Strategy-proofness versus efficiency for small domains of preferences over public goods

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.