Optimality and fairness of partisan gerrymandering

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).