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Varieties of failure of monotonicity and participation under five voting methods

机译：五种投票方式下单调性和参与性失败的种类

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摘要

In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can occur. Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity.
机译：在投票理论中，单调性是公理，选民对候选人的排名提高不会导致原本会赢的候选人输掉。参与公理指出，对选民偏好的真诚报道不会导致该选民认为其结果不如该选民不参与所产生的结果更具吸引力。本文在可能导致单调性或参与性失败的情况类型中确定了三种二进制区别。三项区别中的两项适用于单调性，而其中一项和第三项适用于参与。单调性独特的区别在于，排名改变的选民显示出单调性是好是坏。参与所独有的区别是边缘参与的选民是导致其第一选择失利还是其最终选择获胜。重叠的区别是，选民排名的轮廓是Condorcet赢家还是排名靠前的周期。本文追溯了投票方法中所有结果组合特征的出现，这些特征组合可能表现出单调性失败。

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