Econ Papers Daily / 期刊论文
关于投票份额与否决份额规则的序数贝叶斯激励相容性
On the ordinal Bayesian incentive compatibility of vote share and veto share rules
摘要
We study the structure of random ordinal Bayesian incentive compatible (OBIC) rules. We restrict attention to some special class of priors that we call “uniform-like” priors. We consider a class of priors, called top uniform priors: for any two alternatives a and b, a prior is top uniform if the aggregate probability (under the prior distribution) of preferences with respectively a and b at the top are the same. Over the unrestricted domain the uniform prior is a member of this class. We consider a class of random voting rules—random vote share rules, a generalization of plurality rule. For top uniform priors and arbitrary domains, Theorem 4.1 shows that every top monotonic and symmetric random vote share rule is OBIC. Over a domain satisfying some natural “richness” condition, we demonstrate that if a symmetric and strongly top responsive random vote share rule is OBIC with respect to some prior, then that prior must necessarily be a top uniform prior. We also provide some analogous results for veto share rules that are probabilistic generalizations of anti-plurality rule.
中文摘要
我们研究了随机序数贝叶斯激励相容（OBIC）规则的结构。我们关注一类特殊的先验分布，称之为“类均匀”先验。我们考虑一类称为顶部均匀先验的先验：对于任意两个备选方案a和b，若在先验分布下，分别以a和b为顶部的偏好总概率相同，则该先验为顶部均匀先验。在无限制域上，均匀先验属于此类。我们考虑一类随机投票规则——随机投票份额规则，这是多数规则的推广。对于顶部均匀先验和任意域，定理4.1表明，每个顶部单调且对称的随机投票份额规则都是OBIC的。在满足某些自然“丰富性”条件的域上，我们证明，若一个对称且强顶部响应的随机投票份额规则相对于某个先验是OBIC的，则该先验必然为顶部均匀先验。我们还为否决份额规则提供了类似的结果，这些规则是反多数规则的概率推广。