树的单交叉性
The single-crossing property on a tree
摘要：
将经典的单交性质推广到树上的单交性质，得到了构造Condorcet域的新方法，该域是线性序的集合，具有由这些序组成的每个剖面具有传递多数关系的性质.我们证明，对于任何树存在的配置文件是单交叉的树，而且，树是最小的，在这方面至少有一个这样的配置文件。最后，我们提供了一个多项式时间的算法来识别是否一个给定的配置文件是单交叉关于一些树。我们还表明，发现赢家Chamberlin-Courant规则是多项式的配置文件是单交叉的树木。
英文摘要：
We generalize the classical single-crossing property to single-crossing property on trees and obtain new ways to construct Condorcet domains which are sets of linear orders which possess the property that every profile composed from those orders have transitive majority relation. We prove that for any tree there exist profiles that are single-crossing on that tree; moreover, that tree is minimal in this respect for at least one such profile. Finally, we provide a polynomial-time algorithm to recognize whether or not a given profile is single-crossing with respect to some tree. We also show that finding winners for Chamberlin-Courant rule is polynomial for profiles that are single-crossing on trees.
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