标题： 有弃权的孔多塞陪审团定理 显示英文标题

标题： Condorcet's Jury Theorem with Abstention

摘要： 著名的康多塞陪审团定理指出，随着人口规模趋于无穷大，多数规则在两个可用选项中以概率一选择最佳选项。 我们在一种不对称的两候选人框架下研究这一结果，其中两位候选人的支持者可能具有不同的参与成本。 当不投票的决定是完全理性的，即投票的关键性是平局的概率时，唯一的均衡结果是一个平凡的均衡，其中除了那些投票成本为零的选民外，其他所有选民都选择不投票。 我们提出并分析了一个更实际的、有限理性的模型，其中选民高估了自己的关键性，并表明在该模型下，非平凡的均衡出现，两位候选人的获胜概率都远离于一。 我们证明，当关键性估计强烈依赖于胜利的差距时，在任何非平凡的均衡中，无论人口规模如何，都没有一个候选人能确保胜利，这与康多塞的断言相反。 而当关键性估计对胜利差距的依赖较弱时，康多塞陪审团定理得以恢复。 显示英文摘要

摘要： The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric two-candidate setup, where supporters of both candidates may have different participation costs. When the decision to abstain is fully rational i.e., when the vote pivotality is the probability of a tie, the only equilibrium outcome is a trivial equilibrium where all voters except those with zero voting cost, abstain. We propose and analyze a more practical, boundedly rational model where voters overestimate their pivotality, and show that under this model, non-trivial equilibria emerge where the winning probability of both candidates is bounded away from one. We show that when the pivotality estimate strongly depends on the margin of victory, victory is not assured to any candidate in any non-trivial equilibrium, regardless of population size and in contrast to Condorcet's assertion. Whereas, under a weak dependence on margin, Condorcet's Jury theorem is restored.