论文标题

连接箭头定理,投票理论和旅行销售人员问题

Connecting Arrow's Theorem, voting theory, and the traveling salesperson problem

论文作者

Saari, Donald

论文摘要

大多数对成对投票的问题是箭头的定理所代表的,那些发现封闭路径长度的人所捕获的封闭路径(TSP)似乎没有任何共同点。实际上,它们是连接的。如图所示,成对投票和TSP的版本共享相同的域,其中可以通过将其限制为互补区域以消除外部术语来简化每个系统。这样做的核心是Borda Count,其中表明其结果最准确地反映了选民的偏好。

Problems with majority voting over pairs as represented by Arrow's Theoremand those of finding the lengths of closed paths as captured by the Traveling Salesperson Problem (TSP) appear to have nothing in common. In fact, they are connected. As shown, pairwise voting and a version of the TSP share the same domain where each system can be simplified by restricting it to complementary regions to eliminate extraneous terms. Central for doing so is the Borda Count, where it is shown that its outcome most accurately refects the voter preferences.

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