Would The Right Social Preference Model Please Stand Up! Dinky Daruvala Karlstad University

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1 Would The Rght Socal Preference Model Please Stand Up! Dnky Daruvala Karlstad Unversty Abstract A number of competng socal preference models have been developed nspred by the evdence from economc experments. We test the relatve performance of some of these models usng an expermental desgn that s amed at capturng pure dstrbutonal concerns n a mult-person settng. We fnd that the ndvduals n ths study are heterogeneous and that they do not follow any sngle noton of farness or nequalty averson. In addton, the results suggest that effcency concerns are not confned to students of economcs but are mportant to students of all dscplnes. Keywords: Dfference Averson, Effcency, Inequalty Averson, Maxmn Crteron, Socal Preferences. JEL Classfcaton: A3, C9, D63.. Introducton A number of socal preference models have been developed n an effort to explan and organze the evdence from economc experments. It has been found that people share wth others n dctator games, reject offers n ultmatum games, cooperate n publc good games etc., all of whch s n drect conflct wth tradtonal mcroeconomc utlty theory. Fehr (2) dstngushes between two approaches used when explanng the behavour observed n experments. The frst assumes that some agents have socal preferences such that ther utlty depends not only on ther own materal payoff but also on how much the other players receve. The second approach deals wth ntenton based recprocty where t s assumed that the player cares about the ntenton of her opponent. Although there s much evdence that perceved ntentons are often mportant, ths paper focuses solely on the former. Thus, the experments desgned here am to capture pure socal preferences,.e. the nature of dstrbutonal concerns rather than strategc or retalatory preferences. Consequently, ths study examnes how people respond to unfar outcomes rather than unfar ntentons. More specfcally, the purpose

2 of ths paper s to test the performance of some of the better known socal preference theores of dfference-averson, maxmn preferences and effcency concerns usng real money dstrbutonal experments. One category of socal preference models are dfference averson models such as those put forward by Loewensten, Bazerman and Thompson (989), Fehr and Schmdt (999) and Bolton and Ockenfels (2). These models presume that ndvduals are averse to dfferences n relatve payoffs and would therefore never sacrfce from ther own payoff or reduce the payoff of others f the acton resulted n a less equtable outcome. An alternatve to the dfference averson models are socal welfare models that combne dstrbutonal concerns wth preferences for effcency (surplus maxmzaton). The Quas-maxmn model by Charness and Rabn (2) s one of the more promnent socal welfare models where Rawlsan maxmn preferences are ntegrated wth effcency concerns. The varous socal preference models provde dfferent explanatons for the expermentally observed behavour, but t s sometmes possble to explan the same expermental data usng dfferent models. For example, sharng n dctator games s explaned by Andreon and Mller (22) as beng due to maxmn preferences whle the same results can be explaned by dfference averson accordng to Bolton and Ockenfels (2) and Fehr and Schmdt (999). Smlarly rejectons n ultmatum games and cooperaton n prsoner s dlemma games s ascrbed to dfference averson by Bolton and Ockenfels (2) and Fehr and Schmdt (999) whle Rabn (993) nterprets such behavour as recprocty. A number of studes have examned and tested varous socal preference models ncludng those dscussed above. The dfference averson models do not ncorporate effcency but there s evdence ndcatng that effcency s an mportant component n preferences. Studes by Charness and Grosskopf (2), Krtkos and Bolle (2), Andreon and Mller (22), Charness and Rabn (2, 22) as well as Engelmann and Strobel (24) found that a majorty of partcpants are effcency rather than equty orentated. Furthermore Andreon and Mller (22) construe partcpants who equalze 2

3 payoffs as exhbtng what Charness and Rabn (2) descrbe as socal-welfare preferences rather than dfference averson. Engelmann and Strobel compared the performance of the Bolton-Ockenfels and Fehr-Schmdt models and found a clear nfluence of effcency and maxmn preferences. Overall they found that the Fehr- Schmdt model fared better than the Bolton-Ockenfels model, but only when predctng the same choces as the Rawlsan prncple. The jury s stll out on ths ssue however. Fehr, Naef and Schmdt (24) found that effcency was of lttle concern when they replcated the experments of Engelmann and Strobel usng non-economst respondents. Furthermore, the authors rased doubts regardng the relevance of the Rawlsan motve n strategc games based partly on the experments by Güth and van Damme (998) as well as those by Frechette, Kagel and Lehrer (23) where lttle concern was shown for the lowest pay-offs suggestng that maxmn preferences are of lttle mportance n strategc nteractons. Further support for the dfference averson theory s gven by Güth, Klemt and Ockenfels (23) who found that farness concerns domnate effcency concerns n dctator dlemma experments where there s a trade-off between farness and effcency. The experments by Güth and van Damme (998), Bolton, Katok and Zwck (998) amongst others are used by Bolton and Ockenfels (22) to support the theory of self-centred farness that s emboded n ther model. These results were not supported by Charness and Rabn (2, 22), 2 who found that ndvduals dd ndeed care about the dstrbutons of pay-offs among other partes. Kagel and Wolfe (2) desgned a 3-person modfcaton of the ultmatum game n order to test the Fehr-Schmdt and Bolton and Ockenfels models. 3 Ther results show nsenstvty to thrd party allocatons and reject both the dfference averson models; furthermore, ther results even fal to support socal-welfare preferences. The lack of concurrence regardng the emprcal evdence motvates further study nto the nature of dstrbutonal concerns. Ths paper tests the relatve performance of some In dctator dlemma games, the recpent receves more than the dctator donates. 2 The authors desgned an experment wth a drect test of Bolton and Ockenfels hypothess that ndvduals are unconcerned about the allocaton among other partes. The results reject the Bolton and Ockenfels model but are consstent wth both the socal welfare and Fehr-Schmdt models. 3 In ths game, one person allocates a sum of money to two others, one of whch s randomly chosen to accept or reject the offer. Rejecton gves both the responder and the proposer zero ncome but a postve consolaton prze s gven to the non-responder. The results show lttle reducton n rejecton rates, holdng offers constant, wth and wthout consolaton przes, contrary to the predcton of both dfference averson models. 3

4 of the more promnent socal preference theores of dfference-averson, maxmn preferences and effcency concerns n dstrbutonal experments usng an approach that s somewhat dfferent to prevous studes. Frstly, wthn the standard approach experments are conducted usng 2 or 3 players and t s therefore of nterest to observe f there s any strong correspondence to any of the socal preference models when there are more players nvolved. In addton, the parameters of the models are rarely estmated n prevous studes as the structures of these games do not usually provde suffcent nformaton because they yeld outcomes from choces that result n the hghest utlty for the ndvduals (dctator games, ultmatum games, bnary choces between dstrbutons etc) rather than ndfference between choces. Fnally and most mportantly, the results from prevous experments do not always allow us to dscrmnate between the dfferent models as the results are often consstent wth more than one model. In ths paper the experments are conducted n groups of ndvduals, where each subject s requred to state what we call ther equalty equvalence for an unequal dstrbuton for the group. We defne equalty equvalence as the value of the egaltaran pay-off for whch the ndvdual s ndfferent between the unequal and the egaltaran outcome. 4 As wll be shown, the ndvduals responses classfy them nto one of the dfferent models and the desgn of the experment s such that membershp n one of the models s mutually exclusve. The rest of the paper s organzed as follows: Secton 2 provdes a descrpton of the expermental desgn and procedure followed by an overvew of the dfferent socal preference models n sectons 3. The results from the study are presented n secton 4 followed by the conclusons n secton 5. 4 Accordng to Rabn (993) as well as Dufwenberg and Krchsteger (24), ntentons play a role when ndvduals are motvated by recprocty consderatons. If so, the ndvduals n ths study, belevng that the other respondents would base ther choces out of kndness would wsh to recprocate ths unselfsh acton. However ths study dsregards such effects assumng that the ndvduals responses reflect only ther dstrbutonal concerns. 4

5 2. The Experment 2. Expermental Desgn We desgn an experment where ndvduals preferences and the performance of the dfferent models are evaluated by observng the equalty equvalence (S) for three dfferent dstrbutons of money among the subjects. The respondents were presented wth three questons, for each of whch there were two alternatves. Alternatve was a gven (unequal) dstrbuton for the group whle Alternatve 2 was the egaltaran dstrbuton where the ndvdual s task was to choose the level of money (S) n each case so that she s ndfferent between the pay-off dstrbutons n Alternatves and 2. In all three questons, the total surplus n Alternatve s 8 SEK whle the ndvduals pay-off s 3 SEK. 5 The dstrbutons n Alternatve dffer n that the payoffs become more equal and n queston 3 the lowest pay-off ncreases from to 5 SEK. Furthermore, the ndvduals own pay-off s the hghest n the group for the dstrbutons n questons 2 and 3. The dstrbutons of the three questons are presented n Fgure below. A translaton of the exact presentaton of the questons s gven n appendx B. Fgure. Descrpton of the dstrbutons. Queston Alternatve Alternatve 2 Indvdual receves 3 SEK Each ndvdual (ncludng ) receves S SEK. 6 ndvduals receve SEK 3 ndvduals receve 3 SEK ndvdual receves 6 SEK Queston 2 Alternatve Alternatve 2 Indvdual receves 3 SEK Each ndvdual (ncludng ) receves S 2 SEK. 5 ndvduals receve SEK 5 ndvduals receve 3 SEK Queston 3 Alternatve Alternatve 2 Indvdual receves 3 SEK Each ndvdual (ncludng ) receves S 3 SEK. ndvduals receve 5 SEK note: s the respondent 5 At the tme the experment was conducted, USD = 7.3 SEK. 5

6 A modfcaton of the ncentve mechansm by Becker DeGroot Marschak (964) s used to avod strategc responses by the partcpants. All partcpants receve the same pay-off f the stated value for S s less than a subsequently drawn random number. Ths random number s also the pay-off of each ndvdual. In the case where S concdes wth or exceeds the randomly drawn number, the pay-offs are n accordance wth Alternatve. Respondents are restrcted to statng values for S less than or equal to 3 whch s ther payoff n Alternatve. Thus, statng one's equalty equvalence s the domnant strategy. The ndvduals can then be categorsed nto the dfferent models. The alternatves were desgned so that membershp s mutually exclusve n that t s not possble for a respondent to belong to more than one group. Whle the behavour of some partcpants appears to be consstent wth the dfferenceaverson models, t s possble that ndvduals may also have surplus concerns. In order to see whether concerns for effcency are present, a follow up queston was put to the partcpants. The queston has smlartes to the one sded dctator dlemma treatment used n the paper by Güth, Klemt and Ockenfels (23). The orgnal dstrbuton s equal for all players so that each ndvdual receves SEK. Indvdual has the possblty to donate money to the others n the group. For every SEK donated, the payoff of every other ndvdual s ncreased by.25 SEK. Thus every SEK gven away by ndvdual wll ncrease the total surplus by.5 SEK. If the values of S gven by ndvdual appear to correspond to the one of the dfference averson models above but a postve donaton s made to ncrease the surplus then ths s suffcent for us to conclude that n at least those cases the models are ncomplete and concern for effcency should be accounted for Expermental procedure A total of 32 undergraduate students from varous dscplnes were recruted on campus at Karlstad Unversty to partcpate n the study. The experment was conducted n 2 sessons n groups of students, although n order to ensure a full head count, 2 students were summoned on each occason. Only the frst arrvals were accepted as partcpants whle the 2 th was pad a show-up fee of 5 SEK. The partcpants were seated ndvdually wth unobstructed vews of all other partcpants. 6

7 Each partcpant was gven an envelope contanng full nstructons (a translaton s avalable from the author upon request) as well as an dentty number. The same dentty number was prnted on the back of the questonnare. The sesson began wth the expermenter explanng how the payment procedure guaranteed complete anonymty for the partcpants after whch the dstrbuton part of the survey was explaned frst along wth the ncentve mechansm. Ths part of the experment took between 2-25 mnutes. The dstrbuton task was explaned usng an example wth a dstrbuton smlar to those n the survey. The ncentve mechansm was llustrated usng tral runs assumng dfferent varyng S-values. The cogntve demand on the students s consderable n ths knd of experment, so great pans were taken to ensure that the students had understood the nature of the task as well as the ncentve mechansm. 6 The three dstrbutons were presented on the overhead and ther characterstcs were descrbed to the subjects n a smlar fashon as descrbed n secton 3. In order to assst the subjects n the dstrbuton questons they were told the followng: If you have dffculty n answerng the questons you may wsh to follow the followng procedure: Set S n Alternatve 2 to 3 SEK and ask yourself whch alternatve you would prefer. If you lke both alternatves equally then set S=3. However, f you prefer Alternatve 2 then lower the value of S slghtly and ask yourself the same queston agan. Repeat the procedure, decreasng or ncreasng the value of S untl you reach a pont where you consder the two alternatves to be equal n value. The partcpants were gven tme to answer the dstrbuton questons before the donaton to the surplus task was presented. The subjects were asked to place ther pens on ther tables to sgnal when they had fnshed each task. Fnally the partcpants were requred to fll n some nformaton regardng ther socoeconomc status. The varables collected were gender, number of sblngs, poltcal preferences and choce of dscplne. 6 Nonetheless, t s possble that some partcpants stll dd not grasp that statng ther equalty equvalence S s the domnant strategy. Thus they were also told that f they dd not fully understand the ncentve mechansm, they should trust the nstructor n that t was n ther best nterest to answer n accordance wth ther preferences and that they had nothng to gan, but could possbly lose by not dong so. They were further told that the nstructor would stay behnd at the end of the sesson to explan the ncentve mechansm more thoroughly f they dd not wsh to ask questons n front of the group. 7

8 Each expermental sesson lasted about 4 mnutes. The questonnares were collected and one was pcked at random. A dce was thrown by the nstructor to establsh for whch of the four questons the payoff would occur. For questons -3 the ncentve mechansm was evoked where a number R was pcked at random from a box. If R S then the pay-offs were accordng to Alternatve whereas f R>S then all the ndvduals receved the same pay-off R. In the former case, dentty numbers were pcked one by one at random wth the assocated pay-offs ncreasng n magntude as the numbers were pcked. The nstructor noted the payoffs on a sheet of paper whch was gven to another person and the partcpants were able to collect ther pay-offs ndvdually usng ther dentty cards. 3. The models The models tested n ths study are the dfference averson models of Fehr and Schmdt (999) and Bolton and Ockenfels (2), the socal welfare model of Charness and Rabn (2) as well as a more general nequalty averson model. In ths secton we present a general overvew of the dfferent models. We begn by consderng the two dfference averson models. Fehr and Schmdt assume a utlty functon of the followng form for ndvdual U = w α max{ w j w,} β max{ w w j,}, n n j whereα β, β < and s the pay-off of ndvdual. The structure of ths model ncorporates both envy and altrusm. The dsutlty from nequalty s greater when another ndvdual has a larger pay-off than vce-versa thus the assumpton s that j envy s stronger than altrusm. The mplcaton behnd w β < s that the dsutlty from recevng more than others s never so great that the ndvdual s wllng to sacrfce money wthout beneftng others. Bolton and Ockenfels present n the theory of Equty, recprocty and competton (ERC) an unspecfed motvaton functon that s gven by V = w, s ), ( 8

9 where w denotes own payoff and s the ndvduals share of the total payoff. It s assumed that that the functon ncreases n own payoff payoff functon s, decreases as the relatve moves away from the socal reference share. Thus for a gven w, the n V s maxmsed when = reference group. In the case where s w n, n beng the number of ndvduals n the s > the margnal rate of substtuton between n absolute and relatve pay-offs wll determne how much the ndvdual s wllng to sacrfce n order to obtan an egaltaran soluton. The dfference between the two dfference averson models s that n the Fehr-Schmdt model the ndvdual compares her own pay-off wth each and every other ndvdual n the reference group. In the Bolton-Ockenfels model the ndvdual s only concern s her share of the total surplus and the pay-offs of other ndvduals do not enter drectly nto the motvaton functon. In the case where a transfer of money s made from an ndvdual wth a hgher pay-off to an ndvdual wth a lower pay-off, utlty wll ncrease n the frst model but reman unchanged n the second. The socal welfare model that we wll test s the Quas-maxmn model of Charness and Rabn (2), whch s bascally a renterpretaton of the Andreon and Mller (22) model 7 where people make sacrfces to ncrease the payoff of all recpents, but especally for the lowest pay-off recpent. The ndvdual s utlty functon s gven by U n = ( ) w + γ[ δ mn{ w, w2... wn} + ( δ ) w j ] j= γ, where the parameter γ [,] corresponds to the weght the ndvdual places on socal welfare, expressed as n, w2... w n } + ( ) w j ] j= [ δ mn{ w δ, versus her own monetary payoff w. When γ = then preferences are consstent wth pure self-nterest. Ifγ =, the ndvdual dsplays purely dsnterested preferences where the ndvdual values the pay-offs of others as much as her own. The parameter δ [,] measures the degree 7 Charness and Rabn refer to the workng paper by Andreon and Mller from 998 that was subsequently publshed n 22. 9

10 of concern for helpng the lowest pay-off recpent versus ncreasng the total surplus. Thus δ = s consstent wth the Rawlsan crteron whle δ = corresponds to maxmsaton of the total surplus. We also ntroduce a more general model where utlty s assumed to be a functon of some measure of nequalty. Wth mult-person experments, t s possble that the level of nequalty per se s an ssue. For example, n the Carlsson et al (25) study ndvduals were found to have strong preferences regardng the level of nequalty per se n the case of ncome. In order to encompass ths we ntroduce a general functon assumng that the ndvdual s utlty s dependent on her own payoff w, the general level of nequalty φ and some functon ν w,..., w ) of the pay-offs of others so that ( n the utlty functon s [ w, φ, ν ( w,..., w )] U = U n The functon ν w,..., w ) may for example represent concerns for the least pay-off ( n ndvdual, concerns for the total surplus, dfferences between the ndvduals own payoff and the pay-off of others or any combnaton of the above. We refran from stpulatng any precse functonal form as the purpose here s merely to obtan some measure of the proporton of subjects that have concerns for nequalty per se. Dependng on the values of the stated equalty equvalence (S) each ndvdual can be categorsed nto one of the dfferent models. Defnng the nequalty premum, E, for a partcular dstrbuton as the maxmum amount of money an ndvdual s wllng to sacrfce from her endowment n order to acheve an equal dstrbuton for the group so that E=3-S, we then have the followng classfcaton of responses. ) If E = E < then the ndvdual s preferences ft the Fehr-Schmdt model. The 2 3 E dstrbutons n questons 2 and 3 are equvalent n ths case as the redstrbuton of payoffs between the other partcpants does not affect the average dstances to the ndvduals own pay-off. It s also necessary that the nequalty premum n queston be hgher than n the other two questons as the average dstance from those wth lower and hgher pay-offs ncreases, and thus the dstrbuton n queston wll gve the ndvdual the lowest utlty.

11 2) If = E = E then the ndvdual s preferences correspond to Bolton and E 2 3 > Ockenfels model. The ERC model assumes that ndvduals care only about ther payoffs relatve to the total and are unconcerned regardng the relatve pay-offs between the other partcpants. The ndvdual s share of the total surplus s the same, and thus the nequalty premums wll be the same n all 3 cases. 3) If E = E > then the ndvdual exhbts quas-maxmn preferences. Snce the 2 E 3 lowest pay-off s the same n the frst two questons and ncreases n the thrd, the nequalty premum wll decrease n the thrd queston. 4) If E > E >, then ths mples that the preferences are consstent wth the more 2 E 3 general case where the ndvdual has an averson for nequalty per se. Thus the premum that an nequalty-averse ndvdual s wllng to pay wll be decreasng as the degree of equalty n the dstrbutons ncreases. 5) If = E = E, then preferences correspond to pure self nterest where the E 2 3 = ndvdual dsregards the pay-off of others. Ths s consstent wth tradtonal mcroeconomc theory. 4. Results The values for the nequalty premums for the frst two questons (E and E 2 ) range from to 3 wth means of and 92 respectvely. The correspondng values for E 3 are from to 2 wth a mean of 57. Detaled tables ncludng the means and standard devatons of the nequalty premums for the total and each group separately are gven n table A n appendx. If we look at the mean values drectly, we have that E > E 2 > E 3. Ths mples that preferences are consstent wth the nequalty averson model that was developed n ths paper. However, ndvduals are heterogeneous between as well as wthn models and we use the nequalty premums of each ndvdual to classfy them nto the dfferent models. Table below presents the number of partcpants whose responses are consstent wth the dfferent models; note agan that the groups are mutually exclusve. The group Other conssts of ndvduals whose preferences do not appear to ft any of the models

12 above. The table also ncludes the number of ndvduals n each category that sacrfced money n order to ncrease the total surplus n the follow-up queston. Table : Frequency of partcpants that qualfy nto the dfferent model categores and gve surplus ncreasng donatons. Number of respondents wthn each category. (% of total) Number of respondents that gave surplus ncreasng donatons. (% of group) Fehr-Schmdt 9 (6,8%) 3 (33.3%) ERC 28 (2,%) 9 (32.%) Quas-Maxm 36 (27,3%) (27.8%) Inequalty-averse 39 (29,5%) (28.2%) Self Interest (7,6%) (.%) Other (7,6%) 3 (3.%) Total 32 (%) 36 (27,3%) The group of responses consstent wth our general model of nequalty averson was the largest wth 39 ndvduals (29.5%). followed by the dfference averson group consstng of the Fehr-Schmdt and the ERC models wth a total of 37 ndvduals. Wthn the dfference averson group the ERC model fares consderably better than the Fehr-Schmdt model wth more than three tmes the number of partcpants fallng nto the former category. The Quas-maxmn model was n close thrd place wth 36 ndvduals. Although the dfference averson models appear to perform at least as well as the Quas-maxmn model, each group recevng roughly 28% of the respondents, nearly a thrd of the respondents n the dfference averson group made donatons n order to ncrease the surplus, thereby also ncreasng the level of nequalty. Ths s n drect conflct wth the predctons of both dfference averson models and the mplcaton would be that for those ndvduals at least, the models do not completely capture preferences. Nor can we exclude possble preferences for effcency among those ndvduals wthn the group who dd not make a donaton as the dsutlty from the lower payoff and ncreased nequalty may not have compensated for the utlty derved from the ncrease n the total surplus. There were ndvduals (7.5%) n the Self nterest group,.e. those ndvduals who were unconcerned wth the pay-off of 2

13 others. 8 The group Others had the same number of ndvduals as the Self Interest group. The only general pattern observed n ths group was that 9 out of of the respondents consdered the dstrbuton n queston 2 to be the worst and as such had the hghest nequalty premums. Apart from statng ther nequalty premum for the three dstrbutons, the partcpants were also requred to answer some questons on ther soco-economc status. A multnomal logt model was used n order to see f t was possble to classfy respondents nto the dfferent model groups based on values of the set of socoeconomc characterstcs. The only varable found to have any effect was gender n the model group Self Interest where 8% of the ndvduals n the group were male. 9 Consequently, we are not able to explan the dfference n preferences usng observable ndvdual characterstcs to any great extent. As mentoned n the ntroducton t s possble to estmate the parameters values of the Fehr-Schmdt as well as the Charness-Rabn utlty functons usng the nformaton provded n the experment. The parameter values of both models were calculated and the descrptve statstcs of these are gven n tables A2 and A3. The Pearson correlaton measure between the two parameters α and β for the Fehr Schmdt group was found to be at a sgnfcance level of.36. Thus, ndvduals wth hgher β values tend to have lower α values and vce versa, or n other words, those who are more altrustc tend to be less envous and vce versa. In the Quas-maxmn group t was found that as many as of the δ parameter values and one of the γ parameter values were greater than whch s clearly unreasonable as δ> mples that the parameter for effcency (-δ) s less than mplyng that an ncrease n effcency lowers the ndvdual s utlty. Wth the numbers n ths partcular experment t s 8 Ths s consderably less than n prevous studes where 3% s the proporton mentoned n some of the lterature but consstent wth results from experments where recprocty s not an ssue, e.g. Charness and Rabn (2) where the proporton of ndvduals motvated solely by self-nterest s around %. 9 Ths corresponds wth results from prevous studes for example Selten and Ockenfels (998 pg 529). However as there are only respondents n the Self Interest group t s not possble to draw any defnte conclusons from ths result. Bolton and Ockenfels do not use a specfc functon to descrbe preferences and n ths study. In addton, we do not specfy a precse functonal form for the comparson nequalty averson model. In both cases the value of the nequalty premum s used as the measure of dfference averson and nequalty averson respectvely. 3

14 suffcent that E 2 >2 E 3 for δ to be greater than. The descrptve statstcs n the appendx also nclude adjusted parameters where values greater than were set equal to. More than 6% of the adjusted parameter values for effcency (-δ) were zero mplyng that effcency was not a factor consdered mportant by most of the respondents. Two of the respondents had adjusted values of γ= mplyng that they have purely dsnterested preferences n that they value the pay-offs of others as much as ther own. The test for effcency n the follow-up queston s rgorous n the sense that those ndvduals who make postve donatons to the common surplus are both sacrfcng money and movng away from the egaltaran soluton, and as such ther concern for effcency s rrefutable. However, although the test above s suffcent n order to ascertan preferences for effcency, we cannot rule out such preferences for those who do not make such a donaton as t s qute possble that the utlty gan from the ncreased surplus does not outwegh the dsutlty from the decrease n own wealth and equalty. Postve donatons were made by 36 (27.3%) ndvduals. Of these, the donatons ranged between 5 and SEK, wth a mean and standard devaton of 28 and 22 respectvely. These results are n stark contrast to the results from the two-person dctator dlemma game by Güth, Klemt and Ockenfels (23) who found that ndvduals never volate the farness constrant n order to ncrease effcency. If we consder effcency n Quas-maxmn model, we found 5 ndvduals (42%) exhbted preferences for effcency wthn the model. 2 Allowng for naccuraces n model specfcatons we thus have at least 4 ndvduals (3%) n ths study who appear to exhbt strong preferences for effcency. Furthermore, we fnd the proporton of respondents makng postve donatons, and as such have strong preferences regardng effcency to be stable between the groups (wth the excepton of the Self-Interest group who as expected exhbted no effcency concerns) whch would lead us to beleve that preferences for effcency are not overrepresented wthn the Quas-maxmn group. If we accept ths noton then the estmate of subjects wth effcency concerns wthn ths One of the two respondents had parameter values δ=γ= whch corresponds to the extreme case where the ndvduals only concern s the for the lowest pay-off recpent. 2 There were 5 respondents wthn the Quas-maxmn model who ether had a postve parameter for effcency (4), gave a surplus ncreasng donaton () or both. 4

15 study would then be 5 or roughly 38.5%. These results support the conclusons of Engelmann and Strobel that dstrbuton concerns are a sgnfcant factor n pure dstrbutonal stuatons, 3 Fehr and Schmdt (24) argue that the relevance of the effcency motve s largely restrcted to students of economcs and busness admnstraton who value effcency rather than equalty. It mght be the case that students of economcs may have been taught that effcency should be consdered as an mportant ssue and as such would value equty less and effcency more than students of other dscplnes so we checked for subject pool effects n ths ssue. 72 of the partcpants were students of economcs who had completed at least one term of economcs whle the remanng 6 partcpants came from varous other dscplnes. Of these 2 economsts (27.8%) and 6 non-economsts (26.7%) gave surplus ncreasng donatons. We tested usng a Ch-2 test whether t s more lkely that economsts gave postve donatons than non-economsts. Smlarly, we also checked for any relatonshp between choce of dscplne and surplus concerns. In addton we conducted t-tests to check f the mean donatons dffered between the two groups n that economsts contrbuted more toward ncreasng the total surplus than others. The results show no sgnfcant dfference between economsts and non-economsts n any of the tests conducted. Thus, our results do not support the argument made by Fehr and Schmdt that effcency concerns are manly restrcted to students of economcs and busness. 5. Conclusons Ths paper uses a dstrbutonal experment n order to test the performance of some of the better known socal preference theores and effcency concerns n a neutral arena n order to examne how people respond to unfar outcomes n mult-person settng. The results show that the ndvduals n ths study are heterogeneous and that they do not follow any sngle noton of farness or nequalty averson. The number of subjects that qualfed nto the three categores was farly even wth the largest proporton of subjects fallng nto the reference nequalty averson model closely followed by the dfference averson and quas-maxmn models. Wthn the dfference averson group we found that the ERC model performed consderably better than the Fehr-Schmdt model wth more than three tmes the number of partcpants fallng nto the former category. 3 Fehr and Schmdt (24) also argue that the relevance of the effcency motve s largely restrcted to non-strategc nteractons. 5

16 Although the dfference averson category appear to perform at least as well as the other two, contrary to the model specfcaton nearly a thrd of the respondents n the group made donatons n order to ncrease the surplus. Whle dfference averson models may provde an nsght nto players wllngness to donate to others when ahead, they cannot explan donatons whch lead to an ncreased level of nequalty. Ths suggests that n at least a thrd of the cases the dfference averson models do not completely capture preferences. Fnally, we found that roughly one thrd of the respondents have qute strong concerns for the total surplus. It s sometmes argued that the relevance of the effcency motve s largely restrcted to students of economcs and busness admnstraton and s of less concern to students of other dscplnes. Ths study found no such correlaton. 6

17 References Andreon, J. and Mller, J. (22). Gvng accordng to GARP: An Expermental Test of the Consstency of Preferences for Altrusm, Econometrca, Vol 7, pp Becker, G.M., DeGroot, M. H. and Marschak, J. (964). Measurng Utlty by a Sngle- Response Sequental Method. Behavoral Scence 9: pp Bolton, G. E. and Ockenfels, A. (2). ERC: A Theory of Equty, recprocty and Competton, Amercan Economc Revew, 9(), pp Bolton, G. E. and Ockenfels, A. (22). Self-centered farness n games wth more than two players, forthcomng: Handbook of Expermental Economcs Results Carlsson, F., Daruvala, D. and Johansson-Stenman, O. (25). Are People Inequalty-Averse, or Just Rsk-Averse?, Economca, Vol. 72, Iss. 287, pp Charness, G. and Rabn, M. (2). Socal Preferences: Some Smple Tests and a New Model, Workng paper, Unversty of Calforna. Charness, G. and Rabn, M. (22). Understandng Socal Preferences wth Smple Tests, Quarterly Journal of Economcs 7 (3), pp Charness, G. and Grosskopf, B. (2). Happness and Relatve Payoffs An Expermental Study, Journal of Economc Behavor and Organsaton 45 (3), pp Dufwenberg,M. and Krchsteger, G. (24). A theory of sequental recprocty, Games and Economc Behavor 47, pp Engelmann, D. and Strobel, M. (24). Inequalty Averson, Effcency, and Maxmn Preferences n Smple Dstrbuton Experments, Amercan Economc Revew, v. 94, ss. 4, pp Fehr, E and Schmdt, K. M. (999). A Theory of Farness, Competton and Cooperaton, Quarterly Journal of Economcs 4, pp Fehr, E., Naef, M. and Schmdt, K. M. (24). "The Role of Equalty, Effcency, and Rawlsan Motves n Socal Preferences: A Reply to Engelmann and Strobel," forthcomng, Amercan Economc Revew. Fehr, E. (2). Theores of Farness and Recprocty: Evdence and Economc Applcatons, Workng Paper 75, Insttute for Emprcal Research n Economcs, Unversty of Zürch,. Frechette, G. R., Kagel, J.H. and Lehrer S.F. (23). Barganng n Legslatures: An Expermental Investgaton of Open versus Closed Amendment Rules, Amercan Poltcal Scence Revew 97, pp

18 Güth, W and Van Damme, E. (998). Informaton, Strategc Behavor and Farness n Ultmatum Barganng: an Expermental Study, Journal of Mathematcal Psychology 42, pp Güth, W., Klemt, H. and Ockenfels, A. (23). Farness versus effcency: An expermental study of (mutual) gft gvng, Journal of Economc Behavor and Organzaton Vol 5, pp Kagel, J.H. and Wolfe, K. (2). Tests of farness models based on equty consderatons n a three-person ultmatum game, Expermental Economcs, Vol 4, pp Krtkos, A. and Bolle, F. (2). Dstrbutonal Concerns: Equty or Effcencyorented?, Economcs Letters 73 (3), pp Loewensten, G., Bazerman, M. and Thompson, L. (989). Socal Utlty and Decson Makng n Interpersonal Contexts, Journal of Personalty and Socal Psychology, LVII, pp Rabn, M. (993). Incorporatng Farness nto Game Theory and Economcs. Amercan Economc Revew, Vol 83, pp Selten, R., Ockenfels, A. (998). An expermental soldarty game, Journal of Economc Behavor and Organzaton 34, pp

19 Appendx A-Descrptve statstcs tables Table A: Descrptves of the Equalty premums for all categores. Total Fehr-Schmdt ERC Quas maxmn Inequalty averson Self nterest Others E E2 E3 E E2 E3 E E2 E3 E E2 E3 E E2 E3 E E2 E3 E E2 E3 Mean Std. devaton Mnmum Maxmum Table A2: Estmatons of the parameter values for the Fehr- Schmdt category. Mean Std. Devaton Mnmum Maxmum α β Table A3: Estmatons of the parameter values for Quas-maxmn category. Mean Std. Devaton Mnmum Maxmum γ_adjusted δ_adjusted unadjusted γ values unadjusted δ values

20 Appendx B- Translaton of the exact presentaton of the questons n the questonnare. Questons -3. You have just been shown an example of your task by the montor. You wll now be requred to answer three questons that are smlar to the example. For Alternatve, the total allocaton of money s 8 SEK for all three questons and your share s always 3 SEK. The questons dffer n that the allocaton between the partcpants becomes more even. The dstrbuton n queston 2 s more even than n queston and queston 3 n turn, s more even than n queston 2. In addton the lowest pay-off ncreases to 5 SEK n queston 3. The dstrbutons for Alternatve for the three questons are presented below. Alternatve Queston Queston 2 Queston Number of persons Number of persons Number of persons SEK SEK SEK You receve 3 SEK You receve 3 SEK You receve 3 SEK 6 people receve SEK 5 people receve SEK people receve 5 SEK 3 people receve 3 SEK 5 people receve 3 SEK person receves 6 SEK Alternatve 2 All partcpants (ncludng you) receve the same amount _S_ SEK. 2

21 Answer I lke the dstrbuton n Alternatve n queston as much as the dstrbuton n Alternatve 2 when S= SEK. Answer 2 I lke the dstrbuton n Alternatve n queston 2 as much as the dstrbuton n Alternatve 2 when S= SEK. Answer 3 I lke the dstrbuton n Alternatve n queston 3 as much as the dstrbuton n Alternatve 2 when S= SEK. Queston 4. In ths queston you have the possblty to gve away money, f you so wsh, from your allocaton to the others n the group. For every SEK you choose to gve away, each of the other partcpants wll receve.25 SEK more. Each person n the group receves SEK. Answer 4 I wsh to gve away SEK from my SEK to the others n the group. 2