Linear Voting Rules
研究了在自愿参与且成本高昂、无货币转移时，社会如何在两个备选方案间选择，发现使用线性投票规则（投票权重因方案而异，加权和低于阈值则默认方案胜出）是功利最优的，且自愿参与比强制参与更能提升福利。
How should a society choose between two social alternatives if participation in the decision process is voluntary and costly, and monetary transfers are not feasible? Assuming symmetric independent private values, we show that it is utilitarian‐optimal to use a linear voting rule: votes get alternative‐dependent weights, and a default obtains if the weighted sum of votes stays below some threshold. Any combination of weights and threshold can be optimal. A standard quorum rule can be optimal only when it yields the same outcome as a linear rule. A linear rule is called upper linear if the default is upset at every election result that meets the threshold exactly. We develop a perturbation method to characterize equilibria of voting rules in the case of small participation costs and show that leaving participation voluntary increases welfare for any two‐sided upper linear rule that is optimal under compulsory participation.