Abstract

We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles, and we also demonstrate how to choose weights that realize desirable results from a given profile. The analysis ultimately boils down to thinking about positional voting systems in terms of doubly stochastic matrices.

中文翻译：

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位置投票和双重随机矩阵

摘要

我们提供有关位置投票系统类别中固定配置文件可能产生的几种结果的基本证明。我们的论点实现了对矛盾分布图的简单而明确的构造，并且我们还演示了如何从给定分布图中选择实现理想结果的权重。分析最终归结为关于双重随机矩阵的位置投票系统的思考。