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

Abstract

Two fundamental notions in microeconomic theory are ef-ficiency—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 pref-erences. When social outcomes are probability distributions (or lotteries) over alternatives, there are varying degrees of these notions depending on how preferences over alterna-tives 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 weaken-ing of SD based on Savage’s sure-thing principle (ST). While random serial dictatorship is SD-strategyproof, it only sat-isfies 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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