弱序的单峰一致性很容易
Single-Peaked Consistency for Weak Orders Is Easy
摘要：
在经济学和社会选择中，单峰性是最重要和最常被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。在弱偏好序中，无差异性必须是传递性的。我们发现，单峰弱序的一致性是在P为三个不同的变种的单峰弱序。具体来说，我们认为黑色的原始定义的单峰弱订单，黑色的定义单一平台的偏好，和存在模型最近推出的Lackner。我们通过将这些单峰一致性问题中的每一个转化为确定0-1矩阵是否具有连续1属性的问题来完成我们的结果。
英文摘要：
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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