Analyzing the Effects of Partisan Correlation on Election Outcomes Using Order Statistics

Abstract

The legislative representation of political parties in the United States is dependent not only on way that legislative district boundaries are drawn, but also on the way in which people are distributed across a state. That is, there exists a level of partisan correlation within the spacial distribution of an electorate that affects legislative outcomes. This work aims to study the effect of this partisan clustering on election outcomes and related metrics using analytic models and order statistics. Two models of North Carolina, one with a uniformly distributed electorate and one with a symmetrically clustered electorate, are considered both independently and in comparison. These models are used to study expected election outcomes, the proportionality of legislative representation for given state-wide vote fraction, and the sensitivity of vote share to seat share across different correlation length scales. The findings provide interesting insight into the relationship between district proportionality and legislative proportionality, the extent to which the minority party is expected to be underrepresented in seat share for given state-wide vote share and correlation length, and the extent to which the responsiveness of seat share is dependent on state wide vote share and correlation length.