On the tradeoff between economic efficiency and strategy proofness in randomized social choice

Two fundamental notions in microeconomic theory are efficiency---no agent can be made better off without making another one worse off---and strategyproofness---no agent can obtain a more preferred outcome by misrepresenting his preferences. When social outcomes are probability distributions (or lotteries) over alternatives, there are varying degrees of these notions depending on how preferences over alternatives are extended to preference over lotteries. We show that efficiency and strategyproofness are incompatible to some extent when preferences are defined using stochastic dominance (SD) and therefore introduce a natural weakening of SD based on Savage's sure-thing principle (ST). While random serial dictatorship is SD-strategyproof, it only satisfies ST-efficiency. Our main result is that strict maximal lotteries---an appealing class of social decision schemes due to Kreweras and Fishburn---satisfy SD-efficiency and ST-strategyproofness.

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