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A measure of distance between judgment sets

机译:判断集之间的距离的度量

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摘要

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming’s metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in ${A cap B}$ jointly imply that the propositions in A?B share the same truth value, then the disagreement between A and B over those propositions in A?B should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings.
机译:在关于判断聚合的文献中,一个重要的开放性问题是如何测量任意两个判断集之间的距离。这与社会选择问题有关:如果两个人持有不同的信仰,那么我们可能希望找到介于两者之间的折衷方案。我们提出了一组唯一确定距离度量的公理。此度量不同于广泛使用的汉明度量。海明度量标准与我们的度量标准之间的差异归结为一个公理。给定判断集A和B,这个公理说,如果$ {A cap B} $中的命题共同暗示A?B中的命题具有相同的真值,那么A和B之间的分歧就在于A?B中的命题。 B应被视为单一分歧。我们考虑将指标应用到判断汇总中,并使用该指标来衡量偏好排名之间的距离。

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  • 来源
    《Social Choice and Welfare》 |2012年第4期|855-867|共13页
  • 作者

    Conal Duddy; Ashley Piggins;

  • 作者单位

    Government of Ireland Scholar J.E. Cairnes School of Business and Economics National University of Ireland Galway University Road Galway Ireland;

    J.E. Cairnes School of Business and Economics National University of Ireland Galway University Road Galway Ireland;

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  • 正文语种 eng
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