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Collective choice under dichotomous preferences. (English) Zbl 1112.91048

Summary: Agents partition deterministic outcomes into good or bad. A mechanism selects a lottery over outcomes (time-shares). The probability of a good outcome is the canonical utility. The utilitarian mechanism averages over outcomes with largest “approval”. It is efficient, strategy-proof, anonymous and neutral.
We reach an impossibility if, in addition, each agent’s utility is at least \(\frac{1}{n}\), where \(n\) is the number of agents; or is at least the fraction of good to feasible outcomes. We conjecture that no ex ante efficient and strategy-proof mechanism guarantees a strictly positive utility to all agents, and prove a weaker statement.

MSC:

91B14 Social choice
91B06 Decision theory
91B10 Group preferences
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References:

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