Abstract
The most widely used economic models of social preferences are specified only for certain outcomes. There are two obvious methods of extending them to lotteries. If we do so by expected utility theory, so that the independence axiom is satisfied, our results imply that the resulting preferences do not exhibit ex ante fairness. If we do so by replacing certain outcomes with their expected utilities for each individual, so that individual risk preferences are preserved, then ex ante fairness may be preserved, but neither the independence axiom nor ex post fairness is satisfied. Both ex ante and ex post fairness can be satisfied but then the individual does not have well defined preferences over own lotteries.
Highlights
If people have both a preference for fairness and continuous preferences, they are willing to make a small sacrifice for a more egalitarian outcome
The “obvious” extensions of standard models of fairness and social preference used in experimental research fail to incorporate both ex ante and ex post fairness, though there are relatively straightforward variants of these models that do reflect both concerns; these variants necessarily violate the independence property as well as the individualistic risk preference property
We consider simple lotteries generated by tossing a fair coin with equal 50% probability welfare function that is a non-linear function of the expected utility of different individuals, and so violates the independence axiom 2 Note that the domain we study does not allow preferences to depend on past actions, and that “fairness” here refers to fair allocations and not, for example, reciprocity
Summary
If people have both a preference for fairness and continuous preferences, they are willing to make a small sacrifice for a more egalitarian outcome. We show that if preferences over lotteries are transitive and stateindependent, and the induced preferences over own lotteries are “individualistic” in the sense of not depending on other people’s consumption, a weak form of ex post fairness is necessarily violated. This is true, for example, for Fehr-Schmidt preferences extended to lotteries by replacing money income with expected money income. We conclude that experimental research on social preferences should pay more attention to preferences over lotteries, and that decision theorists should consider what classes of tractable preferences are broadly consistent with the resulting data
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