Implementing partisan symmetry: Problems and paradoxes

TL;DR

This paper critically examines existing measures of partisan symmetry, revealing mathematical issues and practical problems through analysis and case studies, which question their reliability for evaluating redistricting fairness.

Contribution

The paper identifies fundamental mathematical flaws in current partisan symmetry metrics and demonstrates their limitations using real-world voting data from multiple states.

Findings

Mathematical properties of symmetry metrics are surprising and problematic.

Case studies show issues with current measures in real voting patterns.

Concerns raised about the reliability of existing partisan symmetry scores.

Abstract

We consider the measures of partisan symmetry proposed for practical use in the political science literature, as clarified and developed in Katz, King, and Rosenblatt (2020). Elementary mathematical manipulation shows the symmetry metrics to have surprising properties that call their meaningfulness into question. To accompany the general analysis, we study measures of partisan symmetry with respect to recent voting patterns in Utah, Texas, and North Carolina, flagging problems in each case. Taken together, these observations should raise major concerns about the available techniques for quantitative scores of partisan symmetry -- including the mean-median score, the partisan bias score, and the more general "partisan symmetry standard" -- as the decennial redistricting begins.