Strategy-proofness versus efficiency for small domains of preferences overpublic goods

It has long been known that when agents have von Neumann-Morgenstern prefer ences over lotteries, there is an incompatibility between strategy-proofnes s and efficiency (Gibbard, [9]; Hylland, [12]) - a solution satisfying thos e properties must be dictatorial. We strengthen this result by showing that it follows from the same incompatibility on a series of much smaller domai ns of preferences. Specifically, we first show the incompatibility to hold on our smallest dom ain, in which two agents are restricted to have linear preferences over one private good and one public good produced from the private good (Kolm tria ngle economies). This result then implies the same incompatibility on incre asingly larger domains of preferences, ending finally with the class of von Neumann-Morgenstern preferences over lotteries. JEL Classification Numbers : C70, D70, H41.