投票理论中弱策略证明性的探讨
Exploring Weak Strategy-Proofness in Voting Theory
摘要：
投票是个人偏好的集合，以选择获胜的替代方案。获胜者的选择是通过投票规则来完成的，例如，排序表决、多数表决、多数原则、赞成表决。应采用哪种投票规则？在社会选择理论中，投票规则的理想性质被表示为要满足的公理。本论文主要探讨选民策略操纵的公理。有时，选民可能故意歪曲他们的真实偏好，以改变对自己有利的结果。例如，在多数原则中，如果选民知道他们的首选候选人会输，那么他们可能会投票给他们的第二选择候选人，以避免更不理想的结果。当没有一个选民联盟能够在战略上操纵时，那么投票规则就被认为满足了战略证明性公理。一个限制性较小的公理是弱战略证明（如Dasgupta和Maskin（2019）所定义的），它允许除最小联盟外的所有联盟进行战略操纵。在一定的直观条件下，Dasgupta和Maskin（2019）证明了满足策略证明性的投票规则只有排序投票和多数规则。在我的论文中，我推广了他们的结果，通过证明排序投票和多数规则仍然是唯一满足弱策略证明的投票规则。
英文摘要：
Voting is the aggregation of individual preferences in order to select a winning alternative. Selection of a winner is accomplished via a voting rule, e.g., rank-order voting, majority rule, plurality rule, approval voting. Which voting rule should be used? In social choice theory, desirable properties of voting rules are expressed as axioms to be satisfied. This thesis focuses on axioms concerning strategic manipulation by voters. Sometimes, voters may intentionally misstate their true preferences in order to alter the outcome for their own advantage. For example, in plurality rule, if a voter knows that their top-choice candidate will lose, then they might instead vote for their second-choice candidate just to avoid an even less desirable result. When no coalition of voters can strategically manipulate, then the voting rule is said to satisfy the axiom of Strategy-Proofness. A less restrictive axiom is Weak Strategy-Proofness (as defined by Dasgupta and Maskin (2019)), which allows for strategic manipulation by all but the smallest coalitions. Under certain intuitive conditions, Dasgupta and Maskin (2019) proved that the only voting rules satisfying Strategy-Proofness are rank-order voting and majority rule. In my thesis, I generalize their result, by proving that rank-order voting and majority rule are surprisingly still the only voting rules satisfying Weak Strategy-Proofness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
