度量空间的康多塞维度
The Condorcet Dimension of Metric Spaces
AI总结：
研究在二维空间中基于接近投票的选举，证明康多塞维度在曼哈顿范数和无穷范数下最大为3。
摘要：
康多塞获胜集是指一个候选人集合，使得没有其他候选人在所有成员上被至少一半的选民更偏好。康多塞维度是该集合的最小基数，已知其在候选人数量上是对数级的。我们研究了在二维空间中，选民和候选人位置，并基于接近投票确定偏好情况的选举情况。我们的主要结果是，在曼哈顿范数和无穷范数下，康多塞维度至多为3，这两种范数在选举系统中是自然的度量。
英文摘要：
A Condorcet winning set is a set of candidates such that no other candidate is preferred by at least half the voters over all members of the set. The Condorcet dimension, which is the minimum cardinality of a Condorcet winning set, is known to be at most logarithmic in the number of candidates. We study the case of elections where voters and candidates are located in a $2$-dimensional space with preferences based upon proximity voting. Our main result is that the Condorcet dimension is at most $4$, under both the Manhattan norm and the infinity norm, which are natural measures in electoral systems. We also prove that any set of voter preferences can be embedded into a metric space of sufficiently high dimension for any $p$-norm, including the Manhattan and infinity norms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
