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Monotonicity properties and their adaptation to irresolute social choice rules

机译：单调性及其对不确定的社会选择规则的适应

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摘要

What is a monotonicity property? How should such a property be recast, so as to apply to voting rules that allow ties in the outcome? Our original interest was in the second question, as applied to six related properties for voting rules: monotonicity, participation, one-way monotonicity, half-way monotonicity, Maskin monotonicity, and strategy-proofness. This question has been considered for some of these properties: by Peleg and Barberà for monotonicity, by Moulin and Pérez et al, for participation, and by many authors for strategy-proofness. Our approach, however, is comparative; we examine the behavior of all six properties, under three general methods for handling ties: applying a set extension principle (in particular, G?rdenfors’ sure-thing principle), using a tie-breaking agenda to break ties, and rephrasing properties via the “t-a-t” approach, so that only two alternatives are considered at a time. In attempting to explain the patterns of similarities and differences we discovered, we found ourselves obliged to confront the issue of what it is, exactly, that identifies these properties as a class. We propose a distinction between two such classes: the “tame” monotonicity properties (which include participation, half-way monotonicity, and strategy proofness) and the strictly broader class of “normal” monotonicity properties (which include monotonicity and one-way monotonicity, but not Maskin monotonicity). We explain why the tie-breaking agenda, t-a-t, and G?rdenfors methods are equivalent for tame monotonicities, and how, for properties that are normal but not tame, set-extension methods can fail to be equivalent to the other two (and may fail to make sense at all).
机译：什么是单调性？应该如何重铸这样的属性，以便将其应用到允许在结果中建立联系的投票规则？我们最初的兴趣是第二个问题，该问题适用于投票规则的六个相关属性：单调性，参与性，单向单调性，中途单调性，Maskin单调性和策略证明性。对于某些特性，已经考虑了这个问题：Peleg和Barberà认为具有单调性，Moulin和Pérez等人则考虑了参与性，许多作者都考虑了策略的可靠性。但是，我们的方法是比较性的。我们使用三种处理联系的通用方法来检查所有六个属性的行为：应用集合扩展原理（特别是G？rdenfors的确定性原理），使用打破平局的议程来打破联系以及通过重新定义属性来重新定义“ tat”方法，因此一次仅考虑两种选择。在试图解释我们发现的相似和差异的模式时，我们发现自己不得不面对将这些属性识别为一类的确切问题。我们建议区分以下两种类别：“ tame”单调性属性（包括参与性，中途单调性和策略验证性）和严格更广泛的“正常”单调性属性类别（其中包括单调性和单向单调性，而不是Maskin单调性）。我们解释了为什么平局打破议程，tat和G？rdenfors方法对于驯服单调性是等效的，以及对于正常但不是驯服的属性，集合扩展方法如何不能等同于其他两种（并且可能完全没有意义）。

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