PRIMES: Researching and Teaching Mathematics of Fairness and Equity

在过去的几十年里，正式的数学模型为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一起研究了及时和重要的问题，包括立法机构和多成员选区的公平代表权——在这些选区中，多个候选人而不是一个人被选举来代表一个司法管辖区——以产生更能反映投票人口的立法机构。首席研究员将对公共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为党派得失而重新划分选区的反应。除了这种学术研究之外，该项目还将增加黑人男性在课程作业和合作数学研究中的参与度，特别是在公平与公平的数学方面，这一领域与莫尔豪斯学院（Morehouse College）的社会正义目标密切相关，莫尔豪斯学院是一所历史悠久的黑人学院。这个项目将推进投票和代表的数学研究。民意调查委员会审查多成员选区的潜力，连同支持的选举方法，以产生公平的代表权。这项工作的一个方面是通过空间模型考虑对人口中个人的公平，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。政治中的空间模型得到了很好的研究，但对于同时选举多个候选人的多成员地区，研究较少。指数将发展和扩展多成员地区选举空间模型的理论和实验工作。除了这一推动力，其他研究成果将更广泛地来自与其他数学科学家在Simons Laufer数学科学研究所的算法、公平和公平科学项目中建立的研究合作。该项目由数学科学部基础设施项目和传统黑人学院和大学卓越研究项目共同资助。该奖项反映了美国国家科学基金会的法定使命，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.