Public good economies where agents are endowed with strictly convex continuous single-peaked preferences on a convex subset of Euclidean space are considered. Such an economy arises for instance in the classical problem of allocating a given budget to finance the provision of several public goods where the agents have monotonically increasing strictly convex continuous preferences. A probabilistic mechanism assigns a probability distribution over the feasible alternatives to any profile of reported preferences. The main result of the paper establishes that any strategy-proof (in the sense of A. Gibbard, Econometrica 45 (1977), 665--681) and unanimous mechanism must be a random dictatorship. Journal of Economic Literature Classification Numbers: D70, D71, H40, C60.
Dutta, B., Peters, H. J. M., & Sen, A. (2002). Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods. Journal of Economic Theory, 106, 392-416. https://doi.org/10.1006/jeth.2001.2896