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Characterising scoring rules by their solution in iteratively undominated strategies
Economic Theory ( IF 1.423 ) Pub Date : 2021-04-09 , DOI: 10.1007/s00199-021-01353-w
Christian Basteck

We characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.



中文翻译:

通过迭代无控制策略中的解决方案来表征评分规则

我们根据选民有策略地投票,采用反复无主的策略时执行的社会选择对应关系来描述投票程序的特征。在具有三名候选人的选举中,Borda规则是唯一的位置计分规则,可以满足全体一致U)(即,在一致通过时选出候选人),并且在消除最差候选人MEW后即成为多数派(即,如果存在一个一致不喜欢的候选,多数优选的其他两个中当选)。在更广泛的规则类别中,批准投票的特征是一个单一公理,该公理同时包含UMEW,但比Condorcet一致性弱(CON)-这是唯一的直接机制评分规则,在消除了Pareto主导的候选人MEPD之后成为多数派(即,如果有Pareto主导的候选人,则在其他两个候选人中选出多数优先);在满足MEPD的所有有限评分规则中,批准投票是最决定性的。但是,它没有令人满意的单调性:为某个偏好配置而选出的候选人一旦获得进一步的知名度,可能会失去竞选资格。相比之下,Borda规则是满足UMEW单调性MON)的唯一直接机制评分规则)。没有满足MEPDMON的直接机制评分规则,也没有满足CON的有限评分规则。

更新日期:2021-04-09
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