It has long been known that when agents have von Neumann-Morgenstern preferences over lotteries, there is an incompatibility
between strategy-proofness and efficiency (Gibbard, [9]; Hylland, [12]) – a solution satisfying those properties must be dictatorial.
We strengthen this result by showing that it follows from the same incompatibility on a series of much smaller domains of
preferences.
Specifically, we first show the incompatibility to hold on our smallest domain, in which two agents are restricted to have
linear preferences over one private good and one public good produced from the private good (Kolm triangle economies). This
result then implies the same incompatibility on increasingly larger domains of preferences, ending finally with the class
of von Neumann-Morgenstern preferences over lotteries.
Keywords and Phrases: Strategyproof Public goods - Lotteries. - JEL Classification Numbers: C70 - D70 - H41.
Received: February 6, 1997; revised version: January 29, 1998