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

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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.