Quasiconcave preferences on the probability simplex: A nonparametric analysis

A nonparametric approach is presented to test whether decisions on a probability simplex could be induced by quasiconcave preferences. Necessary and sufficient conditions are presented which can easily be tested. If the answer is affirmative, the methods developed here allow us to reconstruct bounds on indifference curves. Furthermore we can construct quasiconcave utility functions in analogy to the utility function constructed in the proof of Afriat's Theorem. The approach is of interest for ex ante fairness considerations when a dictator is asked to choose probabilities to win an indivisible prize. It is also of interest for decisions under risk and stochastic choice. It allows nonparametric interpersonal comparisons.