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Optimality and fairness of partisan gerrymandering.

Antoine Lagarde1, Tristan Tomala2

  • 1HEC Paris, 1 rue de la Libération, 78351 Jouy-en-Josas, France.

Mathematical Programming
|November 15, 2021
PubMed
Summary

Optimal partisan gerrymandering involves cracking and packing voters to maximize electoral advantage. Fairness measures show gerrymandering strategies are less fair than uniform districting.

Keywords:
Bayesian persuasionDistrictingFairnessGerrymanderingOptimality

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Area of Science:

  • Political Science
  • Mathematics
  • Economics

Background:

  • Partisan gerrymandering aims to manipulate electoral district boundaries for political gain.
  • Key strategies include 'cracking' (spreading opposing voters thinly) and 'packing' (concentrating them in few districts).
  • The problem is influenced by the finite number of districts and voter uncertainty within each district.

Purpose of the Study:

  • To analyze the optimal strategies for partisan gerrymandering under uncertainty.
  • To explore the relationship between gerrymandering, fairness, and the number of districts.
  • To model gerrymandering as a function concavification problem, akin to optimal Bayesian persuasion.

Main Methods:

  • Mathematical modeling of the gerrymandering problem.
  • Analysis of optimal gerrymandering payoff as uncertainty decreases and district number increases.
  • Introduction of a fairness measure to compare different districting strategies.

Main Results:

  • Optimal gerrymandering payoff increases with reduced uncertainty and a larger number of districts.
  • In the limit of infinite districts, the problem simplifies to function concavification.
  • Optimal gerrymandering strategies are shown to be less fair than uniform districting.

Conclusions:

  • The study provides a mathematical framework for understanding optimal partisan gerrymandering.
  • Fairness is inversely related to the effectiveness of gerrymandering strategies.
  • Optimal gerrymandering is closer to 'full cracking' (uniform districting, most unfair) than 'full packing' (community districting, very fair).