RUI: Mathematical Analysis of Voting and Representation in Multimember Electoral Districts

这个项目的首席研究员将对投票和代表进行数学分析，将他的研究与教育活动结合起来，在这些活动中，他将指导本科生的研究项目，并开发一门关于政治数学模型的课程。研究部分应用理论模型和分析结果来描述投票和组成代表机构的方法的相对公平性。P.I.审查多个选区的投票制度，重点是累积投票的方法，寻找可预测的均衡条件，并分析它们的潜力，使少数族裔人口能够在代表机构中获得公平份额。除了应用不平等的衡量标准和尽量减少失实陈述的最优化方法外，该项目还需要大力发展普遍选举的空间建模理论。P.I.S理论将描述和分析选民倾向、选民政策理想的分布以及多人选区中的候选人行为。在与政治学同事的合作下，P.I.将准备随后的工作，分析选举和实验的数据，以解决该理论对经验数据的影响，并使用经验结果为理论模型提供依据。此外，P.I.将指导本科生开展与他自己的工作相关的研究项目，他将开发一门课程，数学与公平：政治和经济系统的应用，在这门课程中，来自数学、政治学和经济学的学生将研究关于公平和不平等衡量标准的政治现象的形式理论和模型。这个项目建立在关于投票和代表理论的知识基础上。P.I.S的工作将有助于量化选举方法对民众、群体和个人的公平性。特别关注累积投票法，将其与其他选举方法进行比较，以实现公平代表，特别是少数群体，因为在某些投票方法下，少数群体容易被剥夺代表权。这项研究将为公众讨论多人地区选举方式的相对公平性提供一定的数学基础。这一数学基础还可以为考虑选举方法的政策制定者和司法官员提供服务，以解决争端，如涉嫌违反《选举权法》的行为。与该项目相关的许多学生将从研究和课程经验中受益，这些研究和课程经验应该会激励和帮助他们为数学和社会科学的研究生学习和职业生涯做好准备。

The principal investigator of this project will conduct mathematical analysis of voting and representation, integrating his research with educational activities in which he will direct undergraduate student research projects and develop a course on mathematical models in politics. The research component applies theoretical models and analytical results to describe the comparative fairness of methods of voting and composing representative bodies. The P.I. examines voting systems in multimember electoral districts, with emphasis on the method of cumulative voting, searching for predictive equilibrium conditions and analyzing their potential to enable a minority population to achieve a fair share of a representative body. The project requires considerable development of the theory of spatial modeling of at-large elections, in addition to application of measures of inequality and of optimization methods to minimize misrepresentation. The P.I.'s theory will describe and analyze voter tendencies, distributions of voters' policy ideals, and candidate behaviors in multimember electoral districts. In collaboration with political science colleagues, the P.I. will prepare for subsequent work analyzing data from elections and experiments so as to address the implications of the theory on the empirical data and use the empirical results to inform the theoretical models. Additionally, the P.I. will guide undergraduates on research projects interrelated with his own work, and he will develop a course, Mathematics and Fairness: Applications to Political and Economic Systems, in which students from mathematics, political science, and economics will examine formal theory and models of political phenomena with respect to measures of fairness and inequity.This project builds on the body of knowledge about the theory of voting and representation. The P.I.'s work will help to quantify fairness of election methods to populations and to groups and individuals therein. Particular attention is devoted to the method of cumulative voting, comparing its potential against other election methods to make fair representation possible, especially to minority populations, who are vulnerable to denial of representation under certain voting methods. The research will provide some mathematical basis for public discourse about the relative fairness of multimember district election methods. This mathematical basis also can serve policy makers and judicial officials who consider election methodology in resolving disputes, such as alleged violations of the Voting Rights Act. Numerous students associated with this project will benefit from research and course experiences that should inspire and help prepare them for graduate study and careers in the mathematical and social sciences.