单峰选民的不完全偏好
Incomplete Preferences in Single-Peaked Electorates
摘要：
不完整的偏好很可能出现在现实世界的偏好聚合场景。本文讨论了不完全偏好曲线是否为单峰曲线。这是有价值的信息，因为许多棘手的投票问题变得易于处理的单峰偏好。我们证明了识别单峰的问题是\NP -完全的不完整的配置文件组成的偏序。尽管这个棘手的结果，我们发现几个多项式时间算法合理的限制设置。特别是，我们给出了多项式时间识别算法的弱订单，这可以被看作是与冷漠的偏好。
英文摘要：
Incomplete preferences are likely to arise in real-world preference aggregation scenarios. This paper deals with determining whether an incomplete preference profile is single-peaked. This is valuable information since many intractable voting problems become tractable given single-peaked preferences. We prove that the problem of recognizing single-peakedness is \NP-complete for incomplete profiles consisting of partial orders. Despite this intractability result, we find several polynomial-time algorithms for reasonably restricted settings. In particular, we give polynomial-time recognition algorithms for weak orders, which can be viewed as preferences with indifference.
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