Districting that minimizes partisan bias

Aaron Brick,Cameron Brick

doi:10.1057/s41599-021-00809-7

Abstract

The shapes of electoral districts determine how votes translate into seats. When districts favor certain political parties, electoral results can be disproportionate and the public may lose faith in the political process. Disagreement about appropriate district shapes is subjective, rarely resolved, and often leads to lawsuits. Previously, many authors have called for objective districting criteria. We offer a novel synthesis of models that enables the proactive comparison of district maps, by relating a planar graph partition, the single-member plurality rule, the maximin decision rule, and any agreed measure of partisan bias with a territorial map and historical vote results. Historical vote totals avoid the complexity and uncertainty associated with counterfactual models of vote swing. Districting plans could be objectively compared on such criteria as party proportionality or compact shape to reject plans with worse bias. Objective tools to reduce partisan bias in district maps could boost collaborative participation, increase perceptions of fairness and justice, and reduce costs.

Highlights

Drawing fair constituency boundaries is an outstanding problem in political science
Model We present a novel definition of districting criteria to minimize partisan bias that is suitable for combinatorial optimization
This system combines the concepts of the planar graph partition, the single-member plurality election model, a measure of partisanship, the maximin decision rule, a territorial map, and historical vote results

Summary

Introduction

Drawing fair constituency boundaries is an outstanding problem in political science. First-past-the-post elections, in which different maps create different outcomes for the same vote, produce partisan bias. One leading model for electoral fairness is partisan symmetry (Katz et al, 2020) This principle suggests that two parties should receive the same number of seats if they receive the same proportion of the vote. The cosine of the angle between the seat and vote vectors is one in the case of perfect proportionality This model is among the best available measures of partisan electoral bias. Model We present a novel definition of districting criteria to minimize partisan bias that is suitable for combinatorial optimization This system combines the concepts of the planar graph partition, the single-member plurality election model, a measure of partisanship, the maximin decision rule, a territorial map, and historical vote results. Public-key cryptography or a blockchain could establish proof of authorship

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