Collective choice under dichotomous preferences

Agents partition deterministic outcomes into good or bad. A direct revelation mechanism selects a lottery over outcomes — also interpreted as time-shares. Under such dichotomous preferences, the probability that the lottery outcome be a good one is a canonical utility representation. The utilitarian mechanism averages over all deterministic outcomes “approved” by the largest number of agents. It is efficient, strategyproof and treats equally agents and outcomes. We reach the impossibility frontier if we also place the lower bound 1 n on each agent’s utility, where n is the number of agents; or if this lower bound is the fraction of good outcomes to feasible outcomes. We conjecture that no ex-ante efficient and strategyproof mechanism guarantees a strictly positive utility to all agents at all profiles, and prove a weaker version of this conjecture.