Lying to be Fair. Gönül Doğan and Rikstje Anneke Roggema. Abstract

Transcription

1 Lyng to be Far Gönül Doğan and Rkste Anneke Roggema Abstract We expermentally nvestgate whether lyng arses because people thnk others wll le. Subects answer questons that measure ther analytcal ablty. They are then nformed of the payoff scheme. We employ three payoff schemes (pece-rate, pe-sharng, tournament), and also change whether only one person n a par or both can le. Overall, we observe that a small mnorty of subects le. There s no lyng n the tournament. We fnd no effect of varyng who can le; there s no evdence for lyng to be far. We propose a model that captures that lyng can be used as a farness tool, and show that t can predct ntermedate levels of lyng even n a tournament payoff scheme. 1

2 1. Introducton In many real lfe stuatons, whether people behave honestly depends on ther belefs about how others behave. If a person expects dshonest behavour by many others, then honesty may not be perceved as the socal norm anymore and ths mght help lower the moral cost of cheatng. Consder tax evason. In countres wth hgh tax evason levels, people state government corrupton as one of the most mportant reasons that ustfy tax evason. Tax complance correlates postvely wth the strength of the perceved socal norm of tax complance. Also, acceptance atttudes towards tax evason correlate wth the number of tax evaders a person knows (see e.g. Wallschutzky, 1984; Becker et al. 1987; Wenzel, 2004). All of these fndngs pont to the fact that cheatng on taxes s easer when complance norm s broken. Cheatng can also serve as a tool for establshng the far outcome; that s, the outcome that would have been acheved f everyone were to be honest. Contnung wth the tax example, consder the effect of non-complance by a large group of people: Because the burden created by non-complers are substantal 1, tax evason can be seen as a way of off-settng the nustce done by other tax evaders. Therefore, people who would have honestly pad ther taxes f everyone were to be honest mght prefer cheatng on ther taxes when expectng others to cheat as well. The recent scandal n professonal cyclng consttute another good example of how cheatng can be used as a farness tool. When Lous Armstrong was convcted of cheatng, hs man lne of defence was that everyone else was dong t. In an ntervew, he sad that he dd not vew dopng as cheatng, but rather, as a level playng feld (Telegraph Sport, 2013). Thus, n professonal cyclng, not only the honesty norm was broken, but also, the only way a cyclst would have a chance of wnnng a competton was by cheatng. In ths paper, we study whether lyng s used as a tool for restorng the far outcome. We ntroduce a real effort task and gve some people the opportunty to le over ther outcome. The task conssts of answerng some analytcal questons. Partcpants are matched n a par. To fnd out whether cheatng takes place to restore equty, we vary who can le: In the one-party treatments only one person n the par can le, and n the two-party treatments both partes can le. If lyng serves as a farness tool,.e., f recprocty does ndeed play a role, then we should expect less lyng 1 Such a burden can ndeed be very large; the estmated effect of tax evason on ncome nequalty n 2005 n Greece was a 9.7 percent change n the Thel measure of the ncome dstrbuton mplyng huge costs on honest tax-payers (Matsagans and Flevotomou, 2010). 2

3 n the one-party treatments than n the two-party treatments. We mplement three payoff schemes that vary the effect of lyng on the fnal outcome. These are the pece-rate, tournament, and pe-sharng. In the pece-rate payoff, the only effect of one s lyng on the other s va the weakenng of the socal norm of honesty. In the tournament payoff, however, cheatng mght take place to restore the far outcome. Fnally, we ntroduce pe-sharng payoff n whch partes get a share of a fxed-szed pe accordng to the rato of ther declaratons. Pe-sharng gves lower ncentves for cheatng than both the pece-rate and the tournament. We fnd that overall, few people le, and maxmal lyng s rare. Most lyng occurs n the pece-rate and there s no evdence for lyng n the tournament. Contrary to what we expected, recprocty plays no role n lyng behavour. In our analytcal task, women perform worse than men, and they do le more, but only n the pece-rate. There s no evdence that women le n the tournament or pe-sharng. Men seem unresponsve to the payoff scheme. As our ndrect research questons, we further look nto the relatonshp between lyng behavour and subects belefs on farness and ther (ncentvsed) estmatons on the performance dstrbuton. Our results suggest that lyng behavour s not related to ablty, nor belefs on farness. We, however, fnd a relatonshp between a person s ablty and her estmaton of the ablty dstrbuton: Lower ablty people underestmate the ablty of others whereas hgher ablty people overestmate (the so-called Dunnng-Kruger effect). Our analyss also shows that farness consderatons are postvely correlated wth one s ablty: the hgher the ablty of a person, the more that person thnks t s far to dstrbute money unequally. Fnally, we ntroduce a model that ncorporates honesty as a socal norm whle allowng cheatng to work as a tool to mplement the far outcome. Our model deals wth the moral cost of dshonesty by makng devatons from the honest outcome costly regardless of the source of devaton. Therefore, n addton to the moral cost of one s own dshonesty, we allow for dsutlty from the others dshonesty even f one s payoff s not affected by t. Devatons from the honest outcome have a decreasng margnal cost. Thus, our model captures stuatons n whch a preference for honesty mght be overruled by the dspleasure of others cheatng and thereby lettng cheatng to serve as a level playng feld. We show that our model can predct ntermedate levels of lyng commonly observed n experments on decepton. 3

4 2. Lterature Ths paper contrbutes to the lteratures on cheatng and gender dfferences. We know from the growng expermental lterature on cheatng that people do have a preference for honesty, even at a cost to themselves. For example, Gneezy (2005) studed the effect of the absolute and relatve consequences of les on the partcpants propensty to le. In a two player cheap-talk senderrecever game, he vared the sze of the le by varyng the gans of both the sender and the recever. He found that people cared about the cost of ther les. Another common fndng s that most people le a lttle rather than maxmally n many dfferent type of experments (see e.g., Lundqust, Ellngsen, Grbbe and Johannsson, 2009; Erat and Gneezy, 2012; Fschbacher, and Heus, 2008; Gneezy, Rockenbach, and Serra-Garca, 2013) Recent work on the effect of competton on cheatng behavour provdes mxed results. Whereas some studes fnd hgher levels of cheatng wth competton (for status or money), other studes report no change. Schweren and Wechselbaumer (2010) conducted a computerzed maze solvng game comparng cheatng behavour n tournament and pece-rate payoff schemes. They found that percentage of subects nvolved n cheatng s about 40 rrespectve of the payoff scheme. Ths s however drven by gender dfferences n performance: Women cheated more under tournament and men less, but when performance was taken nto account, the gender dfferences dsappeared. They therefore concluded that low ablty drves cheatng under competton and gender plays no role. Belot and Schröder (2013) found a much lower rate of cheatng n ther condentfyng game (about 10 percent), and cheatng behavor was sgnfcantly hgher under tournament for a fxed prze compared to pece-rate and flat-rate payoff schemes. In Pascual- Ezama, Prelec, and Dunfeld (2013), subects were pad for fndng 10 nstances of two consecutve letters on a sheet wth a seemngly random sequence of letters. Apart from replcatng the orgnal Arely, Kamenca and Prelec (2008) study, they also employed a socal competton (announcement of the wnner to other subects) and economc competton (addtonal money for beng a wnner) treatments. They found more cheatng under both of the competton treatments. Ther desgn, however, does not allow for an estmaton of percentage of cheaters, nor the analyss of gender. Emprcal and expermental studes on sabotage n tournaments provde evdence for consderable sabotage actvtes, and the results on gender are mxed. Two notable studes looked at sabotage n tournaments emprcally. Garcano and Palacos-Huerta (2006) studed Spansh football league 4

5 games after a rule change by FIFA, and found that ncreased ncentves for wnnng led to hgher sabotage. Balafoutas, Lndner and Sutter, (2012) studed Judo fghts from two consecutve World Champonshps before and after a rule change that allowed for sabotage. They found a consderable ncrease n the use of sabotage. In the laboratory, Falk et al., (2008), Harbrng et al., (2007), and Harbrng and Irlenbusch (2008) studed Tullock contests wth sabotage, and found sabotage to be prevalent; n all of these studes, there was no real effort. Carpenter et al. (2010) studed sabotage wth a real effort experment: they asked subects to prepare letters and envelopes. They employed pece-rate and tournament schemes, and they also found substantal sabotage n the tournament regardless of gender. Charness, Masclet, and Vlleval (2013) also report more sabotage when competng for status regardless of gender whereas Dato, and Neken, (2014) fnd more sabotage and more cheatng n rank-order tournaments, and ther results are drven solely by men. Fnally, Rgdon and D Esterre (2012) let ther subects nflate ther own performance and also sabotage the other partcpant s performance. They found that people nflated ther own performance to some extent, but they were not wllng to sabotage the work of someone else. They dd not fnd an effect of competton for ether type of cheatng behavour. The mxed results of the effect of competton on cheatng mght stem from dfferent expectatons of what others would do n dfferent games. When the possblty of cheatng s obvous, and subects expectaton of cheatng s hgh, we would expect to see hgh levels of cheatng, whereas otherwse, we would expect to see lttle. In ths paper, our man contrbuton s to study exactly whether there s recprocal cheatng. For ths purpose, we control who can le n noncompettve and compettve payoff structures. To our knowledge, ths s the frst study n the lterature to nvestgate the possblty of cheatng as a farness tool. 3. Expermental desgn Procedures The experments were conducted at the Center for Research n Expermental Economcs and poltcal Decson Makng (CREED) of the Unversty of Amsterdam. Subects were recruted va the onlne recrutment system of CREED and were mostly undergraduates from a wde varety of maors. Each subect could partcpate n only one sesson, and all treatments were across subects,.e. n each sesson only one treatment was run. There were 7 treatments conducted across 24 5

6 sessons wth 472 students from dfferent dscplnes. The experments lasted about one hour ncludng the tme spent on payment. Average pay was 10,7 euros ncludng 3 euros show-up fee. At the begnnng of the experment, nstructons are read out loud. In each sesson, partcpants are randomly assgned to one of three player labels: Player A, B or C. Subects are told that there are two parts n the experment, and ther payment n the experment s based on the task that they do n the frst part. Further, they are nformed that the determnaton of ther payment s conducted n the second part. The task nvolves 14 questons, and all subects are gven 10 mnutes to note ther answers on the answer sheet 2. A and B players are randomly matched for the payment of the task, and the C players correct the answer sheets. A and B players are told that the task forms the bass of ther payment and that they should note as many correct answers as possble. Snce they are not told about the payoff scheme untl after they fnsh answerng the questons, we do not expect to have any treatment effects on the real performance of our subects. After fnshng the task, all player As and Bs are nstructed to put ther answer sheets blank page facng up, and an expermenter collects the answer sheets. There are no dentfers n the answer sheets, and the only way we keep track of whch answer sheet belongs to whch table s va the order of collecton. The answer sheets are gven to the randomly assgned C players. Player C s are nstructed to hghlght the correct answers wth a hghlghter. We made sure that the answer sheets are corrected n that same order. The payment of C players are done by randomly pckng one of the corrected answer sheets, and controllng whether the correcton s fully correct. If the hghlghted answers are correct, the C player earns 10 euros, otherwse nothng. C players can take as much tme as they wsh to make the correctons. After C players correct the answer sheets, the answer sheets are dstrbuted back to A and B players, agan blank page facng up. We explaned ths procedure n detal n the nstructons. After the players A and B receve ther corrected answer sheets, the nstructons for the second part of the experment are dstrbuted and then read out loud. In ths part, the payment of A and B players s determned. After the payoff scheme s explaned, subects are told who wll receve a declaraton form (only A players n the one-party treatments or both A and B players n the two- 2 We employed a real effort task because whether money s earned by puttng n effort or by a random devce makes a dfference n other experments. Hoffman et. Al (1992, p. 370) state that there s a dfference n generosty n whether a player gets assgned the role of dvder or earn ther rght to be so. Ruffle (1998) states that there s also a dfference n the behavour of the proposer n a dctator and ultmatum game when the recever has performed a task to earn the sze of the surplus that s to be dvded. 6

7 party treatments), and that the declaraton forms wll be used by the expermenters to calculate ther payment. Smlar to the frst part, all forms are collected blank page facng up such that the expermenter does not see what s declared, and transferred to another expermenter who s not nvolved n the runnng of the experment to calculate the payoffs and subects know ths-. Fnally, the answer sheets of all players are handed back to C players for all answers to be hghlghted. Ths was to mnmze the rsk of cheatng across sessons by usng the rght answers from subects of prevous sessons. Fnally, the declaraton forms and the answer sheets are returned to the subects. Subects are told that they can keep the declaraton forms and the answer sheets. After the experment s fnshed, subects are asked to fll n a questonnare statng ther gender, studes, the number of experments they partcpated n that academc year, the number of tmes they took a GRE/GMAT type of test, ther belefs on the dstrbuton of correct answers, ther guess of the average correct answer, and how they thnk some money should be dvded between a par under dfferent combnatons of correct answers. To elct the A and B players belefs on the dstrbuton of correct answers, they were told that a certan number of people have done the task before 3, and they were asked to guess how many of those subects have answered 0, 1, 2, 14 correct answers. They could earn an addtonal 6 Euros f ther guesses matched that of the real dstrbuton, and otherwse every dfference cost them 50 Eurocents. Payment Structures We mplemented three dfferent payoff structures that vary the effect of lyng. These payoff structures are depcted across the three rows of Table 1. To study the effect of recprocty n lyng, we vared who can le. In one case, only one player n the par could le, and n the other both players could le. These are depcted n the columns of Table 1. As a baselne, pece-rate payoff s mplemented: each correct answer gves 1.5 Euros. In the pecerate, the les of one party do not harm the other party, and the beneft of each le s constant. We further vared whether only one person can le or both partes can le n the pece-rate. The payoff structures of the two treatments are depcted n the second row of Table 1. 3 We ncreased ths number n the later expermental sessons n accordance wth the ncreasng number of observatons we had for the correct answers. The ratonale for such a change was to correct for the small sample sze errors. All results reported n ths paper are standardzed and take ratos nto account. 7

8 In the pe treatments, players earned a porton of a fxed amount of money accordng to the rato of ther own declaraton to the total declaraton wthn the par. We chose 15 Euros as the fxed amount based on the results of our plot whch showed approxmately fve correct answers per person 4. We then multpled fve answers by the pece-rate payoff of 1.5 Euros for two persons. In the pe treatment, lyng ncreases one s payoffs at a cost to the other, and the beneft from each le and the cost to the other party s the same. However, the margnal cost of a le to the other party s decreasng n the number of les. The pe payoff structure s summarzed n the thrd row of Table 1. Fnally, the thrd payoff structure s the tournament as commonly mplemented n the lterature, and s depcted n the fourth row of Table 1. In the tournament, the party wth the hgher number of correct answers becomes the wnner, and earns 3 Euros per correct answer whereas the one wth the lower number of correct answers earns nothng. The multpler of three s chosen to equalze the expected payoff of the persons n the medan of the correct answer dstrbuton to that of the pece-rate 5. Unlke the pe treatment, n the tournament, the beneft of a le and ts cost to the other party s dscontnuous. As long as one s declaraton s lower than the matched partner s declaraton, lyng has no benefts nor has any costs. If lyng changes the wnner, then the cost to the other party s qute hgh (1.5 Euros tmes the other s declaraton), but t also gves a hgh beneft of 3 Euros per declaraton. Lastly, f the losng party te-breaks by lyng, ts cost to the other party s equal to ts beneft (1.5 Euros tmes the declaraton). Overall, we conecture that there wll more lyng n the two-party treatments compared to oneparty treatments. That s because, f our premse of lyng as a farness tool s correct, and f subects do antcpate lyng by the other party, then they could also le wthout much moral cost. In the tournament payoff scheme, t goes one step further: f a person thnks that she should be the rghtful wnner, but also antcpates a lot of lyng from the other party, then she mght le to wn. Therefore, we expect most lyng to be n the tournament, and the least n the pe payoff scheme. 4 As t wll be explaned n the results secton, the true average turned out to be 3.61 correct answers nstead of 5. Ths makes the stakes wth the pe sze 15 Euros somewhat hgher than that of pece-rate. 5 Ths expectaton s condtonal on the matched partner beng honest, and the persons n the medan of the dstrbuton correctly belevng that they are n the medan of the answer dstrbuton. Whenever there s varaton n the outcome of a task across dfferent persons, tournament cannot gve the same expected payoff as n pece-rate for all person s nvolved. Snce n ths study we are nterested n the effect of dfferent payoff schemes on lyng, such a dfference s of no prmary concern for us. 8

9 Table 1 : Payment Structure n Dfferent Treatments One-party (OP) Two-party (TP) Pece rate P A = 1.5 Clam A P B = 1.5 Real B P A = 1.5 Clam A P B = 1.5 Clam B Pe Tournament Clam A P A = 15 Clam A + Real B Real B P B = 15 Clam A + Real B P wnner = 3 Clam(Real) Wnner P loser = 0 P te break = 1.5 Clam Clam A P A = 15 Clam A + Clam B Clam B P A = 15 Clam A + Clam B P wnner = 3 Clam Wnner P loser = 0 P te break = 1.5 Clam 4. Results The performance of subects who cannot le s depcted n Table 2. Wth no lyng, the average number of correct answers s The dsperson of the performance s rather hgh, wth a standard devaton of We can see from the frequency dstrbuton that about 85 percent of the correct answers are less than or equal to 5. The medan of the dstrbuton s 4 correct answers. The mode of the dstrbuton s fve; almost one ffth of the subects had fve correct answers. Notce that there s only one person out of 152 subects who dd nne correct, and no one solved more than nne questons correctly. Table 2. Dstrbuton of correct answers wthout lyng Correct Answers Percentage of Subects Average=3.61, Standard Devaton= 2.03, N=152 Table 3 depcts the average declaratons per treatment. The type of competton s lsted n rows, and who can le n the columns. The comparson of the declaratons of each treatment wth the no-le condton s stated below the correspondng treatment values. The last column compares the column treatments. All p-values are when usng one-sded Mann-Whtney exact test. 9

10 Table 3 Declaratons per treatment No-Le 3.61 (2.03) N=152 One-Party Two-Party p* Pece-rate 4.90 (2.90) 5.11 (3.65) N=41 N=38 p= p=0.017 Pe 4.23 (3.53) 4.81 (2.83) N=40 N=42 p= p=0.012 Tournament 4.26 (2.84) 3.84 (3.02) N=42 N=38 p=0.110 p=0.355 *Mann-Whtney exact test, one-taled. A frst observaton s that overall, there s very lttle lyng. Most lyng happens n the pece-rate, and even then, the average amount of les are approxmately 1.40 correct answers. Gven that there were 14 questons, the amount of les are about 14 percent of the total possblty. Furthermore, the declaratons n the tournament treatment as well as the pe treatment wth only one party lyng are not sgnfcantly dfferent than no-le condton. Lyng n the pe treatment only happens when both partes can le, and the average declaraton s 1.20 unts hgher than the No-le condton. When we look at the effect of recprocty, we conclude that n none of the payment schemes, recprocty plays a role. Moreover, n the tournament treatment, the effect s n the opposte drecton than expected. Moreover, we do not fnd any support for our conecture that there wll be more lyng n the twoparty treatments of tournament and pece-rate. There s weak support for more lyng wth twoparty n the pe payoff scheme. The comparson of the declaratons across the payoff schemes reect our second conecture: Tournament has the lowest level of les (statstcally ndstngushable from the No-le condton) whereas pece-rate has the hghest. Furthermore, the dfference between pe and tournament s not sgnfcant. We wll provde further support for these results n the next secton. Fnally, we can try to estmate the percentage of lyng across dfferent treatments. Although our desgn does not let us know the exact amount of les, we can nfer from the No-le dstrbuton that 10

11 any declaraton that s 9 or hgher s almost surely a le. Ths gves a lower bound on the percentage of lars. In Table 4, we report the number of persons who declared a number between 9 and 14 n each treatment and the cumulatve percentage of those people. One can see that the hghest percentage of lyng s n the Pe Two-Party treatment wth 14.3 percent, and the lowest s n the one-party tournament treatment wth only 1 person out of 42. If we leave out these persons who declared 9 or hgher, and repeat the statstcal test on the comparson of each treatment wth the No-Le treatment, we see that none of the treatments turn out to be statstcally sgnfcantly dfferent than the No-Le treatment 6. Such a result mples that lyng wth lower declaratons are at most n very few cases, therefore we can conclude that percentage of lars are close the cumulatve percentages reported n Table 4. Table 4. Frequency of declarng 9 or hgher Cumulatve Percent No-Le N= Pece-rate One-Party N= Pece-rate Two-Party N= Pe One-Party N= Pe Two-Party N= Tournament One-Party N= Tournament Two-Party N= Gender Results We frst look at whether there s a performance dfference between the genders. The averages per gender n the no-le condton are reported n Table 5. Snce there was a mstake wth labellng the questonnares n one of our sessons, we have n total 122 observatons for gender. We can see that women perform sgnfcantly worse than men and the dfference s about 0.9 questons. 6 The relevant p-values from the comparson wth the No-le treatment wth one-sded Mann-Whtney exact test whle excludng declaratons 9 or hgher are as follows: Pece-Rate One-Party, 0.102; Pece-Rate Two-Party, 0.164; Pe One- Party, 0.332; Pe Two-Party, 0.167; Tournament One-Party, 0.141; Tournament Two-Party,

12 Table 5. Averages per gender n the No-Le condton Average 3.61 (2.03) N=152 Females 3.12 N=60 Males 4.01 N=62 Two-taled Mann-Whtney exact test p=0.005 To nvestgate whether women and men behave dfferently under dfferent payment schemes, we run a lnear regresson to explan the dfference between a person s outcome from the average n the No-Le condton of hs or her gender controllng for gender, payment scheme and the nteracton effects. Ths way, we can solely focus on the devatons from the average n the No-le treatment. Thus, the regresson s as follows: Declaraton AvgNoLe gender() = α + βgender + γpece + δpe + ηrecprocty + θinteracton Terms + ε If people of dfferent genders le sgnfcantly dfferently, then we expect to see the gender varable to have a sgnfcant effect. Moreover, f dfferent genders behave dfferently under dfferent schemes, we expect to see the nteracton effect of the treatment wth gender to be sgnfcant. Table 6 reports the results of the regresson that ncludes (Model I) and excludes recprocty (Model II). The frst column n the table depcts the varable name, the estmated coeffcent and the sgnfcance results of each model are below the models. Notce that ths specfcaton results n all comparsons beng made wth the tournament. The regresson ncludng recprocty terms (Model I) shows no sgnfcant effect of any of the varables, not even the ntercept that establshes that there s lyng. Droppng the recprocty terms gves us Model II. We can then see that wthout the recprocty terms, lyng becomes margnally sgnfcant (ntercept p-value=0.072), and there s no effect of the type of competton nor gender. The only weak effect comes from the fact that women le more n the pece-rate than men (p=0.082). Fnally, to clarfy how lyng depends on gender, we nclude the averages wth respect to men and women usng the pooled data for each payoff scheme n Table 7. We also report the relevant twosded Mann-Whtney exact test results. We can see that whle men are unresponsve to the payoff scheme and le about the same rate n all treatments, women only le n the pece-rate. 12

13 Table 6. Regresson Results Model I Model II Coeffcent Std. Error Sg Coeffcent Std. Error Sg Intercept Female Pece-Rate Pe Recprocty Female x Pece-Rate Female x Pe Female x Recprocty Pece-Rate x Recprocty Pe x Recprocty Female x Pece-Rate x Recprocty Female x Pe x Recprocty R 2 =0.029 R 2 =0.022 Table 7. Gender averages per payoff scheme Female Male p* Pece-rate 5.10 (3.36) 4.74 (2.90) N=21 N=31 Pe 3.92 (2.92) 5.09 (3.34) N=37 N=44 Tournament 3.44 (2.37) N= (3.30) N= * Two-sded Mann-Whtney exact test 5. Belefs: We elcted two types of belefs after the experment: belefs about farness and belefs about the dstrbuton of correct answers. To elct the subects farness deas, we asked how a fxed amount of money (15 Euros) should be dstrbuted wthn a par assumng dfferent combnatons of correct answers. In total they were asked to state 12 choces wth the followng correct answers wthn a par: (14,0), (12,2), (10,4), (8,6), (7,7), (14,7), (6,5), (6,4), (6,3), (6,2), (6,1), (6,0). Snce there s almost no varaton n the subects choces for (7,7) 7, t s dropped from our subsequent analyss. To elct the subects belefs about the dstrbuton of correct answers, we asked them to guess 7 The reason that we ncluded (7,7) was to capture concave preferences that value an extreme dstrbuton over an equal one. We dd not fnd any evdence for such preferences. 13

14 the average number of correct answers. Addtonally, we asked them to estmate how many subects answered 0 queston correctly, 1 queston correctly,, 14 questons correctly. We ncentvzed the answers by payng 6 Euros for a fully correct estmaton wth 50 eurocents reducton per devaton. If there were 12 or more dfferences, the earnngs were zero. We standardzed ther answers to ratos. By lookng at the subects answers, we can also calculate the average of the dstrbuton they guessed. We also report the dfference between the estmated dstrbuton average and ther guessed average. The mean and the standard devaton of all the varables are ncluded n the Table 8. We exclude the far dvson (7,7) and the dfference between the averages from further analyss, and are therefore left wth 28 varables. These varables are hghly correlated wth one another n a specfc pattern. As can be expected, the results on the far dvson of the pe and the guesses of the dstrbuton of correct answers are not correlated. The far dvson answers hghly correlate wth each other, and the dstrbuton of correct answers hghly correlate wth each other and wth the guessed average. Ths leaves room for factor analyss so that we can reduce the number of varables n a way that explans the most varance. The rotated matrx of the factor analyss s reported n the Appendx. The results of the factor analyss shows that there are ndeed two blocks of varables whch are hghly correlated wth one another. The resultng number of factors are sx; four varables mostly consst of the estmaton of the dstrbuton of correct answers and the averages, and the other two varables are about the dvson of money. We also run non-parametrc Mann-Whtney exact tests to compare the dstrbuton of the varables as well as the resultng factors between each treatment and the No-le condton. We do not fnd any sgnfcant dfference n the dstrbutons of factors, nor varables, and thus, we conclude that there s no sgnfcant dfference n the questonnare answers across dfferent treatments 8. The frst, thrd, ffth and sxth factors are derved from the estmatons of the dstrbuton. Followng the lterature, we focus only on varables wth correlaton levels larger than 0.30 n absolute value. The contrbuton of the averages (both the guessed, and derved from the 8 Gven that there are 28 varables per treatment, there are 168 comparsons n total, therefore the threshold for sgnfcance have to be adusted by 1/168 (Bonferron adustment). Ths s necessary to rule out fndng sgnfcance due to a large number of tests. Wth the usual p-level of 0.05, 11 of these comparsons show up as sgnfcant, but none of them survve the adusted threshold. 14

15 dstrbuton) to the frst factor are very hghly postve. The rato of persons who had 0, 1, 2,3 or 4 correct answers have a negatve relatonshp whereas the rato of persons wth 6, 7,, 11 correct answers are postve. Notce that the subects thnk that the average correct answers are about fve (whereas the real average s 3.61). Ths also explans why the rato of persons below fve has a negatve effect on ths factor whereas the rato of persons larger than fve has a postve effect. Table 8. Averages of farness answers and estmated dstrbuton Farness Answers N Mean (Std Dev) Dvson 14, (2.05) Dvson 12, (1.74) Dvson 10, (1.46) Dvson 8, (1.25) Dvson 7, (0.45) Dvson 14, (1.46) Dvson 6, (3.89) Dvson 6, (1.29) Dvson 6, (1.38) Dvson 6, (1.63) Dvson 6, (1.87) Dvson 6, (2.53) Estmated Dstrbuton N Mean (Std Dev) Average Correct Answers (1.69) Percentage of 0 correct (0.07) Percentage of 1 correct (0.08) Percentage of 2 correct (0.08) Percentage of 3 correct (0.09) Percentage of 4 correct (0.08) Percentage of 5 correct (0.09) Percentage of 6 correct (0.08) Percentage of 7 correct (0.07) Percentage of 8 correct (0.05) Percentage of 9 correct (0.04) Percentage of 10 correct (0.03) Percentage of 11 correct (0.02) Percentage of 12 correct (0.02) Percentage of 13 correct (0.02) Percentage of 14 correct (0.02) Average from Estmaton (1.53) 15

16 Dfference between Avg s (1.21) The thrd factor s a combnaton of average and the derved averages as well as the ratos of persons who declare 9 or hgher. The ffth factor s a combnaton of the guesses of 0 and 1 correct answers (negatve correlaton) and 4 and 5 correct answers (postve correlaton). Notce that the cut-off from negatve to postve correlaton s dfferent n the ffth factor than n the frst factor provdng evdence for two dfferent types of people: The frst type guesses about fve correct answers, and ths s the maorty. The second type guesses about three correct answers. Fnally, the last factor s a combnaton of the guesses to 2 and 5 correct answers. The second and fourth factors are related to the answers to the far dvson questons. The dvson of (14,0), (12,2), (10,4), (6,4), (6,3), (6,2), (6,1), and (6,0) correlate hghly postvely wth the second factor. Answers to the dvson of (10,4), (8,6), (14,7), (6,5), (6,4), (6,3), and (6,2) are postvely correlated wth the fourth factor. These two factors together mply two types of answers that are somewhat dstnct from one another. Keep n mnd that the contrbuton of the second factor s much more than the contrbuton of the fourth factor. Usng these factors, we can study the relatonshp between declaratons and estmated ablty dstrbuton as well as the relatonshp between ablty and farness consderatons. We know from the Dunnng Kruger effect (Dunnng and Kruger, 1999; Schlösser, Dunnng, Johnsonand Kruger, 2013) that people tend to thnk others are lke them when udgng the ablty dstrbuton. Thus, low ablty people underestmate the ablty of others whereas hgh ablty people overestmate the ablty of others. If such an effect exsts n our experment, then we would expect to see a postve effect of the factors 1, 3, and 5. The second relatonshp that we can nvestgate s the one between perceptons of farness and ablty. There s some research that study whether farness consderatons take effort nto account (see for example Almås, Cappelen, Sørensen, and Tungodden, 2010; Cappelen, Hole, Sørensen, and Tungodden, 2007) however to our knowledge there s no study that nvestgates whether ablty and farness consderatons are correlated. We expect hgher ablty people to thnk that hgher ablty people should get a large share of the pe whereas low ablty people to opt for a farer share of the pe. If our premse s correct, we would expect to have a postve effect of the factors 2 and 4. 16

17 Table 9 depcts the regresson results usng the varables derved from factor analyss. The dependent varable s, as n the prevous regressons, the dfference between one s performance and the mean of hs or her gender n the No-Le condton. The control varables are the sx factors, gender, treatment, and gender and treatment nteracton effect. Note that the magntude of the factored varables are not easy to nterpret, therefore we wll only focus on the sgn of the estmated coeffcents. We can see from Table 9 that the ncluson of the sx factors help explan a substantal amount of varance n the ndependent varable (the dfference between a person s declaraton and the average correct answers for that gender), and the R 2 ncreases from to Among the sx factors, the frst, second and the ffth have a sgnfcantly postve effect on the dfference of the declaratons from the baselne. Table 9. Regressons results usng factors Varable Coeffcent Std. Error Sgnfcance Intercept Factor Factor Factor Factor Factor Factor Female Pece-Rate Pe Female*Pece-Rate Female*Pe R 2 =

18 The estmated rato of the persons n the populaton wth 0, 1, 2, 3, 4 correct answers correlates negatvely wth Factor 1, whereas the rato of the persons wth 6, 7,..11 correct answers correlate postvely. Thus, the postve coeffcent of the frst factor n the regresson tells us that people who declare hgher than the real average of 3.6 guess a dstrbuton to the rght of the average estmated dstrbuton (centered at 5 correct answers), and persons who guess a dstrbuton to the left of the average estmated dstrbuton declare lower than the real average. To put t dfferently, any person who thnks most others dd four or fewer correct answers declares less than 3.6, and any person who thnks that most others dd sx or more declares more than 3.6. Ths ponts to possbly two dstnct bases: a general overestmaton of the populaton ablty, and a bas n the udgment of performance of others n the drecton of one s own performance. However, the regresson n Table 9 alone cannot tell us whether the latter bas s related to lyng or only stems from the msudgement of other s ablty. We wll further analyze ths n the next subsecton. Factor 5 also has a sgnfcantly postve effect. Remember that ths factor s related to the guesses of 0 and 1 correct answers (negatve correlaton) and 4 and 5 correct answers (postve correlaton pontng to a dfferent type of partcpant than the one captured by Factor 1. Ths second type guesses about three correct answers, and they are closer to the real dstrbuton of the populaton. However, the bas wth respect to the udgment of others performance beng close to one s own performance (Dunnng-Kruger effect) remans. Answers to the far dstrbuton questons also matter. The effect of the second factor s sgnfcantly postve. Ths factor s manly drven by the answers to how to dstrbute 15 Euros when a par of players have (14,0), (12,2), (10,4), (6,4), (6,3), (6,2), (6,1), (6,0) correct answers. Snce the effect of the factor s postve, there s evdence that people wth hgher declaratons thnk people wth hgher declaratons should earn more. We wll further nvestgate whether there s any systematc dfference n the farness factor wth or wthout lyng. Fnally, we can confrm from ths regresson that there s no systematc sgnfcant effect of gender n the amount of les nor the type of competton except n the pece-rate. Relatonshp between belefs, farness and lyng: If lyng s not dependent on ablty, then we would expect everyone to le about the same rate, and the Dunnng-Kruger effect would be observed rrespectve of whether the observatons come from 18

19 the No-Le treatment or lyng treatments. It s however, possble that low and hgh ablty people le at dfferent rates. The regresson n Table 9 cannot say whether that s the case. Smlarly, f there s a correlaton between what one consders far and the rate of lyng, we would not be able to capture that effect wth the prevous regresson. To test whether lyng s dependent on ablty or s correlated wth farness atttudes, we frst run separate lnear regressons wth all the factors wth the No-Le and le treatments. The No-Le treatment gves us the populaton estmates. Any dfference n the estmated coeffcents between the No-Le treatment and the le treatments standardzed wth the estmated standard errors s approxmately dstrbuted wth a t-dstrbuton 9. We can thus test whether lyng or the possblty thereof- changes the perceptons of what s far 10. Table 10. Separate Lnear Regressons No-Le Le Coeffcent Std. Error p B Std. Error p Constant Factor Factor Factor Factor Factor Factor Male N=115, R 2 =0.465 N=200, R 2 =0.188 From Table 10, we can see that most of the estmated coeffcents n both the No-Le and le treatments are smlar. Among the sx factors, only the thrd factor s sgnfcantly dfferent n the 9 Formally, f the estmated coeffcent s β and the standard error s σ from the Le treatments, and the estmated coeffcent s β from the No-Le treatment, then (β β) σ s dstrbuted wth a t-dstrbuton wth (Number of observatons-number of varables-1) degrees of freedom. 10 Notce that we coded only the scores of the hgher performer; the other person s payoff was 15-ths score by constructon. Therefore, we would expect to see at least half the share of the payoff for the hgher performer n all our answers. 19

20 two condtons wth a two-sded t-test p= Snce ths thrd factor s drven by the estmated ratos of persons who declare 9 or hgher, there s evdence that people who estmate a relatvely hgh percentage of hgh declaratons declare hgh values themselves only n the lyng treatments. Ths suggests that lars thnk that others dd qute well. However, t s mportant to note that none of the factors that sgnfcantly contrbuted to explanng the varance n declaratons have a sgnfcantly dfferent coeffcent n the No-Le and le treatments. Therefore, we can conclude that low and hgh ablty people do not le at dfferent rates and there s no correlaton between what s consdered far and the rate of lyng. 6. A Model of Lyng We would lke to have a model that ntroduces dsutlty from lyng because lyng changes payoff outcomes, but not because honesty s a rgd moral norm from whch devaton s costly 11. Such a model should thus take nto account how much the fnal outcome changes compared to the honest outcome when one les. Thus, lyng s costly whenever t changes the fnal outcome, and ts cost s ncreasng n the amount of change t nduces. If lyng changes the fnal outcome a lot compared to the honest outcome, then t ntroduces a large cost, whereas f lyng does not change the fnal outcome, t does not have a cost. Ths way, we can focus on the effect of les rather than the magntude. Suppose by lyng only a small amount, a person can change the whole dstrbuton of payoffs wthn a group of people, we expect that such a le s unlkely wth even low le-averson levels because of ts large effect n the group. A model that only takes nto account the magntude of les would however would predct otherwse. We would further lke our model to ncorporate the possblty of lyng to serve as a level playng feld. We therefore suggest that the dsutlty of lyng s decreasng n the other person s le. Consder otherwse: If one s lyng decson s ndependent of the other person s lyng level, then the optmal level of lyng would only be drven by the comparson of ts payoff benefts to ts moral cost. Ths would then mean that an honest person s honest, and a lar s lyng regardless of how many other people are lyng as long as they are not affected by others les. We, however, know from the large lterature n psychology on conformty -startng wth the Asch conformty 11 It s possble that for some people lyng s costly regardless of ts consequences, however, we suspect that ths s a mnorty of the people. Ths premse s not wthout support: Recently emergng lterature on moral behavor suggest that only a few people are Kantans who strctly adhere to a moral norm. See for example the work by Falk and Szech (2013). 20

21 experments- that people adhere by the norms of a group and tend to behave lke others. Therefore, there s no reason to expect one s honesty norm not to conform to the group. Addtonally, as ponted out n the ntroducton, a varety of studes as well as routne declaratons by professonal sportsmen show that cheatng correlates wth the amount of (expected) cheatng by others. To sum up, we would lke to have a model that compares the monetary beneft of lyng to ts cost where the cost s measured by the amount of devaton from the honest outcome. We propose the followng utlty functon n a two persons game to capture both of these aspects: U ( l / x, y, l ) = π ( x + l, y + l ) µπ( x + l, y + l ) π( x, y ), n whch (x,y ) denotes the honest outcome of person and, respectvely; x +l s the declaraton of person, and y +l s the declaraton of person. π ( x + l, y + l ) denotes the payoff when ( x + l, y + l ) s declared. µ s the dsutlty parameter and measures the cost of a unt devaton from the honest outcome. We assume that µ s constant 12. π ( x + l, y + l ) π ( x, y ) s the Eucldan dstance of the declared payoff from the honest payoff. Ths dstance, together wth µ, determnes the dsutlty of lyng by takng nto account the les of both partes nvolved n a par. Notce that, snce the dstance s appled to the dfference n payoffs, not to les, changng the payoff functon also changes the shape of the dsutlty term. Regardless, ths utlty functon captures lyng as a farness tool: f a person suspects that the other les a lot, the dsutlty of a unt of le s smaller than the dsutlty of a le f the other person does not le. Moreover, f lyng helps the person get closer to the far outcome, lyng would only be benefcal because t would reduce the cost of devaton from the far outcome. Thus, such a model can explan everybody else was dong t argument n tournaments. Below we report the optmal strateges by applyng ths utlty functon to the dfferent payoff schemes reported n ths paper. To make exposton smpler, we use the word ntermedate levels when referrng to stuatons wth at least one person has an optmal strategy that s not maxmal lyng wthn a sub-range of the specfed le-averson parameter. Ths defer all calculatons of Nash equlbrum wth any possble combnaton of µ levels wthn the par to Appendx A. Snce, the utlty functon s constructed n such a way that lowers the cost of a le when expectng the other 12 A more realstc model would let µ also depend on the level of les, but the essence of our arguments can be captured wth the smpler model assumng µ s constant. 21

22 one to le, all two-party treatments should gve at least as much lyng as one-party treatments. Below, we focus only on two-party predctons. In the pece-rate payoff scheme, f the other party cannot le, lyng becomes a bnary decson: f the dsutlty from a unt of le s hgher than ts utlty ( µ > 1), then there s no lyng, otherwse ( µ < 1), there s maxmal lyng. If the other party can le, however, the dsutlty of devaton from the honest outcome mght lead a le-averse 13 player towards lyng. The optmal level of lyng depends on how much the other party les as well as the level of le-averson. Even wth moderate levels of le-averson (1< µ < 2), any level of les can be supported n equlbrum. In the pe payoff scheme, f we assume players have the same le averson level µ, lyng does not depend on whether the other party can le or not; the only determnant of the amount of les s the magntude of the le-averson parameter µ: If the dsutlty from a unt of le s hgher than ts utlty ( µ > 1/ 2 ), then there s no lyng, otherwse ( µ < 1/ 2 ), there s maxmal lyng. Table 11: Optmal strateges Pece rate If µ<1, max le If µ>1, ntermedate levels Pe If µ<1/ If µ>1/ 2, max le 2, ntermedate levels Tournament If µ<1/ 2, max le If µ>1/ max le or wns 2 : x y x y any te break In the tournament payoff scheme, when only one party can le, unlke other payoff schemes, there can be ntermedate levels of lyng, maxmal lyng, or no lyng. If µ>1, there s no lyng, and f µ < 1/ 2 there s maxmum lyng when the performance of the partes are unequal. For the leaverson parameters n between, lyng to te-break can be preferred over lyng to wn when the 13 In ths paper, we wll call persons wth µ > 1le-averse, snce the dsutlty of lyng for such persons s hgher than ts monetary beneft wthout a second player. 22

23 honest outcome s losng. Fnally, when there s a te-break, no lyng can also be an equlbrum wth low levels of le-averson. When both persons can le, and f µ < 1/ 2, max le by both partes s the only equlbrum. If µ > 1/ 2 ntermedate levels of lyng are also supported n equlbrum. That s because, f a player would wn or te-break wth the honest outcome, then lyng to wn or te-break s always preferred over no lyng regardless of the µ. Therefore, there are equlbra n whch a person les to wn, and the other person declares one unt less. Ths, however, does not mean that any combnaton of les are supported n equlbrum. Dependng on the leaverson level, after a certan le-level, only lyng maxmally can be an equlbrum. Fnally, whether a player les to wn when he was to lose wth the honest outcome depends on hs le-averson parameter as well as the honest outcome: f the le-averson s moderate (ust above 1), lyng to wn can be supported. Therefore, wth moderate levels of µ, we would also expect maxmum lyng n equlbrum. Taken together, the above results suggest that, wth even moderate le-averson levels, we would get ntermedate levels of lyng f people beleve others are honest or le mnmally. Thus, as n our experment, there s overall very lttle lyng, then we should expect the payoff scheme not to have an effect. On the other hand, n tasks wth a hgh percentage of subects lyng wth the correct belefs about the les of others, we would expect hgher levels of lyng n tournament compared to pece-rate Dscusson and Concluson In ths paper, we expermentally nvestgated whether lyng s used as a tool for restorng equty. We ntroduced a real effort (analytcal) task that gave some people the opportunty to le. To fnd out whether cheatng takes place to restore equty, we ntroduced the one-party treatments n whch only one person n the par can le and compared the results to the two party treatments. We found that overall, only few people le, and most lyng s at an ntermedate level. Our results showed that recprocty plays no role n lyng behavour. Furthermore, somewhat at odds wth the results of prevous studes, we found that most lyng occurs n the pece-rate and that there s no 14 An approprate test for ths clam could be done by elctng the belefs about others lyng and analyzng whether ths correlates wth one s own lyng behavor. Our experment does not let us study ths: Snce we wanted to make sure that our expermental subects remaned gnorant about our research questons, we never used the word lyng, nor suggested the possblty of lyng anywhere n the experment ncludng n the questonnares. 23