Econ Papers Daily / 期刊论文
受限效用函数集合上的防策略随机社会选择
Strategyproof randomized social choice for restricted sets of utility functions
摘要
Social decision schemes (SDSs) map the voters’ preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (Econometrica 45(3):665–681, 1977) has characterized the set of SDSs that are strategyproof with respect to all utility functions and his result implies that all such SDSs are either unfair to the voters or alternatives, or they require a significant amount of randomization. To circumvent this negative result, we propose the notion of U -strategyproofness which postulates that only voters with a utility function in a predefined set U cannot manipulate. We then analyze the tradeoff between U -strategyproofness and various decisiveness notions that restrict the amount of randomization of SDSs. In particular, we show that if the utility functions in the set U value the best alternative much more than other alternatives, there are U -strategyproof SDSs that choose an alternative with probability 1 whenever all but k voters rank it first. On the negative side, we demonstrate that U -strategyproofness is incompatible with Condorcet-consistency if the set U satisfies minimal symmetry conditions. Finally, we show that no ex post efficient and U -strategyproof SDS can be significantly more decisive than the uniform random dictatorship if the voters are close to indifferent between their two favorite alternatives. Similar content being viewed by others
中文摘要
社会决策方案（SDSs）将选民对多个备选方案的偏好映射为这些备选方案上的概率分布。在开创性成果中，Gibbard（Econometrica 45(3):665–681, 1977）刻画了所有效用函数下均满足策略防护性的SDS集合，其结论表明此类SDS要么对选民或备选方案不公，要么需要大量随机化。为规避这一负面结论，我们提出U-策略防护性概念，该概念仅要求具有预设集合U中效用函数的选民无法操纵。进而分析U-策略防护性与限制SDS随机化程度的各种决定性概念之间的权衡关系。特别地，我们证明：若集合U中的效用函数对最优备选方案的估值远高于其他方案，则存在U-策略防护性SDS，当除k名选民外的所有选民均将某方案列为首选时，该方案以概率1被选中。在负面结论方面，我们证明当集合U满足最小对称性条件时，U-策略防护性与孔多塞一致性不可兼容。最后，我们证明若选民对其最偏好的两个备选方案近乎无差异，则不存在比均匀随机独裁更具显著决定性的事后有效且U-策略防护性SDS。