Consider an economy with equal amounts of N types of goods, to be allocated to agents with strict quasi-convex preferences over lotteries. We show that ex ante, all Pareto-efficient allocations give almost all agents lotteries over at most two outcomes. Our results provide a simple criterion showing that many popular allocation mechanisms are ex ante inefficient. For the case of identical preferences, we establish existence of an efficient solution where all lotteries used are equally attractive. Assuming the reduction axiom, social welfare deteriorates by first randomizing over these binary lotteries. Efficient ex ante equality is achieved if agents satisfy the compound-independence axiom. (JEL D44, D61, D82)
Dillenberger et al. (Wed,) studied this question.