PRIMES: Researching and Teaching Mathematics of Fairness and Equity

在过去的几十年里，正式的数学模型对政治科学的进步做出了越来越大的贡献，这些年来，数学家和经济学家与政治科学家联手研究及时和重要的问题，包括在立法机构和多成员选区中的公平代表性-在这些选区中，多个候选人而不是只有一个候选人当选代表一个司法管辖区-以建立更能反映投票人口的立法机构。首席研究员将为公众和公民话语做出重大贡献，并促进对美国代议制民主本质的理解，包括对州和地方司法管辖区党派得失的选区划分的反应。除了这一学术调查，该项目将增加参与课程和合作数学研究的黑人男子，特别是在公平和公正的数学，一个领域密切相关的莫尔豪斯学院，历史上的黑人大学的社会正义的目标。PI审查了多成员选区的潜力，结合支持选举方法，以产生公平的代表性。这项工作的一个方面是通过空间模型来考虑对人口中个人的公平性，其中选民的理想由m维空间中的点表示，其中“政策空间”中m维点的每个坐标代表公民在特定问题或利益上的立场。政治中的空间模型研究得很好，但对于多个候选人同时当选的多成员区，研究得较少。PI将开发和扩展多成员地区选举空间模型的理论和实验工作。除了这一推力，其他研究成果将更广泛地产生于与其他数学科学家在算法，公平，西蒙斯劳弗数学科学研究所的公平科学计划。该项目由数学科学部和历史上的黑人学院和大学的基础设施计划共同资助-卓越研究该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Over the past several decades, formal mathematical models have contributed increasingly to advances in political science, and over these years mathematicians and economists have joined forces with political scientists to study timely and important issues, including fair representation in legislatures and multimember districts - in which multiple candidates rather than only one are elected to represent a jurisdiction - to produce legislative bodies more reflective of voting populations. The Principal Investigator will make significant contributions to public and civic discourse and advance understanding of the nature of U.S. representative democracy, including responses to the gerrymandering of districts for partisan gain and loss in state and local jurisdictions. Beyond this scholarly inquiry, the project will increase engagement of Black men in coursework and collaborative mathematical research, specifically in the mathematics of fairness and equity, an area closely connected to the social justice aims of Morehouse College, a historically Black college.This project will advance research in the mathematics of voting and representation. The PI examines the potential of multimember electoral districts, in conjunction with supporting election methods, to yield fair representation. One facet of this work is to consider fairness to individuals in a population through spatial models, in which the ideals of voters are represented by points in m-dimensional space where each coordinate of an m-dimensional point in a "policy space" represents the position of the citizen on a particular issue or interest. Spatial models in politics are well studied, but less so for multimember districts with multiple candidates elected simultaneously. The PI will develop and extend theoretical and experimental work on spatial models of multimember district elections. Beyond this thrust, other research results will arise more broadly from research collaborations established with other mathematical scientists during the Algorithms, Fairness, and Equity scientific program at the Simons Laufer Mathematical Sciences Institute.The project is funded jointly by the Infrastructure program of the Division of Mathematical Sciences and the Historically Black Colleges and Universitites-Excellence in Research (HBCU-EiR) Program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.