or dshonest-lookng. Subjects n PREDICT cheated by msreportng de roll outcomes to match ther predctons that they submtted before self-reportng de rolls, so dshonest-lookng predctons can be perceved as a sgnal that the partcpant spent tme plannng to cheat. 8 In contrast, subjects n REPORT cheated by msreportng predctons after the de rolls. Hence, for those who value the appearance of honesty, t may be easer to hde behnd the possblty that cheatng s mpulsve n REPORT, whle harder to do so n PREDICT. Comparng decsons between PREDICT and REPORT enables us to shed lght on our man research queston: can cheatng be deterred f a possble ntent to cheat must be revealed before a dshonest act? We argue that dfferences n behavor between PREDICT and REPORT may be connected to dfferences n the way behavors are perceved between those two treatments. To provde evdence on ths ssue, we collected opnons from ndependent evaluators regardng the appearance of honesty n the REPORT and PREDICT treatments. These evaluators had not partcpated n CONTROL, REPORT or PREDICT. They were gven the nstructons of REPORT and PREDICT, and were asked to evaluate dentcal scenaros from the two treatments. Evaluators were rewarded f ther answers matched the majorty s answers (ths elctaton approach s detaled n Houser and Xao, 2011). We fnd that, ceters parbus, the same acton was more lkely to look lke cheatng n PREDICT than REPORT. Ths suggests the percepton of honesty s dampened by evdence that cheatng could have been premedtated n PREDICT. It may be worth notng that, to our knowledge, the use of external evaluators to assess the appearance of honesty, and thus to provde evdence on the source of the dfferences n behavors we fnd, s novel to our study. 9 Our man result s that sgnfcantly less cheatng occurred n PREDICT than REPORT. To shed further lght on ths result, we conducted a type-classfcaton analyss usng an algorthm (adapted from El-Gamal and Grether, 1995). Whle the vast majorty of subjects (95%) exhbted a strong preference for appearng honest, we found that less than half of subjects value the actualty of honesty. The prevalent preference for appearng honest offers mportant nsghts for desgnng nsttutons to deter msconduct, especally when montorng or contractng on all possble contngences are too costly or even nfeasble (Wllamson, 1975). Our results also help to explan the puzzle of ncomplete cheatng. Prevous research strongly suggests that people of all ages are averse to lyng (see, e.g., Gneezy, 2005; Hannan et al., 2006; Buccol and Povesan, 2009; Fschbacher and Heus, 2013; Greene and Paxton, 2009; Mazar et al., 2008; Houser et al., 2012; Lundqust et al., 2009). One pattern reported n these studes s that, when gven the opportunty, people do cheat but shy away from cheatng for maxmum earnngs. Our results suggest that a source of ncomplete cheatng may be more ted to a desre to mantan an honest appearance, rather than an ntrnsc averson to cheatng. The paper proceeds as follows. Secton 2 revews related lterature; Secton 3 descrbes the desgn of the experment; Secton 4 specfes our hypotheses; Secton 5 reports the results; and the fnal secton concludes the paper. 6 For the sake of dscusson, we consder only rsk-neutral ndvduals. However, our results are more general, as rsk preferences are controlled for, due to random assgnment to treatments and that we compare between treatments. 7 Decevers wth no evdence of havng cheated ntentonally are more lkely to be forgven and avod retrbuton (Von Hppel and Trvers, 2011). The attrbuton of ntent s crtcal n dealng wth decepton and fraud (Schwetzer et al., 2006; Stouten et al., 2006). Ths aspect s codfed n law by punshng premedtated crmes more severely than crmes of passon. In the result secton we report that out ndependent evaluators agree wth ths percepton. 8 It s mportant to note that our experment was a one-shot game, so there was no tme pressure whatsoever. Subjects had plenty of tme to make ther decsons n both PREDICT and REPORT. 9 For example, ths approach was not followed n the closely related paper by Jang (2013).
L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 55 2. Lterature revew Recent years have seen substantal research nterests n cheatng behavor. In ths secton, we brefly revew the papers most relevant to our study. Gneezy (2005) showed that people exhbt an averson to lyng. In hs sender-recever game, only Player 1 was nformed about the monetary consequences of the two optons, and Player 2 chose whch opton should be mplemented based on the message sent from Player 1. Hence, Player 1 could ether: () tell the truth and obtan Opton A, n whch hs payoff was lower than Player 2 s; or () le and obtan Opton B for a slght monetary gan at a greater cost to Player 2. In an otherwse dentcal dctator game, Player 1 chose between Optons A and B; Player 2 had no choce but to accept the payoff dvson. The paper reported that the proporton of Opton B was sgnfcantly lower n the sender-recever game than n the dctator game, thus suggestng an averson to lyng as opposed to preferences over monetary allocatons. In addton, Gneezy (2005) also found that people le less when the le results n a greater cost to others. Gneezy s (2005) fndngs stmulated subsequent work that reported consstent results (see, e.g., Gbson et al., 2013; Hurkens and Kartk, 2009; Lundqust et al., 2009; Rode 2010; Sánchez-Pagés and Vorsatz, 2007, 2009). For example, Gbson et al. (2013) provded evdence that there s a great level of heterogenety n preference for truthfulness. Lundqust et al. (2009) found that lyng averson s greater when the sze of the le (.e., the dfference between the truth and the le) s greater. In ther experment, Player 1 reported hs type to Player 2, who decded whether to enter nto a contract wth Player 1. Upon completng the contract, Player 1 always ganed. Player 2 ganed f Player 1 s type was above a threshold, but otherwse lost. The authors found that the further Player 1 s type was from the threshold, the less lkely he would le about hs type. Mazar et al. (2008) argue a theory of self-concept mantenance; they observe that people behave dshonestly enough to proft, but honestly enough to delude themselves of ther own ntegrty. The authors suggest two mechansms that allow for such self-concept mantenance: () nattenton to moral standards; and () categorzaton malleablty. For example, n one of ther experments, subjects self-reported ther own performance on a real-effort task, and were pad accordngly. However, some subjects were asked to wrte down the Ten Commandments before the task, whle others were not. The result s that those who were remnded of moral standards led less, thus supportng the hypothess that nattenton to moral standards serves as a mechansm through whch people cheat for proft wthout spolng a postve self-concept. In Fschbacher and Heus s (2013) experment, subjects rolled a sx-sded de prvately and self-reported the frst roll. The outcome of the frst roll was the amount of payment they receved for the experment. The fracton of self-reported hghest payoff outcomes was sgnfcantly hgher than one sxth, as expected; however, the fracton of the second hghest payoff was also sgnfcantly hgher than one sxth. Ths s a type of ncomplete cheatng, whch the authors speculate mght be due to greed averson and the desre to appear honest. Buldng on Fschbacher and Heus (2013), Jang s (2013) mnd game shares a smlar dea to our man cheatng treatments, although developed ndependently. In Jang s throw-frst treatment, subjects frst rolled a sx-sded de, where the outcome was denoted by x = 1, 2, 3, 4, 5, or 6, and then subjects chose between two earnng schemes, so that ther earnngs were ether () x euros or () 6-x euros. In the report-frst treatment, subjects chose the earnng scheme before they rolled the de. Jang (2013) found that subjects cheated more n throw-frst than n report-frst, whch s consstent wth our results. In addton to the presence of the CONTROL treatment and other dfferences, the most substantal dfference of our paper s that we elcted the percepton from ndependent evaluators on the lkelhood that subjects have cheated. 3. Expermental desgn Our nnovaton les n the subtle dfference between PREDICT and REPORT. In PREDICT, the ntent to cheat was manfested as predctons that dffer drastcally from the objectve dstrbuton (.e., unform). Even worse, predctons were submtted well before the acton of cheatng on prvate de roll outcomes, whch sent a strong sgnal that the cheatng was premedtated. In REPORT, however, predctons were submtted after the de rolls, and cheatng occurred va ms-reportng predctons. Hence, there was no obvous evdence that ntent to cheat was pre-conceved before acton. Another novelty of our experment s the use of ndependent evaluators who were ncentvzed to evaluate the cheatng behavor n the man treatments. By comparng these evaluatons and the cheater s behavor n PREDICT and REPORT, we gan a deeper understandng about the cheatng behavor and perceptons. Subjects were recruted va emal from regstered students at George Mason Unversty. Upon arrval, subjects were seated n ndvdual cubcles, separated by parttons, so that others could not observe ther actons. Sessons lasted 40 mn on average, and earnngs ranged between $6.25 and $25, n addton to a show-up bonus of $5. 3.1. Desgn Our man experment ncluded three treatments: CONTROL, REPORT, and PREDICT. After the treatments, a fnal group of subjects were asked to evaluate whether partcpants n gven scenaros from REPORT and PREDICT treatments appeared to have cheated. We used a between-subject desgn, so no one partcpated n more than one sesson from the man treatments and the evaluaton sessons. All nstructons and decsons sheets are attached n Appendx A.
56 L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 3.1.1. CONTROL treatment There were two stages. In the frst stage, the subject predcted the percent chance that each face of a far four-sded de would turn up n a sngle roll, and then submtted hs/her predcton to the expermenter on paper. The ndvdual probabltes had to be between 0% and 100% (nclusve), and the four probabltes had to add up to exactly 100%. In the second stage, the subject rolled a far four-sded de. The expermenter observed and recorded the outcome. Subjects earned more for accurate predcton, accordng to a quadratc scorng rule detaled n the next subsecton. 3.1.2. PREDICT treatment Identcal to CONTROL, except that the de roll n the second stage was prvate, and the subject knew before he made predctons that hs rollng would not be montored by the expermenter. To make subjects comfortable, they were encouraged to roll the de prvately as many tmes as they wshed, but to only remember the frst roll and report t to the expermenter va paper. 10 3.1.3. REPORT treatment Identcal to CONTROL, except that n the frst stage, the subject was asked to keep hs predctons n mnd, and wat untl after the de roll outcome was observed and recorded n the second stage. Then, the subject recalled hs predctons and submtted them on paper. As noted above, ths recall was asssted by a spreadsheet open on each subject s computer on whch ther predctons could be dsplayed for ther own use. Several features of our desgn are worth notng. Frst, we dd not explctly nvte subjects to cheat. We dd, however, endeavor to ensure that subjects understood they had opportunty to cheat. Ths s especally mportant n the PREDICT treatment (whle at the same tme dong our best to avod any expermenter demand effects), as t was emphaszed three tmes that the de roll would be prvate at the begnnng, the mddle, and the end of the nstructons. Hard copy nstructons were at the subjects dsposal durng the entre experment. Addtonally, the expermenter llustrated the experment wth fve examples, ncludng the earnngs-maxmzng strategy. A comprehenson quz was conducted, and subjects were requred to answer all questons correctly before proceedng to the experment. Fnally, t s worth emphaszng that subjects were gven no tme pressure to make ther decsons n all treatments. In fact, we observed no dfference n the actual total tme spent on decson-makng n the two cheatng treatments. We used far dce and made sure subjects were clearly nformed about t; thus, predctons that dffered from the objectve dstrbuton could not be attrbuted to suspcons that the dce mght be based. However, we also encouraged subjects to play hunches f they beleved certan outcomes were more lkely than others. The goal was to ensure subjects felt comfortable makng predctons other than the unform probablty predcton. 11 3.1.4. Evaluaton sessons A fnal group of subjects served as ndependent observers to evaluate whether a partcpant n a gven scenaro from the man treatments appeared honest or not. These evaluators receved detaled debrefng about the PREDICT and REPORT treatments, ncludng the orgnal nstructons (for detals see Appendx A). There were two parts to ther evaluaton task. The frst part conssted of evaluatng twelve scenaros, where hghest-payoff outcomes were obtaned n all cases. Scenaros 1 6 were all from the PREDICT treatment, and dffered only accordng to p max values, whch were 50%, 60%, 40%, 25%, 85%, and 100%, respectvely. 12 Scenaros 7 12 were from the REPORT treatment, repeatng the same sequence of p max as the frst sx scenaros. To avod any framng effects, we used Experment 1 and Experment 2 for the PREDICT and REPORT treatments, respectvely. For example, the frst scenaro was as below, Scenaro 1: In Experment 1, a partcpant frst revealed hs or her predcton that outcome 2 would occur wth 50% chance, and that was the hghest probablty the partcpant placed on any outcome. The partcpant then rolled the de prvately, and reported that the de roll was 2. Queston 1: Do you thnk the majorty of people n ths room beleve that ths partcpant cheated? ( Yes or No ) The second part ncluded 6 questons askng evaluators to drectly compare dentcal scenaros between the two treatments, e.g., If your answers n Scenaros 1 and 7 are the same, do you thnk the majorty of people n ths room beleve that the partcpant more lkely to have cheated n Scenaro 1 or n Scenaro 7? Subjects could choose among three answers: Scenaros 1, Scenaros 7, and equally lkely. Three questons, one from each set of sx questons, were randomly selected for payment, and subjects earned $5 for each answer that was n agreement wth the majorty of the evaluators n the room. 10 To mnmze dfferences, subjects n all three treatments were asked to roll the de as many tmes as they wsh. The only dfference s that the frst roll n CONTROL and REPORT treatments was observed and recorded by the expermenter. 11 Snce the goal was to observe and study cheatng behavor, our nstructons were wrtten to make cheatng feel more comfortable and natural. To allevate concerns regardng expermenter demand effects, we stress that dentcal words were used n all three treatments, so between-treatment comparsons are mnmally affected. 12 We frst chose sx values for p max that spanned from ts mnmum value of 25% to ts maxmum 100%. We then randomzed the order n whch they were presented to subjects. Note that p max = 25% ndcates objectve predctons, and evaluators should not have vewed ths predcton as dshonest. We ncluded ths one to verfy that subjects understood the experment.
L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 57 3.2. Payoff n the man experment In the man experment, each subject s frst-stage probablstc predcton was compared wth the relevant roll n the second stage. Earnngs were calculated accordng to the followng quadratc scorng rule, whch rewards predcton accuracy. 4 Earnngs = $25 $12.5 ( p ) 2 (1) =1 { } where. ndexes the four faces of the de: 1, 2, 3, 4., and p s the probablty that the subject assgned to face. The 4 ndcator. s 1 f face s the outcomef the roll, and 0 otherwse (so we have =1 = 1). In the frst stage, the subject 4 submtor of four probabltes: p = (p 1, p 2, p 3, p 4 )., where 0 p 1, and =1 p = 1. 13 Quadratc scorng rules are wdely used ncentve-compatble mechansms for elctng subjectve probabltes n expermental studes (see e.g., Nyarko and Schotter, 2002; Andersen et al., 2010). 14 Kadane and Wnkler (1988, p. 359) showed that an expected utlty maxmzer would report truthfully, assumng the ndvdual s utlty s lnear n money. 15 To facltate subjects understandng of the payoffs, we provded an nteractve Excel spreadsheet n whch subjects could type n any probablstc predcton and vew the payoffs condtonal on the rollng outcome (a screenshot s shown below n Fg. 1). 16 4. Hypotheses We start wth a few defntons. A predcton s an objectve predcton f t s dentcal to the objectve dstrbuton (25%, 25%, 25%, 25%). For subject s predcton of four probabltes, we sort them from hghest to the lowest and denote the hghest probablty by p max, and the correspondng outcome that the subject assgned p max to s called a hghest-payoff outcome. 17 The hghest probablty and ts correspondng outcomes are key varables, as the only way to ncrease earnngs s to concentrate more probabltes on fewer outcomes.e use predctons n CONTROL to defne what s consdered honestlookng. For subjects who desre to appear honest, a smple strategy s to make predctons as f they are not beng montored. Intutvely, a predcton n PREDICT would be honest-lookng f t dd not dffer from typcal predctons n CONTROL. To defne typcal, we must draw nferences from the emprcal predctons n CONTROL. The hghest probablty p max s crtcal for a predcton to appear honest because t determnes the hghest possble payoff. We examne the dstrbuton of p max, and fnd that 99th percentle s 50%; thus, the vast majorty of subjects (69 out of 70) n CONTROL stated 50% or less as the hghest probablty p max. Hence, ths emprcally determned 50% s used as the upper bound to defne typcal or honest-lookng predctons 18 ; we call a predcton honest-lookng f t assgns no more than 50% probablty to any sngle outcome of the de roll. Our frst hypothess concerns the preference for appearng honest, whch s made more salent n PREDICT than n the REPORT treatment, measured n our experments by the fracton of honest-lookng predctons. We predct that the PREDICT treatment has at least as many honest-lookng predctons as the REPORT treatment. Hypothess 1 (Preference for Appearng Honest). The fracton of honest-lookng predctons n PREDICT s greater than that n the REPORT treatment. Next, we predct that people cheat when they are gven opportuntes to do so, as n both REPORT and PREDICT treatments. We wll be able to draw nferences about cheatng n aggregate f subjects make statstcally more accurate predctons (and consequently hgher earnngs) than random chance. Hence, our second hypothess follows: Hypothess 2 (Preference for Beng Honest). Cheatng occurs when gven the opportunty. Fnally, we compare the level of cheatng between REPORT and PREDICT, and predct that cheatng s deterred n PREDICT compared to the REPORT treatment. One of the man reasons s that ndvduals n REPORT can more easly hde evdence that ther cheatng was premedtated. Hypothess 3 s summarzed as below, Hypothess 3 (Preference for Beng Honest). The level of cheatng n REPORT s greater than cheatng n PREDICT. 13 The payoff functon further demonstrates that PREDICT and REPORT are dentcal to those who do not value appearng honest: one ether cheats on or cheat on p, for any gven level of ntrnsc averson to lyng. 14 Scorng rules are not the only belef elctaton methods. Alternatve methods are more robust to rsk preferences have been proposed (see e.g., Karn, 2009) and assessed wthn populatons that nclude naïve respondents (Hao and Houser, 2012). 15 The other assumpton, the no-stakes condton, s not volated here, because subjects wealth outsde the laboratory experment s ndependent of the outcome of the de roll. 16 We thank Zachary Grossman for provdng us the orgnal verson of ths tool. 17 In the event of tes, there are multple hghest-payoff outcomes. 18 Ths threshold says that roughly 99% of the tme, a random draw from CONTROL s no greater than 50%. In the CONTROL treatment, the hghest predcton s 57%, whch s followed by two predctons at 50%, and qute a few predctons between 50% and 45%. Hence, 50% seems a natural focal pont that subjects n CONTROL were comfortable wth. The 95th percentle of the dstrbuton of p max n CONTROL s 48%. If we nstead use the 95th percentle to defne the upper bound of typcal or honest-lookng predctons, 90% of predctons n PREDICT were honest-lookng. More mportantly, usng 50% as the cutoff s supported by ndependent observers, as the majorty of our evaluators agree that 50% s the threshold for appearng dshonest (see more detals are n the result secton).
58 L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 5. Results A total of 255 subjects partcpated n our experment, ncludng 48 ndependent evaluators, and 70, 61 and 76 subjects n CONTROL, REPORT, and PREDICT, respectvely. Due to the nature of the experment, we do not, and wll never, know whether a partcular ndvdual cheated. However, we are able to make nferences about whether subjects n a treatment cheated at all by comparng ther de roll outcomes to the objectve dstrbuton from rollng a far de. We are also able to nfer whether subjects n one treatment cheated more than those n another treatment. Our results are organzed as follows. Before analyzng the man treatments, we frst show that evaluators perceve that behavor n PREDICT are more lkely to be dshonest than the same behavor n REPORT. Ths lends external support to the dfference n mantanng an honest appearance between the two treatments. For the man treatments, we measure the preference for appearng honest va subjects probablty predctons n PREDICT and REPORT aganst an honest-lookng predcton defned by predctons n CONTROL. We found that the fracton of honest-lookng predctons n REPORT s sgnfcantly hgher than CONTROL, whle they do not dffer between PREDICT and CONTROL. Then, we measure the preference for beng honest va the accuracy of subjects probablty predctons and subjects earnngs. Gven the opportunty to cheat, f subjects predctons about de rolls were sgnfcantly more accurate than those n CONTROL (whch mples hgher earnngs), we can conclude wth confdence that cheatng occurred. Indeed, we found a sgnfcant amount of cheatng occurred n both REPORT and PREDICT, and the level of cheatng s sgnfcantly hgher n REPORT than n PREDICT. Fnally, we defne three models of cheatng and estmate whch mxture of cheatng models best characterze our subject populaton va an adapted verson of El-Gamal and Grether s (1995) algorthm. 5.1. Perceptons of (ds-)honesty Ths subsecton reports 48 ndependent evaluators perceptons of the Decson Maker s (DM hereafter) honesty n the PREDICT and REPORT treatments. We frst conduct a consstency check for the evaluatons, focusng on two types of sgnfcant nconsstences: () statng that objectve predctons (p max = 25%) look dshonest; or () a hgher p max looks more honest than a lower p max. Eght subjects fall nto at least one of these two types, and thus are excluded from our analyss. 19 Before proceedng to the man results, we show that the evaluator group provdes external support to our earler noton (n Secton 4) that an honest-lookng predcton s hghest predcton p max does not exceed 50%. Fg. 2a summarzes drect percepton measure of cheatng, from evaluators answers n Decson Sets A and B (see nstructons for evaluators n Appendx A) on whether evaluators thnk the Decson Maker has cheated at each of the sx dfferent scenaros (=25%, 40%, 50%, 60%, 85%, or 100%). For example, n the scenaro where the DM predcted p max = 50% and chose the hghest outcome, 70% (28 out of 40) evaluators n PREDICT thnk the D p max M has cheated, and 60% (24 out of 40) evaluators thnk the DM cheated n REPORT. The percepton of cheatng at scenaro p max = 50% has a substantal ncrease from the scenaro p max = 40%, whch are 33% and 23% n PREDICT and REPORT, respectvely. Hence, p max = 50% seems to be an agreed-upon threshold where the majorty of the evaluators beleve that the DM appeared to have cheated, n both PREDICT and REPORT treatments. Fg. 2b reports comparatve percepton measure of cheatng, usng results from Decson Set C where evaluators compare scenaros wth dentcal p max between PREDICT and REPORT, and answer whether the two treatments are equally lkely to be dshonest; f not, whch one of the two s more lkely to be dshonest. The horzontal axs lsts all sx scenaros by ts p max. The whte bar (dotted bar) ndcates the number of evaluators who thnk the DM n PREDICT (REPORT) more lkely to have cheated than the DM n REPORT (PREDICT). The dark bar dsplays the number of evaluators who thnk the DM n the two treatments are equally lke to have cheated. Fg. 2b shows that n all scenaros, more evaluators consder actons n PREDICT more lkely to be dshonest than REPORT. Ths leads to Result 1. 5.1.1. Result 1. (Independent evaluatons) Sgnfcantly more evaluators consdered an dentcal acton n PREDICT more lkely to be dshonest than n REPORT. 5.1.2. Evdence Usng the comparatve measure of cheatng from evaluators, we conduct a more rgorous regresson analyss of evaluators opnons. We construct a varable ChosePREDICT, whch s 1 ( 1) f the evaluator chooses the PREDICT (REPORT) treatment more lkely to be dshonest, and 0 f the evaluator s ndfferent. Hence, f the mean of ChosePREDICT s greater (less) than zero, we can conclude that an dentcal acton n PREDICT (REPORT) s more lkely to be perceved as dshonest. To account 19 Our results reman largely the same f we do not exclude these 8 nconsstent subjects.
L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 59 Fg. 2. a. Drect percepton measure of cheatng (Evaluators Decson Sets A and B): fracton of evaluators who thnk the DM cheated n PREDICT/REPORT. b. Comparatve percepton measure of cheatng (Evaluator s Decson Set C): number of evaluators who consder behavor n PREDICT (REPORT) more lkely to be dshonest or ndfferent between the two (N = 40). Note: Each p max scenaro conssts of 40 decsons, one from each of the 40 evaluators. Take the scenaro of p max = 50% for example, 11 evaluators consder those n PREDICT are more lkely to have cheated, n contrast of 5 evaluators who beleved REPORT to be more lkely nvolvng cheatng. The rest 40 11 5 = 24 evaluators consder the two treatments to be equally lkely to have cheatng. for multple evaluatons from the same evaluator, we run the followng GLS regresson, clustered by ndvduals (evaluators). ChosePREDICT = + ε, whereεs..d. N (0, 1). The estmated ntercept s the mean of ChosePREDICT, after takng nto account that we have multple decsons from the same ndvdual. We fnd that ChosePREDICT s 0.0875 (robust standard error = 0.0391), sgnfcantly greater than 0 (p = 0.025, two-sded t-test). Hence, sgnfcantly more evaluators consdered behavor n the PREDICT treatment to be less honest-lookng than REPORT. 5.2. Preference for appearng honest Based on predctons n the CONTROL treatment and the evaluatons, a predcton s consdered honest-lookng f ts p max does not exceed 50%. Usng ths defnton, we compute the fracton of honest-lookng predctons n PREDICT and REPORT, and present our thrd result below. 5.2.1. Result 2. (Test of hypothess 1) The fracton of honest-lookng predctons n PREDICT treatment s sgnfcantly hgher than that n REPORT. 5.2.2. Evdence Fg. 3 plots the cumulatve dstrbuton of p max for all three treatments. The dstrbutons n PREDICT and REPORT treatments are sgnfcantly dfferent (p = 0.003, Kolmogorov-Smrnov test). The fracton of the honest-lookng predctons (.e.,
60 L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 Fg. 3. Cumulatve dstrbuton of predcton p max by treatment. Table 1 Summary statstcs: predctons. Number of observatons CONTROL (n = 70) PREDICT (n = 76) REPORT (n = 61) Fracton of objectve predctons 33% 32% 23% Max of p max 57% 88% 100% Mean (s.e.) of p max 34% (1.0%) 35% (1.4%) 51% (3.5%) Medan of p max 34% 32% 40% Note: Standard errors are n parenthess. probablty of p max 50%), s 95% (72 of 76) n PREDICT, and only 66% (40 of 61 subjects) n REPORT (p < 0.001, two-sded proporton test). The fracton of honest-lookng predctons n PREDICT suggests an almost unversal preference for appearng honest. However, n REPORT, where the ntenton revelaton was delayed, people responded to ths very subtle change by makng predctons that were much less honest-lookng. Ths allowed them a greater opportunty to cheat. Result 2 becomes more evdent as we take a closer look at the dstrbuton of the hghest probablty p max. In Fg. 3, the dstrbutons of p max of the PREDICT and the CONTROL treatments largely overlap wth each other, and both are domnated by p max of the REPORT treatment at every percentle. For example, at roughly 60th percentle, p max s 0.38 n both PREDICT and CONTROL, but 0.49 n REPORT. At 80th percentle, t s 0.40 n PREDICT and CONTROL, and a staggerng 0.86 n REPORT. Table 1 presents key summary statstcs of p max, whch ranges from 25% (n the event of objectve predctons) to 57% n CONTROL, 88% n PREDICT, and 100% n REPORT. It s worth notng that several subjects n REPORT adopted the proftmaxmzng strategy by predctng 100% on the sngle outcome that they later rolled, whle no one pursued ths strategy n PREDICT. About 33% of subjects n CONTROL made objectve predctons, whle only 23% of subjects n REPORT dd so. Interestngly, ths fracton n PREDICT rose to 32%, almost dentcal to the CONTROL treatment. 20 The central tendences are smlar, as the mean and medan n REPORT clearly stand above both PREDICT and CONTROL treatments, whle the latter two treatments are ndstngushable. 5.3. Preference for beng honest We examne the actualty of cheatng behavor va subjects predcton accuracy and earnngs. Gven that the dce are far, we can draw nferences about cheatng f subjects n one treatment make statstcally more accurate predctons (and consequently hgher earnngs) than subjects n another treatment. 21 5.3.1. Predcton accuracy To measure predcton accuracy, we focus on hghest-payoff outcomes and nvestgate whether they occur more often than what we expect from a far de. 22 Wth a far de, the expected frequency of a hghest-payoff outcome s 25% f p max 20 Incdentally, these numbers are also the ntercepts at hghest p max = 0.25 n Fg. 3. 21 PREDICT s the only treatment n whch subjects self-reported de roll outcomes, and we fnd that these self-reported outcomes margnally dffer from the unform dstrbuton (p = 0.10, ch-squared test). In contrast, de roll outcomes from CONTROL or REPORT do not dffer from the objectve dstrbuton (p = 0.42 and p = 0.60, respectvely, ch-squared test). 22 As objectve predctons yeld dentcal payoffs for all outcomes, they are excluded from ths analyss.
L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 61 Table 2 Expected and emprcal frequences of hghest-payoff outcomes (excludng objectve predctons). Hghest-payoff outcomes CONTROL (n = 47) PREDICT (n = 52) REPORT (n = 47) Expected Frequency 32% 30% 29% Emprcal Frequency 36% 71% 85% Expected vs. Emprcal p = 0.588 p < 0.001 p < 0.001 Notes: All p-values are obtaned va the proporton test (two-sded). Table 3 Earnngs. CONTROL (n = 70) PREDICT (n = 76) REPORT (n = 61) Mn $8.12 $6.25 $9.75 Max $20.81 $24.76 $25.00 Medan $15.63 $15.75 $18.15 Mean (Std. Err.) $15.26 ($0.30) $16.90 ($0.29) $19.15 ($0.52) Standard Devaton $ 2.53 $ 2.52 $ 4.04 Note: Standard errors are n parenthess. Fg. 4. Cumulatve dstrbuton of earnngs by treatment. s unque. When p max s not unque, we adjust the expected frequency by the number of tes. 23 As summarzed n Table 2, the expected frequency of hghest-payoff outcomes s 32%, 30% and 29% n CONTROL, PREDICT and REPORT, respectvely. They are very smlar to each other, and we fnd no statstcal dfference n any par-wse comparsons. Then, we compute the emprcal frequency that subjects actually obtaned hghest-payoff outcomes, whch s 36%, 71% and 85%, respectvely. The dfference between emprcal and expected frequences s sgnfcant n PREDICT and REPORT, but not n CONTROL. Ths contrast provdes strong evdence that people dd cheat n the two treatments when they had the opportunty to do so. The expected frequency of a hghest-payoff outcome accordng to a far de s 25% f a predcton has a unque hghest probablty p max ; otherwse, the expected frequency must be adjusted for tes at p max. For example, for the predcton [32%, 32%, 20%, 16%], the expected frequency of hghest-payoff outcomes s 50%. The emprcal frequency of hghest-payoff outcomes s the fracton of subjects who actually reported that they obtaned the hghest-payoff outcome n the second round. 5.3.2. Subjects earnngs Cheatng s also reflected by hgher earnngs. Recall that n PREDICT or REPORT, a proft-maxmzer could earn the maxmum proft of $25 by makng sure that the predcton and outcome matched perfectly. In CONTROL, however, subjects could only maxmze expected earnngs by submttng an objectve predcton (25% for each outcome), for a guaranteed proft of $15.63, regardless of the outcome. Table 3 summarzes what subjects actually earned n the experment. The maxmum earnngs are $25 n REPORT, $24.76 n PREDICT, and $20.81 n CONTROL. The medans are nearly dentcal between CONTROL and PREDICT, at $15.63 and $15.75, respectvely, and clearly hgher n REPORT, at $18.15. Fg. 4 shows ndvdual earnngs, sorted from the lowest to the hghest wthn each treatment. Comparng predcton accuracy and earnngs between treatments, we present Result 3 and Result 4 below. 5.3.3. Result 3. (Test of hypothess 2) Cheatng occurred n both PREDICT and REPORT where subjects made sgnfcantly ()more accurate predctons and () more money than those n CONTROL. 23 For example, f a subject predcts [32%, 32%, 20%, 16%], t s expected that the hghest-payoff outcome (ether 1 or 2) turns up wth probablty 50%. Hence, the expected frequency s 25% multpled by the number of tes at p max.
62 L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 5.3.3.1. Evdence (). The emprcal frequency of hghest-payoff outcomes subjects obtaned was sgnfcantly hgher than the expected frequency (adjusted by tes) n both PREDICT (71% vs. 30%, p < 0.001, two-sded proporton test) and REPORT (85% vs. 29%, p < 0.001, two-sded proporton test) treatments. By contrast, predctons n CONTROL were not more accurate than expected (36% vs. 32%, p = 0.588, two-sded proporton test). These results suggest that sgnfcant cheatng occurred n PREDICT and REPORT where subjects had the opportunty to do so. 5.3.3.2. Evdence (). Average earnngs n PREDICT were $16.90, sgnfcantly hgher than $15.26 n CONTROL (p < 0.01, twosded t-test). Average earnngs n REPORT were $19.15, sgnfcantly hgher than n CONTROL (p < 0.01, two-sded t-test) treatments. These results confrm Result 1, whch fnds that sgnfcant cheatng occurred n PREDICT and REPORT, where subjects had the opportunty to do so. 5.3.4. Result 4. (Test of hypothess 3) More cheatng occurred n REPORT than n PREDICT, as subjects made more accurate predctons n REPORT than those n PREDICT. 5.3.4.1. Evdence (). Subjects predctons n REPORT were more accurate than those n PREDICT (85% vs. 71%, p < 0.095, twosded proporton test), suggestng that more cheatng occurred n the REPORT treatment. Ths result holds despte the fact that the expected frequency n the REPORT treatment was slghtly lower than that of PREDICT,.e., 29% vs. 30%, respectvely. 5.3.4.2. Evdence (). Shown n Table 3, average earnngs n REPORT were sgnfcantly hgher than those n PREDICT, at $19.15 and $16.90, respectvely (p < 0.01, two-sded t-test). Fg. 4 shows that earnngs n REPORT are unformly greater than those n PREDICT, and earnngs n PREDICT agan greatly exceed those n CONTROL. 5.4. Incomplete cheatng In ths subsecton we nvestgate whether the ncomplete cheatng behavor reported n the lterature occurs as a result of ntrnsc preference for cheatng partally, or as a consequence of preservng an honest appearance. We frst defne a set of types, ncludng honest, ncomplete cheatng, and maxmum cheatng. We then econometrcally choose the optmal mxture from these pre-specfed types that best characterzes subjects decsons. If ncomplete cheatng s (not) ncluded n ths optmal mxture, we conclude that ncomplete cheatng s (not) an ntrnsc preference for beng honest. Before we proceed, we verfy the exstence of truth-tellers n the populaton. 5.4.1. Result 5: a sgnfcant number of people reported truthfully 5.4.1.1. Evdence. Frst, almost one thrd of subjects n PREDICT submtted objectve predctons, suggestng that many people follow the truth-tellng strategy. Moreover, seven out of the 52 non-objectve predctons reported outcomes correspondng to ther lowest payoff n the second stage (13.5%). 24 Ths result ndcates that these people are ntrnscally averse to cheatng even when not beng montored. Results 3 5 reveal that there exsts a mxture of types n our populaton: some people are truth-tellers, whle others are cheatng n some way: ether partally or maxmally, condtonal on one s own predcton. We defne these three types of ntrnsc preferences for honesty as: () truth-tellng ; () maxmum cheatng ; and () one-step cheatng. The truthtellng type descrbes dogmatc truth tellers who report truthfully regardless whether they have opportunty to cheat. The maxmum cheatng type characterzes people who suffer lttle psychc dsutlty from cheatng, and thus when gven the chance always pursue the maxmum proft among all possble outcomes based on ther own predctons. Fnally, the onestep cheatng type devates from truth-tellng, but only partally cheats by gong after the proft one level hgher than the true outcome, whch s not always the hghest payoff. 25 Type 1: (Truth-tellng): The subject truthfully reports the de roll outcome, whch follows the objectve unform dstrbuton. Type 2: (Maxmum cheatng): The subject reports an outcome correspondng to the hghest payoff based on her/hs predctons. Type 3: (One-step cheatng): Gven her/hs predctons, the subject reports the outcome that earns one level hgher than her/hs realzed outcome. In the event that s/he obtaned the hghest-payoff outcome, then the subject reports t truthfully. Note that we use the one-step cheatng type to model the ncomplete cheatng behavor as an ntrnsc preference not to devate too much from honesty (see e.g., Mazar et al., 2008; Lundqust et al., 2009). If people hold such preferences, then one-step cheatng would explan self-reported de rolls better than the maxmum cheatng type. 24 We adopt the common assumpton n the lterature that people would not cheat for worse outcomes. 25 The number of payoff levels n a predcton vares accordng to the number of tes. In partcular, the one-step cheatng type s dentcal to the maxmum cheatng type when there are only two payoff levels.
L. Hao, D. Houser / Journal of Economc Behavor & Organzaton 133 (2017) 52 73 63 Recall that the goal of ths analyss s to determne whch mxture of these three types best characterzes our subjects. As we have only one observaton per subject, our nferences are based on aggregates that can be analyzed usng a varant of the wdely-used El-Gamal and Grether (1995) algorthm (see, e.g., Anderson and Putterman, 2006; Holt, 1999; Houser and Wnter, 2004). Allowng an error rate ε that s the same for all subjects, we say that each subject follows hs/her decson rule (.e., type) wth probablty of 1 ε; wth probablty of ε, he/she trembles and reports all outcomes equally lkely. Importantly, our truth-tellng type also reports all outcomes equally lkely due to the fact that the objectve dstrbuton s unform. Ths mples two mportant features: () that the error rate ε s nterpreted as the fracton of truth-tellers n the populaton; and () that the truth-tellng type s mplctly bult nto each mxture. Before we specfy the components of the lkelhood functon, we defne the followng notatons. Let M denote the number of dstnct payoff levels gven by subject s predcton; rank all payoff levels from the lowest to hghest. Let t (j) { (where } M j 1,..., M ) be the number of tes at the jth lowest payoff level, so we have j=1 t(j) = 4 and that t (M ) s the number of tes at the hghest payoff level. The ndcator D (j) s 1 f subject s reported outcome corresponds to her jth lowest payoff level, and 0 otherwse; thus, we have M j=1 D(j) = 1 and that D (M ) ndcates whether subject s reported outcome corresponds to the hghest payoff. Consder frst the mxture of truth-tellng and maxmum cheatng types. Wth probablty 1- ε, a subject reports the hghest-payoff outcome ( maxmum cheatng ); wth probablty ε, he/she reports each of the four outcomes wth equal probablty of 25% ( truth-tellng ). Ths mples the followng lkelhood functon (adjusted for tes) for the mxture of maxmum cheatng and truth-tellng types. n ) n ( ) D (M ) = =1 ( L t (M ), D (M ) =1 1 ε + ε 4 t(m ) ( ε ) 1 D (M ) 4 (4 t (M ) ) Next, consder the one-step cheatng type, whch predcts that subjects report outcomes correspondng to the next hgher payoff level n relaton to ther realzed outcomes. In partcular, () the hghest-payoff outcome s reported wth the objectve probablty of obtanng the top two hghest payoff levels; () the lowest-payoff outcome s never reported; and () the ntermedate-payoff outcomes (whch exst when M > 2) are reported wth the objectve probablty of obtanng outcomes from the one-step lower payoff level. Adjustng for tes, we obtan the followng lkelhood functon for the mxture of one-step cheatng and truth-tellng : n ( L =1 t (j), D (j) n ((1 ε) t(m ) =1 ( ) n = (1 ε) t(j 1) 4 =1 n ε =1 4 t(1) fd (1) = 1 + t (M 1) 4 + ε 4 t(j) + ε 4 t(m ) ) f D (M ) = 1 ) fd (j) = 1 and 2 j M 1 Fnally, we consder the mxture of all three types, and obtan the lkelhood as follows. 1. For each ndvdual, calculate the lkelhoods for both mxtures: maxmum cheatng and truth-tellng and one-step cheatng and truth-tellng ; fnd the hghest lkelhood; and 2. Multply the obtaned hghest lkelhood across all n ndvduals, and fnd ts maxmum value by choosng the frequency of truth-tellng ε. To select among the three mxtures, we must nclude a penalty that ncreases wth k, the number of types n the mxture. Followng El-Gamal and Grether (1995, pp.1140 1141), our penalty s an unnformatve pror dstrbuton consstng of three parts. The frst term s the pror for havng k decson rules: 1. The second term s the pror for selectng any k tuple 2 k of decson rules out of the unverse of three decson rules: 1. The thrd term says that each ndvdual s assgned to one 3 k of the k decson rules ndependently, wth equal probablty : 1/k n. Hence, our posteror mode estmates are obtaned by maxmzng the followng: n ( ) log( maxl t (j), D (j) ) k log (2) k log (3) n log (k) =1 Table 4 reports the result of our analyss usng data from PREDICT and REPORT, and our fnal result follows. 5.4.2. Result 6: the mxture of maxmum cheatng and truth-tellng best characterzes subjects preference for beng honest