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About the article
Published Online: 2013-06-29
Published in Print: 2013-01-01
The particular functional forms for the utility function that have been suggested differ. For example, Fehr and Schmidt (1999) and Bolton and Ockenfels (2000) suggest specifications designed to capture inequality aversion. Charness and Rabin (2002) incorporate a concern for efficiency. Kirchsteiger (1994) incorporates envy. Each of these articles shows evidence that such specifications improve the ability to accommodate various dimensions of observed behavior, in particular if both fairness-motivated and selfish types exist.
Andreoni and Miller (2002) find that only a quarter of the subjects display preferences that are consistent with pure selfishness, another quarter are consistent with either an equal split of resources or the most efficient outcome, and another quarter spend own resources to reduce the others’ payoff in line with spite or envy. It should be noted that in our verbal explanations we often refer to the case where more resources to the other player increases utility, but this need not hold in general, similar to standard utility functions over non-social goods that need not increase with more of a particular good. None of our arguments hinges on the exact form of the utility function, and in particular it does not rely on the same utility function across individuals.
Andreoni and Miller (2002) vary the budget set and the price at which personal monetary payoff can be exchanged for higher monetary payoff of another person. They find that only of subjects violate the weak axiom of revealed preference, which means that the choices of 98% can be represented by some utility function.
Gneezy, List, and Wu (2006) refer to a similar property as the “internality axiom”.
In this definition, we restrict attention to tangible outcomes such as the joint monetary payoffs of all agents. In the discussion section, we return to this point and elaborate on larger state spaces where utility over outcomes may involve intangibles such as psychological states or beliefs (see, for example, Andreoni and Bernheim 2009; and Battigalli and Dufwenberg 2009).
It is weaker than the monotonicity axiom as it only refers to outcomes in the support of the lottery (i.e. elementary lotteries are considered) and not any other outcome. It is weaker than the betweenness axiom, because it does not involve compound lotteries. To compare with first-order stochastic dominance, the underlying space of outcomes first needs an order, which naturally arises by ordering outcomes by the utility of the certain outcome. Such a notion is present for example in the ordinal first-order stochastic dominance approach in Spector, Leshno, and Ben Horin (1996) and in the approach to dominance in probabilities in Karni and Safra (2002).
In the tradition of Kahneman, Knetsch, and Thaler (1990), who analyzed the endowment effect with coffee mugs, we use coffee mugs, because there are no apparent norms in favor or against buying such mugs.
If the utility of a lottery L over outcomes specifying the realization for each of two players can be written as the utility over expected realizations with u non-linear, then it cannot be represented as expected utility for any function because this is linear in probabilities.
Since we are not aware of an implementation of this thought experiment, we included hypothetical versions of Machina’s parental example in another, unrelated experiment. We asked 56 participants to imagine they are a mother with 2 kids and to have only 1 candy. They had to decide whether to give kid 1 or kid 2 the candy or let a coin toss decide. About 95% chose the coin toss. One hundred and one participants faced a modified version, in which we tried to break indifference: the mother now has a green candy and knows that kid 1 likes green candies best, while kid 2 likes red candies. Here, still 67% choose the coin toss and the remainder to give the candy to kid 1.
Original instructions are written in German and are available from the authors upon request. See the Appendix for translated instructions.
The random allocation to a cubicle also determined an individual’s role in the experiment.
We chose the magnitude of these payments to be well within the range used in other experiments on social preferences.
On average, participants earned 9.4 € including a 5 € show-up fee.
The first choice is between the lotteries : 500,000 € with 100% and : 2.5 million € with 10%, 500,000 € with 89% and 0 € with 1%; the second between : 500,000 € with 11%, 0 € with 89% and : 2.5 million € with 10%, and 0 € with 90%. A violation of EUT involves choosing in one situation but in the other.
A chi-square test comparing all three options also yields no significant difference ().
If we had chosen another individual as the uninformed receiver, we would have had to make sure in the instructions that the subjects know and believe that the receiver is indeed uninformed.
Individuals made the mug choice before they knew their earnings. Since the mug choice is so trivial, they made in addition a decision in an unrelated voting experiment in which they could earn 0, 7, or 10 Euro. The complete (translated) instructions are in the Appendix.
Given the small number of subjects that randomize in the mug experiment, a Fisher exact test seems more appropriate than a Pearson chi-square test. The latter however yields a similar result (). Instead of bundling those who take the money or buy the good, we can test for a relation between experiments using all three choice options (randomization, take the money, or buy the good). Again, both tests indicate a significant difference (Fisher exact test: ; Pearson chi-square test ).
However, in the latter two comparisons, the social good experiment differs from the mug experiment due to the cost of randomization and the receiver being a charity.
Mann–Whitney U tests do not indicate significant differences: when testing decision times for all three choice options/for those who keep the money/for those who buy the social good or the mug. Since too few people choose to randomize in the mug experiment, we cannot test for differences in the time for randomized choices.
See e.g. Kirchsteiger (1994), Levine (1998), Fehr and Schmidt (1999), Bolton and Ockenfels (2000), Ok and Kockesen (2000), and Charness and Rabin (2002) for specific functional forms. See, e.g., Maccheroni, Marinacci, and Rustichini (2008), Sandbu (2008), and Rohde (2010) for specifications founded in the axiomatic tradition of decision-theory.
See also Neilson (2006).
Since these works were concerned with signaling to the receiver, the settings were not double blind. Neither was our experiment. That leaves open the possibility of signaling to the experimenter.
In Bolton and Ockenfels (2010), depending on the treatment, the outcomes of the safe option are (7,7), (7,0), (7,16), (9,9), (9,0), or (9,16) – where in each case the first (second) entry denotes the dictator’s (receiver’s) payoff. The outcomes of the risky option are either (16,16) and (0,0) or (16,0) and (0,16). Since the outcomes of the safe option differ from the outcomes of the risky choice, it is possible to assign utility values to the outcomes that rationalize the findings even within the framework of expected utility theory. Whether such utility values reflect one’s intuition about fairness or inequality aversion is a different matter.
Bolton, Brandts, and Ockenfels (2005) study a different environment and document that responders often reject unfavorable offers if the sender could have chosen an unbiased offer, while the rejection rates go down substantially if no unbiased offer is in the choice set of the sender. This part of their study does not deal with preferences for randomization directly, though.
In Andreoni and Bernheim (2009), decision makers do not choose among lotteries, but choose after the lottery is executed. Charness and Dufwenberg (2011) and Tadelis (2008) have decisions only between one deterministic outcome and one lottery. Dana, Cain, and Dawes (2006) and most of Dana, Weber, and Kuang (2007) consider settings without uncertainty.
This article circulated under the title “Fairness: A Critique to the Utilitarian Approach”.