Towards a Comprehensive Scale for Measuring Partisan Gerrymandering: Integrating Demographic Uniformity and Border Effects

The study of the quantification of partisan Gerrymandering is still a contentious topic in mathematics and statistics. Though a host of techniques have been developed, each having certain strengths and weaknesses, no definitive universally applicable method has been arrived at. This study presents a succinct analysis of leading scales developed to quantify Gerrymandering, primarily focusing on mathematical foundations, empirical results, and weaknesses of each. This study borrows from a comparative study carried out in Warrington (2019) (Ref. 1) and Buzas-Warrington (2021) (Ref. 2) to arrive at leading strengths and weaknesses of scales like Efficiency Gap, Declination, Partisan Bias, and Mean Median Difference. This study uses appropriately developed scales to devise a new method, primarily focusing on demographic unity in neighboring geospatial districts, as a secondary consideration, focusing on border lengths. This method is devised to integrate leading strengths of existing scales developed, along with addressing primarily leading weaknesses, in recording finer levels of Gerrymandering that rely on demographic disunities. The method developed is presented in detail, outlining mathematical expressions, conceptual foundations, and empirical studies to validate. This study will present, through theoretical analysis and simulation studies, a method to quantify Gerrymandering as a far more precise index.