Maximal Domain for Strategy-proof Probabilistic Rules in Economies with One Public Good

We consider the problem of choosing a level of a public good on an interval of the real line among a group of agents. A probabilistic rule chooses a probability distribution over the interval for each preference profile. We investigate strategy-proof probabilistic rules in the case where distributions are compared based on stochastic dominance relations. First, on a "minimally rich domain", we characterize the so-called probabilistic generalized median rules (Ehlers et al., 2002, Journal of Economic Theory 105: 408-434) by means of stochastic-dominance (sd) strategy-proofness and ontoness. Next, we study how much we can enlarge a domain to allow for the existence of sd-strategyproof probabilistic rules that satisfy ontoness and the no-vetoer condition. We establish that the domain of "convex" preferences is the unique maximal domain including a minimally rich domain for these properties