Fairness, Risk Preferences and Independence: Impossibility Theorems

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. * Department of Economics, Harvard University ** Department of Economics, Washington University in St. Louis, St Louis Federal Reserve Bank and European University Institute. We thank Ben Pollak and Tomasz Strzalecki for helpful comments. NSF grants SES0851315 and SES-0951462 provided financial assistance.