Measuring Efficiency and Equity Motives A Comment on “Inequality Aversion, Efficiency, and Maximin Preferences in Simple Distribution Experiments”

Gary E Bolton & Axel Ockenfels *

Dirk Engelmann and Martin Strobel (2004) describe an experiment that challenges the social preference models of equity described by us in Gary E. Bolton and Axel Ockenfels (2000), called ERC, as well as a similar model described by Ernst Fehr and Klaus Schmidt (1999), hereafter FS. In particular, Engelmann and Strobel find evidence, in a simple allocation task, for an efficiency motive as well as self-interest and equity (the equity measure being maximin, making for basically the same combination of preferences proposed by Gary Charness and Matthew Rabin, 2002). This note comments on the nature of the trade-off between efficiency and equity motives, along two dimensions. First, we present new data on the strength of preference for efficiency versus equity. The feature that has brought equity to the attention of economists in recent years is peoples’ demonstrated willingness to pay to obtain it; indeed, a characterization of this willingness-to-pay is what drives social utility models such as ERC and FS. Engelmann and Strobel’s experiment focuses on situations where the decision maker has little or no pocketbook interest at stake. In fact, there is no decision made in the experiment, unconfounded by equity considerations, that implies a subject is willing to pay a positive amount to increase efficiency. The new experiment presented here compares the frequency with which people are willing to

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deviate from their pocketbook interests in support of each principle, efficiency and equity; and among those who deviate, we get a comparison of willingness-to-pay. 1 Second, we look more closely at the role of procedural equity in preferences for efficiency.

In most of Engelmann and Strobel’s treatments, players had an equal opportunity to

capture the efficiency gains. While social utility theory has been focused on allocation equity and has had little to say about procedural equity, preferences for social efficiency are plausibly conditioned on the procedure for distributing the gains. The new experiment examines whether support for efficiency is more likely when the gains are distributed by an equitable procedure. The data suggest two important qualifications to social preferences for efficiency. First, the cost matters; in our experiment, willingness-to-pay for efficiency is substantially lower than it is for equity. Second, preferences for efficiency – even for Pareto gains – are influenced by the distribution procedure; in this sense, preferences for efficiency and equity are not separable. While our main experiment focuses on the trade-off between efficiency and equity motives (and is not designed to test the performance of specific equity measures), we also provide some new data on the efficacy of maximin. In combination with past studies, the new findings speak to the likelihood that a model built on any parsimonious set of social motives will capture the data in all settings.

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The new experiment We investigate the efficiency-equity trade-off in the context of a majority rule voting

game. Voting is a common context for conflicts between fairness and efficiency. 2 In each game, three voters select one of two distributional policies. Alternative A always yields DM 13 each (about $6.10 at the time of the experiment). 3 Compared to A, alternative B increases the total

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payoff by DM 6; but how the efficiency gain is distributed differs by version of the game (Table 1). In game I (Pareto gain) all gains go to person 1 and nobody loses relative to A, in game II (a majority gain, a minority lose) person 2 loses, and in game III (a minority gain, a majority lose) both persons 2 and 3 lose. For all three games, so long as voters have strict preferences over outcomes, voting for one’s most preferred outcome is the unique trembling-hand perfect equilibrium.

By comparing voting across games we can investigate how preferences for

efficiency and equity vary with the pocketbook cost of obtaining them.

Table 1 here.

To study the influence of equality of opportunity, each voting game was run in two modes, the straight mode and the equal opportunity mode. In the straight mode, subjects knew their role (person 1, 2, or 3) before voting. In the equal opportunity mode, subjects conditioned their votes on each of the three player roles, with the role randomly assigned with equal probabilities after the conditional voting decisions were made. The procedure is more equitable in that all have an equal chance of any particular payoff. 4 However, the monetary incentives to vote any particular way in a given role are the same as in the straight mode in that same role. 5 Similar to Engelmann and Strobel, the new experiment was conducted in the classroom, in an introductory course on economics (neither of us was the class instructor; social preferences was not a class topic). In total, 288 management science and economics students participated. None had previously participated in an experimental economics study. Each subject played exactly one of the games shown in Table 1. There were 72 subjects for each game played in the straight mode, and 24 subjects for each game played in the equal opportunity mode, yielding 24

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observations for each person-role in each game, in each mode. Decisions were anonymous: Subjects were exclusively identified via code numbers (e.g., no payoffs receipts were signed), and identities of the group members were not revealed either during or after the experiment.

Table 2 here.

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Results Table 2 shows the number of votes for the egalitarian A distribution. Pooling over all

conditions, 80.65 percent of all votes that affect one’s own payoff are in line with what we would expect from self-interest (the figure does not include persons 2 and 3 whose votes do not affect their own payoffs). Equity or efficiency considerations may nevertheless be present in these votes since a self interested vote is always aligned with either the equitable or the efficient vote. 6 When we analyze the underlying motives for deviations from self interested play, we find that 47 out of 192 (24.48 percent) votes are in favor of A even though B would have yielded a more profitable outcome (person 1 in games I, II, and III, and person 3 in game II), and 18 out of 144 (12.5 percent) votes are in favor of the efficient alternative B when A would have yielded a more profitable outcome (person 2 in games II and III and person 3 in game III). In other words, twice as many deviate from their self-interest to support an equitable outcome than an efficient outcome (Fisher’s exact test, p = 0.006; the simple statistics we report here do not attempt to account for dependencies that arise from equal opportunity mode voters making three choices).

Figure 1 here.

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The impression is strengthened if we control for the potential amount of forgone payoffs to deviating. Figure 1 shows the frequency of choosing A, for each mode separately (games pooled), conditioned on the monetary sacrifice (negative numbers) and benefit (positive numbers) under the assumption that A (instead of B) is actually implemented. Observe, for example, that 13.54 percent of the subjects are willing to sacrifice DM 4 for efficiency, but many more, 31.25 percent, are willing to sacrifice the same amount, DM 4, for equity (figures pooled across modes, Fisher’s exact test, p = 0.015). Overall, under the assumption that one’s own vote is implemented, the average sacrifice when choosing alternative B (efficiency) is DM 6.22, and DM 9.28 when choosing alternative A (equity). That is, the high frequency of ‘equity votes’ compared to ‘efficient votes’ is not due to relatively low costs for equity; the opposite is true. The decision mode matters. Overall, 52.78 percent of all votes in the straight mode are for A, whereas only 41.67 percent of all votes in the equal opportunity mode are for A (Fisher’s exact test, p = 0.027). While the gaps between the straight mode and the equal opportunity mode are rather small for games II and III, and not individually statistically significant, they are strikingly strong in game I, 7 the case in which B is a Pareto-improvement over A. There, the Avotes sharply drop from 40.28 percent in the straight mode to 15.28 percent in the equal opportunity mode (p = 0.001). Inequality becomes acceptable to a large majority, if nobody loses relative to a status quo, and if everybody has an equal opportunity to improve his income. 8

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Discussion In the experiment, willingness-to-pay for social efficiency is rather low, and as a social

good, equity is in greater demand. One way to gauge the magnitude of the difference is to note that in game II (straight mode), an efficiency proposal that benefits two-thirds of the group was

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overridden by a coalition of the potential losers together with the potential winners sympathetic to equity. Of course, the weight of support will be case-specific, dependent on the amount of equity and efficiency at stake. But the larger point is that the demand for efficiency cannot be gauged independent of the cost, where cost includes both pecuniary and equity sacrifices. Our findings also suggest that preferences for efficiency and equity are closely linked in the sense that equal opportunity procedures can soften the tension between equality and efficiency. To date, social utility theory has dealt but a little with equitable procedures. Further study might yield insights into gaining social acceptance for efficiency enhancing economic policies. We agree with Engelmann and Strobel that individual behavior can be driven by a rich variety of social norms. But we would add that no simple, portable model is likely to capture specific attitudes towards equity in all situations. There is now quite a bit of evidence showing that perceptions of fairness depend on context. 9 This is evident within Engelmann and Strobel’s own framework: While they conclude that, in direct comparison, FS performs better than ERC, in fact, there is no such predominance: FS performs better in 3 out of 4 “taxation games”, and ERC does better in all four “envy games” (the models agree on the other treatments). Likewise, while Engelmann and Strobel exhibit cases where maximin outperforms ERC and FS fairness measures, it is not hard to construct games in a similar setting where the opposite is true. Consider, for example, an Engelmann and Strobel kind of game in which the decision maker chooses one of two payoff distributions for six subjects. He gets paid 8 regardless of his choice, and the other five subjects get, respectively, 8, 8, 8, 15, 1 in alternative A, and 2, 2, 2, 33, 2 in alternative B (payoffs in Euro). B strictly maximizes both maximin and efficiency, whereas A is the ERC and FS choice.

In an experimental study of this situation, using the same

procedures reported above, 94 percent (45 of 48 subjects) chose alternative A.

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We add that there is reason to doubt that efficiency is a robust motive across games. In our ERC-paper we looked at data taken from some 47 studies of bargaining, reciprocity and market games. Going through these studies now, we find that efficiency helps little to organize the data, and in fact directly contradicts many of the important patterns our model addresses. Regarding bargaining games like the ultimatum game, the key observation is that Pareto-inferior distributions are frequently preferred over unequal distributions. Efficiency concerns also do not show up in market games such as Bertrand games, where out-of-equilibrium play would often increase the pie to be distributed. Regarding reciprocity games, efficiency cannot contribute to explaining non-selfish responses, the key to understanding reciprocity, in the trust game because all responses are invariant to efficiency concerns.

Nor in the gift exchange game, where

efficiency predicts that workers' efforts are decreasing in firms' wages, but in fact the observed choice behavior is the reverse. 10 If there is no universal set of social motives – independent of context, etc. – then any model that fixes a combination of motives will sooner or later fail boundary tests. But then what is learned from social utility models such as ERC and FS? Here are three critical insights: First, while not everyone measures fairness the same way, the simple measures offered by ERC or FS provide a pretty good approximation to population behavior over a wide range of scenarios that economists care about. Second, there is a tight link between fairness and reciprocity, both age old preoccupations of people everywhere. Third, certain types of institutions (ex., competitive markets) induce “fairmen” to behave as if they are exclusively materially self-interested, whereas other institutions (ex., ultimatum bargaining) induce the “selfish” to behave as if they are fair. Preferences for fairness are not institution-specific, restricted, say, to political or legal spheres,

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rather the institution shapes the expression of preferences. Importantly, for some institutions, a model that takes material self-interest as the sole driver of behavior sacrifices little accuracy. In closing, we would say that the test for social preference theory is not so much whether the model is ‘true’, but more whether the model can usefully organize important behavioral patterns and economic phenomena (in the sense of Alvin E. Roth, 1996). In this regard, our data indicate that more work will have to be done before we can characterize any robust influence an efficiency motive might have.

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References Andreoni, James; Brown, Paul M. and Vesterlund, Lise. “What makes an Allocation Fair? Some Experimental Evidence.” Games and Economic Behavior, July 2002, 40 (1), pp. 1-24. Bolton, Gary E.; Brandts, Jordi and Ockenfels, Axel. “Measuring Motivations for the Reciprocal Responses Observed in a Simple Dilemma Game.” Experimental Economics, December 1998, 1 (3), pp. 207-19. Bolton, Gary E.; Brandts, Jordi and Ockenfels, Axel. “Fair Procedures: Evidence from Games Involving Lotteries.” Economic Journal (forthcoming). Bolton, Gary E.; Katok, Elena and Ockenfels, Axel. “Trust among Internet Traders: A Behavioral Economics Approach.” Analyse und Kritik, December 2004, 26 (1), pp. 185-202. Bolton, Gary E.; Katok, Elena and Zwick, Rami. “Dictator Game Giving: Rules of Fairness versus Acts of Kindness.” International Journal of Game Theory, August 1998, 27 (2), pp. 269-99. Bolton, Gary E.; Brandts, Jordi; Katok, Elena; Ockenfels, Axel and Zwick, Rami. “Testing Theories of Other-regarding Behavior - A Sequence of Four Laboratory Studies,” in: Charlie Plott and Vernon Smith, eds., Handbook of Experimental Economics Results (forthcoming). Bolton, Gary E. and Ockenfels, Axel. “Strategy and Equity: An ERC-Analysis of the Güth-van Damme Game.” Journal of Mathematical Psychology, June 1998, 42 (2), pp. 215-26. Bolton, Gary E. and Ockenfels, Axel. “ERC: A Theory of Equity, Reciprocity and Competition.” American Economic Review, March 2000, 90 (1), pp. 166-93. Bolton, Gary E. and Ockenfels, Axel. “A Stress Test of Fairness Measures in Models of Social Utility.” Economic Theory (forthcoming a).

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Bolton, Gary E. and Ockenfels, Axel. “Self-centered Fairness in Games with More than Two Players,” in: Charlie Plott and Vernon Smith, eds., Handbook of Experimental Economics Results (forthcoming b). Brandts, Jordi and Solà, Carles. “Reference Points and Negative Reciprocity in Simple Sequential Games.” Games and Economic Behavior, August 2001, 36 (2), pp. 138-57. Charness, Gary and Rabin, Matthew. “Understanding Social Preferences with Simple Tests.” Quarterly Journal of Economics, August 2002, 117 (3), pp. 817-69. Elster, Jon. Solomonic Judgements. Cambridge: University Press, 1989. Engelmann, Dirk, and Strobel, Martin. “Inequality Aversion, Efficiency, and Maximin Preferences in Simple Distribution Experiments.” American Economic Review, September 2004, 94 (4), pp. 857-69. Fehr, Ernst, and Schmidt, Klaus. “A Theory of Fairness, Competition, and Cooperation.” Quarterly Journal of Economics, August 1999, 114 (3), pp. 817-68. Fogel, Robert W. The Fourth Great Awakening and the Future of Egalitarianism. University of Chicago Press: Chicago, 2000. Fong, Christina. “Social Preferences, Self-Interest, and the Demand for Redistribution.” Journal of Public Economics, November 2001, 82 (2), pp. 225-46. Güth, Werner; Kliemt, Hartmut and Ockenfels, Axel. “Fairness versus Efficiency: An Experimental Study of (Mutual) Gift Giving.” Journal of Economic Behavior and Organization, April 2003, 50 (4), pp. 465-75. Kagel, John H., and Wolfe, Katherine. “Tests of Fairness Models Based on Equity Considerations in a Three-Person Ultimatum Game.” Experimental Economics, December 2001, 4 (3), pp. 203-19.

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Kahneman, Daniel; Knetsch, Jack L. and Thaler, Richard. “Fairness as a Constraint on Profit Seeking: Entitlements in the Market.” American Economic Review, September 1986, 76 (4), pp. 728-41. Oberholzer-Gee, Felix; Bohnet, Iris and Frey, Bruno S. “Fairness and Competence in Democratic Decisions.” Public Choice, April 1997, 91 (1), pp. 89-105. Rawls, John. A Theory of Justice, 1971, Cambridge, MA: Belknap Harvard Press, (quote at top of paper from p. 75 of revised edition 1999, paperback). Roth, Alvin E. “Individual Rationality as a Useful Approximation: Comments on Tversky's 'Rational Theory and Constructive Choice',” in: K. Arrow, E. Colombatto, M Perlman, and C. Schmidt, eds., The Rational Foundations of Economic Behavior, 1996, Macmillan, pp. 198-202. Selten, Reinhard and Ockenfels, Axel. “An Experimental Solidarity Game.” Journal of Economic Behavior and Organization, March 1998, 34 (4), pp. 517-39. Thibault, John and Walker, Laurens. Procedural Justice: A Psychological Analysis. Hillsdale, N.J.: Erlbaum, 1975. Tyler, Tom R. and Lind, E. Allan. “Procedural Justice,” in: J. Sanders and V.L. Hamilton, eds., Handbook of Justice Research in Law, 2000, New York: Kluwer, pp. 63-91.

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Table 1. Game Payoffs all games

game I

game II

game III

A

B

B

B

person 1

DM 13

DM 19

DM 27

DM 27

person 2

DM 13

DM 13

DM 1

DM 9

person 3

DM 13

DM 13

DM 17

DM 9

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Table 2. Voting results (percentages) A votes

straight mode

Equal opportunity mode

game I

game II

game III

game I

game II

game III

person 1

25.00

33.33

20.83

12.50

25.00

16.67

person 2

47.92

87.50

87.50

16.67

91.67

85.42

person 3* game average mode average

37.50 40.28

52.78

25.00 65.28

52.78

15.28

47.22

62.50

41.67

*For games I and III, person 2 and person 3 are in the same payoff position, and so for these games, the results are averaged together under person 2.

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Figure 1.

Frequencies of A-votes as a function of the corresponding potential

sacrifice/benefit 100% 90%

frequency of A

80% 70% 60%

straight straight

50%

equal op strategy

40% 30% 20% 10% 0% -14

-6

-4

0

payoff in A minus payoff in B

14

4

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*

Bolton: 310k Business Admin Building, Smeal College of Business, Penn State University, University Park, PA

16802, USA; [email protected]. Ockenfels: University of Cologne, Department of Economics, Albertus Magnus Platz, D-50931 Köln, Germany; [email protected]. Bolton gratefully acknowledges financial support from the National Science Foundation.

Ockenfels gratefully acknowledges financial support from the Deutsche

Forschungsgemeinschaft. 1

Other recent experiments (ex., Werner Güth et al., 2003) find that equity considerations can dominate efficiency

considerations when one’s own payoff is at stake, suggestive of the trade-off we seek to measure. 2

Engelmann and Strobel give voting as an example of where their results might directly apply, though they seem to

have larger groups than we use in mind. They also describe the games they study as “degenerate games … of a special kind.” One way of thinking of our study is that it looks at allocation choices in a more canonical context. 3

Since the focus here is on the trade-off between equity and efficiency, we intend to avoid ambiguity with respect to

the measure of equity. An equal split (alternative A) is equally fair by ERC, FS and maximin, and is the natural fairness norm among anonymous players in a homogenous population. Of course, equality is also a common social issue; see e.g. Robert W. Fogel (2000) for a history of egalitarian economic and political reforms in the U.S. 4

As John Rawls (1971) puts it, “If a number of persons engage in a series of fair bets, the distribution of cash after

the last bet is fair, or at least not unfair, whatever this distribution is.” Lotteries have been used to allocate public housing and scarce medical resources, to award oil drilling leases, for admission to educational institutions, for military and athletic drafts, for tax auditing, and for jury selection (Jon Elster, 1989). Felix Oberholzer-Gee et al. (1997) present survey evidence that lotteries are an acceptable procedure for siting nuclear waste facilities. 5

The alternative procedure, to vote for a single allocation and then choose roles, introduces risk, potentially

changing voting incentives. Bolton, Jordi Brandts and Ockenfels (forthcoming) show that narrow procedural aspects of the games (i.e., excluding role assignment rules) can influence judgments of what is fair. Here we extend the investigation to preferences for efficiency. See John Thibault and Laurens Walker (1975), and Tom R. Tyler and E. Allan Lind (2000) for surveys of the psychological literature on procedural equity.

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Social utility models generally allow some agents to have purely self-interested preferences, so all choices of this

sort are technically consistent with any of the models. This is also so in 8 of 11 treatments of Engelmann and Strobel’s study where the decision maker had no payoff at stake. 7

Engelmann and Strobel report that the efficient choice is taken 17 percent less when random role assignment is

removed. Options were not Pareto ranked, and the movement, as with our like cases, not statistically significant. 8

Daniel Kahneman et al. (1986), among others, observe fairness measured with respect to a status quo.

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With colleagues, we have studied this issue extensively. Bolton, Brandts, and Ockenfels (1998) investigate the

impact of past actions on distributional fairness, Bolton and Ockenfels (1998, forthcoming b), Bolton, Elena Katok, Ockenfels and Rami Zwick (forthcoming), Bolton, Katok and Zwick (1998), and Selten and Ockenfels (1998) investigate self-centered versions of distributional fairness, Güth et al. (2003), Bolton et al. (2004) and Bolton and Ockenfels (forthcoming a) investigate how fairness perceptions respond to the payoff menu, and Bolton et al. (forthcoming), study the interaction of menu and procedural allocation rules. Many others, such as James Andreoni et al. (2002), Brandts and Carles Solà (2001), Christina Fong (2001) and John Kagel and Katherine Wolfe (2001), to name some recent papers, have also investigated the nature of fair behavior. 10

This is because the marginal effect of effort on total payoffs is decreasing in the wage offer. So if the firm

chooses minimum wages, the efficiency-maximizing worker should respond with highest possible effort while maximum wages should elicit minimum effort. Efficiency motives might be relevant for first mover behavior. However, in the gift-exchange game most firms chose a wage that is close to the payoff-maximizing strategy, and hardly any first mover went beyond that wage. This is not to say that efficiency does not play a role; it plays an indirect role in that much of the cooperation can be explained as ERC-motivated players reacting strategically to the very high potential efficiency gains in the gift exchange game (Bolton and Ockenfels, 2000, pp. 181-188).

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