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Rationalizations of Condorcet-consistent rules via distances of hamming type

机译：通过汉明类型距离对Condorcet一致规则进行合理化

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摘要

In voting, the main idea of the distance rationalizability framework is to view the voters’ preferences as an imperfect approximation to some kind of consensus. This approach, which is deeply rooted in the social choice literature, 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 of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance-rationalized. In this article, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance-rationalize the Young rule and Maximin using distances similar to the Hamming distance. It has been claimed that the Young rule can be rationalized by the Condorcet consensus class and the Hamming distance; we show that this claim is incorrect and, in fact, this consensus class and distance yield a new rule, which has not been studied before. We prove that, similarly to the Young rule, this new rule has a computationally hard winner determination problem.
机译：在投票中，距离合理化框架的主要思想是将选民的偏好视为某种共识的不完美近似。这种方法深深扎根于社会选择文献中，它允许人们通过共识性的选举和距离级别来定义（“合理化”）投票规则：如果候选人名列第一，则被认为是选举获胜者。最近一次（相对于给定距离）共识选举。众所周知，许多经典的投票规则都可以进行距离合理化。在本文中，我们提供了一些与Condorcet一致的投票规则的距离合理性的新结果。特别是，我们使用类似于汉明距离的距离对Young规则和Maximin进行合理化距离分配。据称，可以通过Condorcet共识类和汉明距离来合理化Young规则；我们证明了这种说法是不正确的，并且实际上，这种共识类别和距离产生了一条新规则，该规则以前从未研究过。我们证明，与Young规则类似，该新规则也存在计算困难的获胜者确定问题。

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  • 来源
    《Social Choice and Welfare》 |2012年第4期|891-905|共15页
  • 作者

    Edith Elkind; Piotr Faliszewski; Arkadii Slinko;

  • 作者单位

    Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637 371 Singapore;

    Department of Computer Science AGH University of Science and Technology Kraków Poland;

    Department of Mathematics University of Auckland Auckland New Zealand;

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