Mathematical Sciences: Mathematics and the Theory of Voting

这个项目将致力于基本问题的数学方面，“什么投票系统是最公平的？”这项调查将使用同调理论的方法来研究多国选举中选民偏好的流动。不同的数学领域，如“凸几何”、NP-完备性、维度理论和同调理论，都将在这一分析中发挥作用。本项目期望从阿罗不可能定理的意义上阐明“选民悖论”的本质，它是完全公平选举制度存在的主要障碍。为了决定一个系统的公平性，将建立几个新的绝对和相对的“权力”或玩家影响力的衡量标准。

This project will be devoted to the mathematical aspects of the fundamental question, "what voting systems are most fair?". The investigation will use methods of homology theory to study the flow of voter preference in a multicandidate election. Mathematical fields as diverse as "convex geometry" NP- completeness, dimension theory, and homology theory will play a role in this analysis. This project expects to clarify the nature of the "voter's paradox" which is the main impediment to the existence of completely fair election systems in the sense of Arrow's Impossibility Theorem. Several new absolute and relative measures of "power", or influence of the players, will be established in order to decide the fairness of a system.