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Rationalizations of Condorcet-Consistent Rules via Distances of Hamming Type

机译:通过汉明距离合理化Condorcet一致规则   类型

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摘要

The main idea of the {\em distance rationalizability} approach to view thevoters' preferences as an imperfect approximation to some kind of consensus isdeeply rooted in social choice literature. It allows one to define("rationalize") voting rules via a consensus class of elections and a distance:a candidate is said to be an election winner if she is ranked first in one ofthe nearest (with respect to the given distance) consensus elections. It isknown that many classic voting rules can be distance rationalized. In thispaper, we provide new results on distance rationalizability of severalCondorcet-consistent voting rules. In particular, we distance rationalizeYoung's rule and Maximin rule using distances similar to the Hamming distance.We show that the claim that Young's rule can be rationalized by the Condorcetconsensus class and the Hamming distance is incorrect; in fact, these consensusclass and distance yield a new rule which has not been studied before. We provethat, similarly to Young's rule, this new rule has a computationally hardwinner determination problem.
机译:{\ em距离合理性}方法的主要思想是将选民的偏好视为对某种共识的不完美近似,这深深扎根于社会选择文献中。它允许人们通过协商一致的选举类别和距离来定义(“合理化”)投票规则:如果候选人在最近的(相对于给定的距离)共识选举中排名第一,则被认为是选举获胜者。 。众所周知,许多经典的投票规则都可以实现距离合理化。在本文中,我们提供了几种一致的投票规则的距离合理性的新结果。特别是,我们使用与汉明距离相似的距离来使杨氏规则和马克西姆规则合理化。我们证明,可以通过Condorcetconsensus类合理化杨氏规则并且汉明距离是不正确的。实际上,这些共识类和距离产生了一个新的规则,这是以前没有研究过的。我们证明,与Young规则类似,该新规则具有计算上难以确定的确定问题。

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