一种近似最优的公平选择机制
A Near-Optimal Mechanism for Impartial Selection
摘要：
我们研究了防策略选举，以在一组代理中选择一个赢家，每个代理都只关心获胜。这个公平的选择问题是由Holzman和Moulin和Alon等人独立提出的。Fisher和Klimm证明了置换机制是公平的和$1/2$ -最优的，也就是说，它选择一个代理人谁的收益，在预期中，至少一半的票数最流行的代理人。此外，他们还表明，如果代理人不能在选举中弃权，则该机制是$7/12$ -最优的。我们表明，一个更好的保证是可能的，提供最流行的代理人收到至少足够大，但恒定的票数。具体来说，我们证明，对于任何$ε>0$，有一个常数$N_ε$（独立于$n$的选民人数），这样，如果最流行的代理的最大票数至少是$N_ε$，那么置换机制是$(\frac{3}{4}-ε)$最优的。这个结果是紧的。此外，在我们的主要结果中，我们证明了近似最优的公正机制存在。特别地，存在对于任何$ε>0$都是$(1-ε)$最优的公正机制，只要最流行的代理的最大投票数至少是常数$M_ε$。
英文摘要：
We examine strategy-proof elections to select a winner amongst a set of agents, each of whom cares only about winning. This impartial selection problem was introduced independently by Holzman and Moulin and Alon et al. Fisher and Klimm showed that the permutation mechanism is impartial and $1/2$-optimal, that is, it selects an agent who gains, in expectation, at least half the number of votes of most popular agent. Furthermore, they showed the mechanism is $7/12$-optimal if agents cannot abstain in the election. We show that a better guarantee is possible, provided the most popular agent receives at least a large enough, but constant, number of votes. Specifically, we prove that, for any $ε>0$, there is a constant $N_ε$ (independent of the number $n$ of voters) such that, if the maximum number of votes of the most popular agent is at least $N_ε$ then the permutation mechanism is $(\frac{3}{4}-ε)$-optimal. This result is tight. Furthermore, in our main result, we prove that near-optimal impartial mechanisms exist. In particular, there is an impartial mechanism that is $(1-ε)$-optimal, for any $ε>0$, provided that the maximum number of votes of the most popular agent is at least a constant $M_ε$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
