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学家联手研究及时和重要的问题，包括立法机构和多人选区的公平代表--在这些选区中，多名候选人被选举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。首席调查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不公正地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，特别是在公平和公平的数学方面，这一领域与历史上的黑人大学莫尔豪斯学院的社会正义目标密切相关。该项目将推进投票和代表数学的研究。独立选举委员会审查有多名成员的选区以及支持选举方法的潜力，以产生公平的代表。这项工作的一个方面是通过空间模型来考虑群体中个人的公平性，在空间模型中，选民的理想由m维空间中的点来表示，其中m维空间中的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，但对于同时当选多名候选人的多成员选区来说，研究较少。该小组将发展和扩展关于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来自西蒙斯·劳弗数学科学研究所在算法、公平和公平科学计划期间与其他数学科学家建立的研究合作。该项目由数学科学部基础设施计划和历史上的黑人学院和大学-卓越研究计划(HBCU-EIR)联合资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.