Single-Peaked Consistency for Weak Orders Is Easy

Zack Fitzsimmons
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引用次数: 17

Abstract

In economics and social choice single-peakedness is one of the most important and commonly studied models for preferences. It is well known that single-peaked consistency for total orders is in P. However in practice a preference profile is not always comprised of total orders. Often voters have indifference between some of the candidates. In a weak preference order indifference must be transitive. We show that single-peaked consistency for weak orders is in P for three different variants of single-peakedness for weak orders. Specifically, we consider Black's original definition of single-peakedness for weak orders, Black's definition of single-plateaued preferences, and the existential model recently introduced by Lackner. We accomplish our results by transforming each of these single-peaked consistency problems to the problem of determining if a 0-1 matrix has the consecutive ones property.
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弱订单的单峰一致性很容易
在经济学和社会选择中,单峰性是最重要和最常研究的偏好模型之一。众所周知,总订单的单峰一致性在p中。然而,在实践中,偏好配置文件并不总是由总订单组成。选民往往对某些候选人漠不关心。在弱偏好顺序中,无差异必须是可传递的。我们证明了弱阶的单峰一致性对于弱阶的三种不同的单峰一致性是在P内的。具体来说,我们考虑了Black对弱订单单峰性的原始定义,Black对单平台偏好的定义,以及Lackner最近引入的存在主义模型。我们通过将这些单峰一致性问题转化为确定0-1矩阵是否具有连续1性质的问题来完成我们的结果。
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