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Inequality Aversion, Efficiency, and Maximin Preferences in By DIRK ENGELMANN AND MARTIN STROBEL* We present simple one-shot distribution experiments comparing the relative impor-tance of efficiency concerns, maximin preferences, and inequality aversion, as wellas the relative performance of the fairness theories by Gary E Bolton and AxelOckenfels and by Ernst Fehr and Klaus M. Schmidt. While the Fehr-Schmidt theoryperforms better in a direct comparison, this appears to be due to being in line withmaximin preferences. More importantly, we find that a combination of efficiencyconcerns, maximin preferences, and selfishness can rationalize most of the datawhile the Bolton-Ockenfels and Fehr-Schmidt theories are unable to explain im-portant patterns. (JEL D63, D64, C99) Among the recent attempts to explain behav- compare the relative importance of inequality ior observed in economic experiments, models aversion, concerns for efficiency, and maximin based on inequality aversion have received spe- preferences1 in simple distribution experiments.
cial attention. The attractiveness of these mod- On the other hand, we compare the performance els is based on their ability to rationalize a of the two theories based on inequality aversion number of well-known anomalies with just two by Fehr and Schmidt (1999, henceforth F&S) motives, selfishness and inequality aversion.
and Bolton and Ockenfels (2000, henceforth The latter is understood as disutility arising from differences between one’s own payoff and Our first treatments that were designed to compare ERC and F&S recognized the potential The aim of this paper is on the one hand to importance of efficiency and thus controlled forit. It turned out that efficiency had a majorimpact (see treatments F and E in Section III).
* Engelmann: CERGE-EI, Charles University and Acad- This finding inspired further experiments to test emy of Sciences of the Czech Republic, P.O. Box 882, its robustness and to investigate to what extent Politickych veznu 7, CZ-11121 Prague 1, Czech Republic inequality aversion is dominated by efficiency (e-mail: [email protected]); Strobel: Depart-ment of Economics and International Institute of Infonom- concerns or maximin preferences. In particular, ics, University of Maastricht, P.O. Box 616, 6200 MD these treatments allow us to compare the ex- Maastricht, The Netherlands (e-mail: Martin.Strobel@ planatory power of ERC and F&S to the model infonomics.nl). We thank Gary Bolton, Colin Camerer, by Gary Charness and Matthew Rabin (2002, Gary Charness, James Cox, Martin Dufwenberg, Armin henceforth C&R), that is based on efficiency Falk, Ernst Fehr, Urs Fischbacher, Alfonso Flores-Lagunes,Simon Ga¨chter, John Kagel, Ulrich Kamecke, Georg Kirch- concerns and maximin preferences and was in- steiger, Wieland Mu¨ller, Hans Normann, Axel Ockenfels, Andreas Ortmann, Frank Riedel, Arno Riedl, Klaus Our results suggest that efficiency concerns Schmidt, Robert Sherman, Nat Wilcox, and participants of and maximin preferences are important in sim- the ESA 2000 annual meeting in New York, the First WorldCongress of the Game Theory Society in Bilbao, the 8th ple distribution experiments. While this does World Congress of the Econometric Society in Seattle, and not necessarily imply that they are equally im- seminars at Humboldt-Universita¨t, CERGE-EI, University portant in other classes of games, common in- of Zu¨rich, University of Maastricht, UCSB, Caltech, New terpretations of several games may well be York University, and the University of Arizona for helpfulcomments. Parts of this research were financed by theDeutsche Forschungsgemeinschaft (through Sonderfors-chungsbereich 373 and Grant No. EN 459/1), the Interna- 1 Efficiency is here simply understood as the sum of tional Institute of Infonomics, the DGZ-DekaBank, and an payoffs, not in the sense of Pareto efficiency. Maximin ESC-postdoctoral fellowship from the CERGE-EI founda- preferences are a desire to maximize the minimal payoff in tion. The financial support is gratefully acknowledged.
confounded with these motives. This may have In Section I we outline the difference be- been given too little attention in the past (see tween ERC and F&S that we focus on. Section Engelmann and Strobel, 2002, for a discussion).
II presents our experimental procedures, and To illustrate, consider the following example.
Section III the experimental results. Section IV First, let person 2 choose only between alloca- tions A and B among persons 1, 2, and 3.
I. Inequality Measures in ERC and F&S
The difference between the inequality mea- sures in ERC and F&S is represented in the motivation or utility function. The motivation function of ERC is given by v ( y , ␴ ), with y denoting subject i’s own payoff and ␴ subject i’s share of the total payoff, and v for given y If person 2 is inequality averse she prefers B being maximal if ␴ ϭ (1/n), n being the number over A, but B is also her preferred choice if she of players. F&S assumes a utility function is driven by efficiency concerns or maximin U ( x) ϭ x Ϫ ␣ [1/(n Ϫ 1)] ¥ preferences. Thus deriving any conclusions from a choice of B concerning the importance ␣ Ն ␤ Ն 0, ␤ Ͻ 1 and x the payoff of sub- of inequality aversion is confounded by effi- ciency concerns and maximin preferences. One cannot tell whether person 2 wants to redistrib- average payoff to be as close as possible to their ute money because she dislikes inequality, cares own payoff while F&S assumes that subjects for efficiency, or cares particularly for the poor- dislike a payoff difference to any other individ- est. Now consider the case that person 2 can ual. According to ERC, a subject would thus be choose from A, B, and C. A choice of B now equally happy if all subjects received the same clearly indicates inequality aversion, since self- payoff or if some were rich and some were poor ishness, efficiency concerns, and maximin pref- as long as she received the average payoff, but according to F&S she would clearly prefer that In our experiments, we disentangle efficiency all subjects get the same. In a real-life situation concerns, maximin preferences, and inequality F&S predicts that the middle class would tax the aversion to compare their relative importance.
upper class to subsidize the poor, whereas ERC In order to exclude, as far as possible, motives like reciprocity, we chose degenerate gameslike the one above that were completely reduced II. Experimental Procedures
to the question of distribution. Since both ERCand F&S are formulated on the basis of distri- We conducted 13 experimental treatments in butions only, these games seem to us the most three sessions. These sessions were all con- neutral playground to compare their predictive ducted as classroom experiments at the end of a lecture during the first weeks of introductory In contrast to previous experiments, in sev- economics courses at Humboldt-Universita¨t zu eral of our treatments ERC and F&S predict Berlin. One hundred thirty-six participants took choices of allocations that are at the opposite part in the first session in 1998, 240 in the ends of the choice set. Here, F&S does better ingeneral. This, however, appears to result fromF&S being in line with maximin preferences in theories that explicitly take intentions into account (e.g., this situation. For a complete explanation of our Rabin, 1993; Armin Falk and Urs Fischbacher, 2000; Mar- results, efficiency and maximin preferences are tin Dufwenberg and Georg Kirchsteiger, 2004) since this would require assumptions about beliefs concerning thechoices of subjects with whom one might be matched. Thesame holds for the full C&R model but we can shed somelight on the basic model, relying on selfishness plus quasi- 2 Other fairness theories could be applied to our setting maximin preferences (maximizing a weighted sum of total as well. Our experiments, however, are not suited to test ENGELMANN AND STROBEL: SIMPLE DISTRIBUTION EXPERIMENTS second session in 2000, and 210 in the third different degrees of redistribution. All choices session in 2001. We had determined a number provide the “middle income” individual with of seats corresponding to the desired number of the same payoff. This is to remove any effects participants in advance. We asked students to of selfishness, so we can focus on motives re- either take one of these seats or leave the class- lated to fairness. For all treatments in this sec- room. Each participant then received a decision tion, the F&S prediction coincides with the sheet with the instructions and a questionnaire.
maximin allocation. This reflects the structure We used the questionnaires to gather some bio- of this class of taxation problems and is not an graphical data and to check whether the partic- artifact of our design. The crucial property of ipants understood the task completely. The total these treatments is that the allocation that min- procedure took about 20 minutes. Participants imizes the difference between the payoffs of were paid after the lecture in the following person 2 and each of the other persons, maxi- week. They were identified by a code that was mizes the difference between the payoff of per- noted both on the decision sheet and on a de- son 2 and the average payoff and vice versa.
tachable identification sheet. They received the Thus ERC and F&S predict choices of opposite payment in a sealed envelope in exchange for this sheet. These procedures implied anonymity In one treatment (F), we choose payoffs so with respect to the other participants.
that efficiency coincides with the F&S predic- The decision sheet contained three different tion and the maximin allocation; in another (E), allocations of money between three persons, of we choose payoffs so that efficiency coincides which the subjects had to choose one. They with the ERC prediction. This allows us to were informed that we would randomly form investigate the extent to which efficiency coun- groups of three later on and would also assign terbalances the various types of fairness con- the three roles randomly, hence subjects faced cerns (F&S, ERC, and maximin) and it ensures role uncertainty. Only the choice of the partic- that efficiency concerns do not bias the results ipant selected as person 2 mattered.3 Two con- in favor of either ERC or F&S.5 We also con- trol treatments assigned fixed roles in advance, sider a variation of treatment F, called Fx, and a but kept the random ex post formation of variation of treatment E, called Ex, in which the groups. To avoid influence by computation er- outcome predicted by ERC involves exactly the rors we also noted the average payoffs of per- “fair share,” i.e., 1⁄3 , for the “middle income” sons 1 and 3 and the total payoff for each individual. The purpose of these treatments is to allocation in the decision sheet. The precise allocations and the resulting predictions of the The allocations for treatments F, E, Fx, and different theories will be presented along with Ex are presented in Table 1 (all payoffs are the results for the individual treatments.4 given in DM, 1 DM corresponded to $0.45 to$0.55 by the time of the various sessions) along III. Experimental Results
with the average payoff of persons 1 and 3, therelative payoff of person 2, and the total pay- off. We also marked which allocations are pre-dicted by ERC, F&S, efficiency concerns, and Details and Predictions: All of the treatments maximin preferences, as well as the actual in this section involve a “middle income” indi- vidual (person 2) choosing payoffs for a “high Each of the treatments E and F was divided income” individual (person 1) and a “low in- into two subtreatments that only differed by the come” individual (person 3). One can think of order in which the allocations were presented on the choices as tax systems corresponding to 3 In other words, we used (a reduced form of) the strat- 5 The preferable way to prevent results from being con- egy method. Apart from generating three times the data, it founded with efficiency would have been that all allocations secured that all participants were considered equally entitled yielded the same total payoff. If the decision maker’s own to the money since all performed the same task.
payoff is fixed, however, ERC implies indifference between 4 Sample instructions can be found in Engelmann and all allocations if the average and thus the total payoff of the TABLE 1—ALLOCATIONS (IN DM), PREDICTIONS BY ERC AND F&S, MAXIMIN AND EFFICIENT ALLOCATIONS, AND DECISIONS the decision sheet.6 All other treatments were maximin preferences. The three allocations divided into six subtreatments, one for each were not chosen with equal probability (p 0.001), in particular the F&S allocation waschosen significantly more often than the ERC RESULTS: The results for treatments E and F (including the subtreatments in the last two results are more dispersed. Slightly more sub- rows) as well as for Fx and Ex are presented in jects chose the allocation predicted by ERC and Table 1. In both treatments F and E there is efficiency than that predicted by F&S and maxi- virtually no difference between the two sub- min preferences, while 23.5 percent chose the treatments (␹2 ϭ 0.08, p Ͼ 0.96 for treatment E, intermediate allocation.9 The hypotheses that all and ␹2 ϭ 0.16, p Ͼ 0.92 for treatment F).7 This three or the two extreme allocations were cho- consistency suggests that our data are not com- sen with equal probability cannot be rejected The results for treatment F are very clear: ments balance the influence of efficiency con- 83.8 percent of subjects chose the allocation cerns, we also study the pooled data. There, predicted by F&S, efficiency concerns, and 60.2 percent of subjects chose the allocation 6 This was done to avoid the conceivable influence of a preference for the center or right allocation. The allocation significance for a multinomial test of the hypothesis that all with intermediate payoffs was always presented on the left, allocations are chosen with the same probability, whereas since it was the one we were least interested in.
will denote the level of significance for a (two-sided) 7 Hence we can conclude that the results are not driven binomial test of the hypothesis that allocations X and Y are by a preference for either the middle or the right column and chosen with the same probability taking the number of we pool the data from the respective subtreatments. For the choices for the third allocation as given.
other treatments we do not report results for the subtreat- 9 The explanation that some of these subjects provided in ments, since the number of subjects in each of the subtreat- the questionnaires indicates that they were looking for a compromise between efficiency and fairness.
ENGELMANN AND STROBEL: SIMPLE DISTRIBUTION EXPERIMENTS predicted by F&S, whereas 22.8 percent de- stantial part of the data are consistent with cided in line with ERC (p Ͻ 0.001, binomial maximin preferences. Furthermore, since most of the choices which are not in line with maxi- Of the 136 choices in both treatments, 61.8 min preferences are efficient (the ERC alloca- percent are in line with the maximization of tion in treatments E and Ex), quasi-maximin total payoffs while 21.3 percent minimize it preferences (as in C&R) are consistent with (p Ͻ 0.001, binomial test). Furthermore, the about 85 percent of the data, if one allows for distribution of decisions clearly differs between treatments E and F (␹2 ϭ 33.07, p Ͻ 0.001).
Since the crucial difference between E and F is the role of efficiency, we see this as substantialevidence that efficiency matters.
Details and Predictions: Treatments F and E The results for treatments Fx and Ex almost demonstrated a major influence of efficiency.
exactly match those for F and E. (Fx: p This inspired us to subject both theories of inequality aversion to a more severe test, in 1; both treatments pooled, ERC vs. F&S allo- which they predict decisions that are Pareto- cation: p Ͻ 0.001, efficiency maximization vs.
dominated. This situation is represented by minimization: p Ͻ 0.003; Ex vs. Fx: ␹2 ϭ treatment N, where the payoff to person 2 is again intermediate and kept constant. In this In treatments Fx and Ex the ERC prediction treatment F&S predicts a choice of C, which is is much more salient than in F and E. Since the Pareto-dominated by the ERC prediction B, results changed only marginally (distributions which is in turn Pareto-dominated by allocation are far from significantly different: ␹2 ϭ 0.69, A (see Table 2 which is structured in the same p Ͼ 0.7 for Ex vs. E and ␹2 ϭ 0.34, p Ͼ 0.84 way as Table 1). We call these games envy for Fx vs. F) and not in favor of ERC, we games, because envy could lead the middle conclude that the poor performance of ERC in class to take money from the poor, only to be our original treatments cannot be attributed to nonsalient differences in relative payoffs. Argu- We also used this treatment as a baseline to ably, these are still not huge, but if nonsalience test the robustness of our results with regard to was the issue, then the performance of ERC the monetary incentives for person 2. To test should improve at least somewhat compared to whether subjects were willing to give up own payoff for their desire to increase efficiency or Explaining their decisions in treatments E to reduce inequality, we let the payoff of person and F, 17 of the 18 subjects who explicitly 2 vary across allocations in the treatments Nx, referred to fairness chose according to F&S and Ny, and Nyi (see Table 2). Since both F&S and one chose the intermediate allocation. Effi- ERC also take selfishness into account, their ciency concerns were stated by 12 subjects as predictions depend on the weight assigned to the reason for their decision. Only one subject selfishness relative to inequality aversion (see referred to relative payoffs in the explanation, Table 2). The purpose of these treatments is to but contrary to ERC, this subject stated that he test whether our results in the other treatments wanted to maximize his own share. In treat- might be artifacts of the irrelevance of the ments Ex and Fx all 15 subjects who explicitly choice for the decision maker’s own payoff, not referred to fairness chose the F&S allocation.
to measure precisely the value subjects attach to Efficiency concerns were mentioned by 16 sub- jects, and 6 indicated maximin preferences.
Thus among the subjects who explicitly men- RESULTS: In treatment N, 70 percent chose tioned fairness as a motivation, F&S did much the Pareto-efficient allocation (which is consis- better than ERC and a substantial part of sub- tent with quasi-maximin preferences) and ERC jects explicitly stated efficiency concerns.
Hence, we conclude for the taxation games 10 We do not claim that the motivation that leads subjects that F&S outperforms ERC and that efficiency to behave in that way is in fact envy, which corresponds to clearly influences choices. Since the F&S pre- the ␣-component of F&S. It only seems a likely influence in diction is always the maximin allocation, a sub- this class of games. Hence our choice of name.
TABLE 2—ALLOCATIONS (IN DM), PREDICTIONS BY ERC AND F&S, MAXIMIN AND EFFICIENT ALLOCATIONS, AND DECISIONS clearly outperforms F&S, but with the aid of payoff, but it is minor.12 Hence the relative importance of the different motives does not seem to change fundamentally if selfishness be- In treatment Nx we added 1 DM for person 2 in allocation A and subtracted 1 DM in C. As Note that Ny and Nyi are the only treatments expected, this increased the number of choices where F&S makes a unique prediction (C) for all subjects, including those which are not in- equality averse, since the decision maker’s own tracted 1 DM (0.5 DM) in allocation A and payoff is maximal and inequality minimal. But added 1 DM (0.5 DM) in C. As expected, this this prediction only covers one-sixth of deci- increased the number of choices of C some- what. However, again the majority chose A, We conclude for the envy games that F&S whereas the choices of B are reduced (Ny: Ͻ 0.001, p Ͻ 0.001, p Ͻ 0.001; Nyi: dominance and that ERC does somewhat better Ͻ 0.011, p Ͻ 0.011, p Ͻ 0.044). Thus but not well, whereas the basic C&R model the results in these treatments are qualitatively well in line with the constant-own-payoff treat-ment N with deviations as expected by standard economic theory.11 This result suggests that our Note that in Ny 76.7 percent of subjects give up 22 percent of their own payoff, apparently to satisfy quasi- results in the other treatments are not plain maximin preferences. While this share corresponds to only a artifacts of the constancy of the decision mak- relatively small absolute payoff, it is often considered strong er’s payoff. There is an (expected) effect of evidence against selfishness if subjects are willing to give up small variations in the decision maker’s own 20 or 25 percent of their payoff to achieve, e.g., equality.
13 The envy games also provide an example that the predictive power of F&S can in some cases substantially beimproved by abstracting from the linear form. If the disutil- 11 The effect should be larger in treatment Ny than in Nyi ity is assumed to be, e.g., quadratic in inequality, F&S could and the number of choices for A should not increase in Ny.
also explain choices of B. In addition, if the restriction ␤ Յ These deviations, however, can be attributed to randomness ␣ is relaxed, then F&S can be consistent with choices of A.
in the data, that naturally follows from the random alloca- Hence the results can be seen as evidence against some tion of the subjects to the treatments. No pair of distribu- forms of inequality aversion but not as evidence against all tions is significantly different at 5 percent, ␹2-test.
possible forms of inequality aversion.
ENGELMANN AND STROBEL: SIMPLE DISTRIBUTION EXPERIMENTS TABLE 3—ALLOCATIONS (IN DM), PREDICTIONS BY ERC AND F&S, MAXIMIN AND EFFICIENT ALLOCATIONS, AND DECISIONS FOR THE RICH AND POOR GAMES, AS WELL AS FOR TREATMENT EY The envy games emphasize the importance of mediate payoff. Our treatments R and P study efficiency and maximin preferences if they situations where the decision maker receives combine to Pareto-dominance. Even then, how- either the highest payoff (i.e., is “rich,” treat- ever, they do not capture all choices and thus ment R) or the lowest payoff (i.e., is “poor,” there is a potential role for other motives like treatment P), which is again constant (see Table 3). Since F&S aggregates over all persons richer In the questionnaires, references to (Pareto) or poorer than oneself, it predicts the same as efficiency are more prominent in treatment Nx ERC in these situations. So these treatments do (21 subjects) than in N (11) or Ny and Nyi (15 not allow us to distinguish between F&S and in total). In all envy games together fewer sub- ERC. They allow us, however, to contrast effi- jects mention fairness (7) than maximin prefer- ciency, maximin preferences, and inequality ences (11) and selfishness (13). One subject aversion. In treatment R person 2 can choose for states preferences in line with ERC.
the other subjects payoffs that are relativelyequal (C) or that are maximal in sum (A). Both F&S and ERC predict a choice of the efficientallocation A, whereas maximin preferences pre- Details and Predictions: In the preceding eight dict C. In contrast, in treatment P inequality treatments person 2 always obtained an inter- aversion predicts a choice of the least efficientallocation C. The minimal payoff is constant, somaximin preferences cannot influence the re- 14 Our results in treatment N do not necessarily imply sults. Hence this treatment allows us to contrast that 30 percent of subjects are inequality averse rather than efficiency and inequality aversion in a frame motivated by efficiency or maximin. The pattern of ob- served proportions declining with the efficiency and maxi-min rank of the allocations well fits a random utility version At this point we also study our last treatment of quasi-maximin preferences. Error rates nearly this Ey. It is identical to Ex except that the alloca- high have been estimated from retest reliabilities in two- tor’s payoff is 9 instead of 12. Ey has the basic alternative lottery choice tasks (see, e.g., T. Parker Ballinger structure of the taxation games, but it does not and Nathaniel T. Wilcox, 1997) and in our treatments the share the crucial property of the taxation games error rates might be higher since they involve the choiceamong three alternatives.
that allowed a comparison of F&S and ERC.
The ERC prediction is shifted from A to C. Not only ERC and F&S, but also maximin and against a primary importance of inequality aver- hence all fairness motives under consideration sion in general form, not just the specific for- predict the choice of the least efficient alloca- mulations of F&S and ERC. According to the tion. Therefore, this treatment serves the same axiomatic characterization of F&S provided by purpose as the poor game, namely the com- William S. Neilson (2002), a choice of C in parison of efficiency concerns and fairness treatment R only contradicts a combination of inequality aversion and linearity.17 A choice ofA in treatments N, Ny, and Nyi contradicts a combination of inequality aversion and posi- and F&S predict the efficient allocation A, only tional asymmetry (which is reflected by the 26.7 percent of the choices were in accordance, condition ␣ Ն ␤). In contrast, in treatments P whereas 53.3 percent of the subjects chose C and Ey, a choice of A is inconsistent with the inequality aversion property alone18 as well as treatment P, where both ERC and F&S predict with non-self-centered inequality aversion and allocation C, 60 percent chose the efficient al- ERC. In both treatments fewer subjects chose the allocation predicted by all versions of in- more subjects chose the efficient allocation equality aversion than the efficient allocation, when it is not minimizing inequality compared although the former is also consistent with com- to the case when it does (p Ͻ 0.08). The distri- petitiveness and in Ey even with maximin pref- bution of choices differs significantly between erences, motives that appear to be of substantial R and P (␹2 ϭ 7.23, p Ͻ 0.03).
The comparison indicates that maximin pref- Treatment P also shows the limits of quasi- erences are important. In R the minimal payoff maximin preferences, since for any positive is maximized in allocation C,15 which was cho- weight on efficiency quasi-maximin preferences sen by the majority of subjects, whereas in P the imply a choice of A, chosen by only 60 percent minimal payoff is constant, so maximin prefer- of the subjects. A third of the subjects instead seems to be guided by either inequality aversion The results of treatment Ey show roughly a tie between the efficient allocation A (40 per- It is conceivable that the role uncertainty that cent) and the least efficient, but supposedly fair subjects faced in the preceding treatments might allocation C (36.7 percent). These results are have enhanced their concerns for efficiency.
well in line with treatment P, since the lower They were clearly confronted with the possibil- number of efficient choices and the marginally ity to end up in any of the three roles and this higher number of choices for C are consistent might have increased their concern for the well- with a positive influence of maximin prefer- being of the subjects in the other roles. It also ences.16 The fundamental difference between might have increased in particular the concern the treatments Ey and Ex is the ERC prediction.
for the subject with the lowest payoff and hence The results are essentially identical (even mar-ginally against ERC), which indicates that ERCis irrelevant in this context.
17 A choice of C would, however, only be consistent with unrealistically extreme forms of inequality aversion thathave absurd implications. Even if the disutility was cubic inthe payoff difference, B would still be preferred over C.
15 Nine of ten subjects who mentioned fairness chose C, 18 The results in P would be consistent with inequality only two subjects explicitly indicated maximin preferences.
aversion if the utility function was highly convex in the 16 From this comparison, though, this influence seems inequality, but this property is just the opposite of what is rather weak. Furthermore, maximin does worse in compar- necessary to reconcile results in R and the basic dictator ison to efficiency than in treatment R (distributions are, game with inequality aversion. Choices for A in Ey are even however, far from significantly different, ␹2 ϭ 1.8, p Ͼ inconsistent with this form of inequality aversion.
0.4). A possible explanation is that the trade-off between 19 Charness and Brit Grosskopf (2001) also study pure efficiency and the minimal payoff is more favorable to distribution experiments and they find that about 10 percent maximin in R than in Ey. Thus the difference is consis- of choices can clearly be attributed to competitive prefer- tent with reasonable parameter distributions in the C&R ences. Falk et al. (2000a) find even 19 percent competitive ENGELMANN AND STROBEL: SIMPLE DISTRIBUTION EXPERIMENTS increased the role of maximin preferences.20 tory variables, with x the payoff to person k in We have conducted control treatments for Ex and P (with 90 subjects each), where subjectsknew their role in advance. Only subjects in the role of person 2 were asked to choose an allo- cation and they knew that their choice would be implemented.21 Treatment P allows us to studythe isolated effect on efficiency, treatment Ex possible effects on both efficiency and maximinpreferences.
The control treatments do not provide any indication that our results are primarily driven by the role uncertainty method. In both treat- ments without role uncertainty the number of choices for the efficient allocation decreases byone-sixth (see Engelmann and Strobel, 2002, for the detailed results). This is in line with the hypothesis that role uncertainty favors effi-ciency, but the differences are small and far from significant (Ex: ␹2 ϭ 1.22, p Ͼ 0.54, P: ␹2 0.65, p Ͼ 0.72). There is also no indication that the role uncertainty increased the focus on maximin preferences (if anything, the data point in the opposite direction). Charness and Rabin (2001) conducted control treatments for 11 games to test whether the role reversal theyemployed in Charness and Rabin (2002) affects Then according to the conditional logit model behavior. They do not find significant or sub- the probability that person i chooses allocation j D. The Relative Importance of the Different g ʦ ͕A,B,C͖ In order to better understand the relative in- fluences of the different motives we pool the Since we only have one decision per subject, we data and estimate a conditional logit model (our cannot take into account any individual differ- situation is captured by McFadden’s choice ences. Hence with this approach we estimate the model, see, e.g., G. S. Maddala, 1983).
preferences of an “average subject” and all het- For each allocation j ʦ {A, B, C} that person erogeneity is incorporated in the error.
i can choose we define the following explana- Considering the ␣ and ␤ components of F&S separately allows us to investigate for both com-ponents individually whether they explain anyof the variance. This, however, causes a col- 20 On the other hand, the role uncertainty could also linearity problem because in all of our treat- enhance the role of inequality aversion since this method ments FS␣ ϭ FS␤ Ϫ 1⁄2 Eff ϩ 3⁄2 Self. To underlines that all players are a priori in the same situation, overcome this problem, in a first approach we so that no one deserves more or less than the others.
exclude Self, because we are not primarily in- The subjects who were assigned the roles of person 1 or 3 were asked how they would have chosen if they had terested in the role of self-interest. In a second been in the role of person 2 and what choice they expected approach, we include a strict version of F&S, person 2 to make. Neither the distribution of the hypothet- FSstrict ϭ FS␣ ϩ FS␤, replacing the separate ical choices nor of the expectations differs significantly components by an aggregate measure of in- from the distribution of actual choices for any group of equality that assumes equal weights assigned to subjects or treatment (␹ Ͻ 3.1, p Ͼ 0.21 for all pairwise disadvantageous and advantageous inequality.
TABLE 4—ESTIMATED ODDS RATIOS FOR THE CONDITIONAL separate F&S components yields qualitatively LOGIT MODEL AND RESULTS OF LIKELIHOOD RATIO TESTS important insight. We now find a highly signif- icant positive effect of FSstrict and a highly significant negative impact of the ERC motive.
This means that if we ignore the maximin mo- tive, F&S appears to be a much better model of distributional preferences than ERC. This pro- vides a deeper understanding of why F&S clearly outperforms ERC in the taxation games, but does poorly in the other games. The superior performance of F&S in the taxation games seems to result from being in line with maximin there, but not from being a more accurate model IV. Conclusion
Bolton (1998) suggests three building blocks to explain behavior in games: motivation, learn-ing, and strategic reasoning. In the presentexperiments we have completely isolated distri- We also conducted another run excluding MM.
butional preferences from issues such as learn- The results are reported in Table 4 along with ing, intentions, and strategic reasoning, because the results of likelihood ratio tests of hypothe- distributions are given the central role in F&S ses that certain subsets of the motives are and ERC. We are thus able to provide a pure test both for the comparison of ERC and F&S If we include both components of F&S sep- and for the relative importance of inequality arately, we find that efficiency and especially aversion, efficiency, and maximin preferences maximin preferences have a clear significant as components of the motivation block. It turns influence. In contrast, neither component of out that inequality aversion does not seem to be F&S has significant impact, with the ␣ compo- a major part in a complete explanation in this nent having a positive impact and the ␤ com- setting. F&S and ERC are unable to explain ponent a negative. Hence the motivation to important patterns in our data. In contrast, a increase poorer subjects’ payoffs is entirely cap- combination of efficiency concerns, maximin tured by the maximin motive. The ERC motive preferences, and selfishness (which amounts to has a negative, marginally significant impact.
the basic C&R model) can rationalize most of Likelihood ratio tests reveal that both F&S com- the data. The conditional logit analysis of the ponents together do not explain additional vari- pooled data shows that the basic C&R model is ance (p Ͼ 0.3) and that F&S and ERC jointly virtually sufficient to explain the data. While add only marginally to the explanation (p Ͼ F&S and ERC do not account for additional 0.1). Including FSstrict and Self instead of the variance, both efficiency and maximin do. Thisis consistent with results for similar simple dis-tribution games in Charness and Grosskopf 22 The odds ratio denotes the factor by which the odds [P /(1 Ϫ P )] are multiplied if the corresponding indepen- dent variable increases by one unit. Choosing the negativeof the inequality as measured by F&S and ERC as explan- 23 All results reported in this section are robust to the atory variables implies that estimating an odds ratio Ͼ1 exclusion of treatments E, F, and Ey (see Engelmann and amounts to an influence in line with F&S or ERC. Note that Strobel, 2002, for details and the motivation for excluding the odds ratios for different explanatory variables are in these treatments). We excluded the control treatments for general not directly comparable because the variables are Ex and P from the analysis because they were run with a ENGELMANN AND STROBEL: SIMPLE DISTRIBUTION EXPERIMENTS (2001), Alexander Kritikos and Friedel Bolle three respects. First, in most treatments the The superior performance of F&S over ERC allocator’s payoff is not affected. Second, there in the taxation games, which we consider the is role uncertainty. Third, there is no strategic most neutral playground for the comparison of F&S and ERC, appears to be driven by the fact Concerning the first two issues, our treat- that F&S is in line with maximin preferences.
ments Nx, Ny, and Nyi as well as the control Hence the results cannot be interpreted in a way treatments for Ex and P provide no indication that more subjects have F&S preferences than that the absence of monetary incentives or the ERC preferences but that F&S takes into ac- role uncertainty substantially change the rela- count that subjects (other things being equal) tive importance of inequality aversion, effi- care about the minimal payoff in the group. It ciency, and maximin preferences. Therefore, we appears a limitation of ERC that it does not can at least clearly refute the claim that our results are entirely driven by these factors.
A further deficiency of both F&S and ERC is that they do not explicitly consider intentions (a change subjects’ decisions, we see no obvious matter that we deliberately designed out of our reason why they should change the relative im- experiments), as is demonstrated by the exper- iments of, e.g., Sally Blount (1995), Falk et al.
The remaining issue is the absence of strate- (2000a, b), and John H. Kagel and Katherine gic interaction in our experiments. It is conceiv- able that apart from the influence of reciprocity, The degenerate games we study are certainly strategic interaction alone might change the im- of a special kind. Hence at the current stage, our portance of different distributional motives. It is results do not discard inequality aversion as a difficult to disentangle this potential effect from motive in general. Both F&S and ERC are, effects of perceived intentions and to the best of however, exclusively formulated on the basis of our knowledge there is yet no persuasive evi- distributions and interaction and intentions dence on this matter.26 It is an issue of substan- should rather appear as confounding factors.
tial importance. If the relative importance of We conclude that theories that are based on different distributional preferences depends on distributions should, in general, carefully clarify the presence and the nature of the strategic under which conditions they are appropriate.
interaction, then the whole approach to test dis- Inequality aversion may do better in situations tributional preferences in one strategic situa- involving perceived intentions, because in these tion, to understand the results in another, games reciprocity may coincide with inequality appears to be problematic. There are, how- aversion and hence the latter may serve as a ever, also important situations, which may black box model of the former, as Fehr and well not be perceived as strategic interaction, Schmidt (1999) suggest. This, however, may be and for these our results are thus more di- an artifact of the classes of games that have rectly applicable. An example would be vot- been the focus of experimental research so far (in particular those where a player who treats As long as there is no conclusive evidence another player unfairly has a higher payoff, as that the relevance of our results is entirely con- fined to noninteractive situations, they also havesome general implications. In interpreting ex-perimental results one should keep efficiency 24 Our results are also consistent with the purely distri- concerns and maximin preferences in mind as butional model by James C. Cox et al. (2002). A similar alternative explanations. They are consistent model is studied by James Andreoni and John H. Miller(2002) and they show that it fits the data of dictator gameswell.
25 Inequality aversion might also be more important when perfect equality is an option. Werner Gu¨th et al.
26 Evidence on this issue so far indicates primarily that (2001) show that in mini-ultimatum games the availability subjects become more selfish when part of the responsibility of only nearly instead of perfectly equal allocations sub- for the outcome can be attributed to the other subject stantially increases the rate of unfair proposals and reduces (Bolton and Rami Zwick, 1995, and Charness and Rabin, 2001, who call this “complicity effect”).
with many results that are readily interpreted as Bolton, Gary E. “Bargaining and Dilemma
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comparison with dictator control experiments, Theory of Equity, Reciprocity, and Competi- to a large part it can be attributed to efficiency concerns. Similarly, a positive relation between the amount sent and the amount returned by the Bolton, Gary E and Zwick, Rami. “Anonymity
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