The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying participation costs and share a possibly heuristic belief about their pivotality (ability to influence the outcome). In a costly voting setup where voters abstain if their participation cost is greater than their pivotality estimate, we identify a single property of the heuristic belief -- weakly vanishing pivotality -- that gives rise to multiple stable equilibria in which elections are nearly tied. In contrast, strongly vanishing pivotality (as in the standard Calculus of Voting model) yields a unique, trivial equilibrium where only zero-cost voters participate as the population grows. We then characterize when nontrivial equilibria satisfy a version of the Jury Theorem: below a sharp threshold, the majority-preferred candidate wins with probability approaching one; above it, both candidates either win with equal probability.

翻译：著名的孔多塞陪审团定理指出，在多数决规则下，随着人口增长，两个备选方案中较优者被选中的概率趋近于一。我们研究了一个非对称情境，其中选民面临不同的参与成本，并共享一个关于其关键性（即影响结果的能力）的可能启发式信念。在一个成本投票模型中，若选民认为其参与成本高于其关键性估计则会选择弃权，我们识别出启发式信念的一个单一属性——弱渐消关键性——该属性导致了多个稳定均衡，在这些均衡中选举结果近乎平局。相比之下，强渐消关键性（如标准投票演算模型所示）则会产生一个唯一的平凡均衡，即随着人口增长，仅零成本选民参与投票。随后，我们刻画了非平凡均衡在何种情况下满足陪审团定理的一个版本：低于一个尖锐阈值时，多数偏好的候选人以概率趋近于一获胜；高于该阈值时，两位候选人获胜概率相等。