[Paper Review] Alleviating partisan gerrymandering: can math and computers help to eliminate wasted votes?

Tanima Chatterjee, Bhaskar DasGupta+3 more|arXiv (Cornell University)|Apr 27, 2018

Game Theory and Voting Systems16 references3 citations

TL;DR

This paper proposes a fast local search algorithm to reduce the efficiency gap—a measure of partisan gerrymandering—by reconfiguring congressional district maps in Texas, Virginia, Wisconsin, and Pennsylvania. It demonstrates that the efficiency gap can be significantly reduced (e.g., from 23.80% to 8.64% in Pennsylvania) while preserving seat allocation, showing that practical redistricting with fairer vote-to-seat ratios is computationally feasible despite theoretical hardness.

ABSTRACT

Partisan gerrymandering is a major cause for voter disenfranchisement in United States. However, convincing US courts to adopt specific measures to quantify gerrymandering has been of limited success to date. Recently, Stephanopoulos and McGhee introduced a new and precise measure of partisan gerrymandering via the so-called "efficiency gap" that computes the absolutes difference of wasted votes between two political parties in a two-party system. Quite importantly from a legal point of view, this measure was found legally convincing enough in a US appeals court in a case that claims that the legislative map of the state of Wisconsin was gerrymandered; the case is now pending in US Supreme Court. In this article, we show the following: (a) We provide interesting mathematical and computational complexity properties of the problem of minimizing the efficiency gap measure. To the best of our knowledge, these are the first non-trivial theoretical and algorithmic analyses of this measure of gerrymandering. (b) We provide a simple and fast algorithm that can "un-gerrymander" the district maps for the states of Texas, Virginia, Wisconsin and Pennsylvania by bring their efficiency gaps to acceptable levels from the current unacceptable levels. Our work thus shows that, notwithstanding the general worst case approximation hardness of the efficiency gap measure as shown by us,finding district maps with acceptable levels of efficiency gaps is a computationally tractable problem from a practical point of view. Based on these empirical results, we also provide some interesting insights into three practical issues related the efficiency gap measure. We believe that, should the US Supreme Court uphold the decision of lower courts, our research work and software will provide a crucial supporting hand to remove partisan gerrymandering.

Motivation & Objective

• To analyze the computational complexity of minimizing the efficiency gap, a recently proposed measure of partisan gerrymandering.
• To develop and test a practical algorithm that can 'un-gerrymander' real-world district maps by reducing the efficiency gap.
• To evaluate whether minimizing the efficiency gap leads to fairer electoral outcomes without altering seat shares.
• To provide empirical evidence that efficient, fair redistricting is computationally tractable in real-world scenarios.
• To support potential judicial adoption of the efficiency gap by demonstrating its feasibility and practicality.

Proposed method

• Formalizing the efficiency gap minimization problem as a combinatorial optimization task.
• Designing a local search algorithm that applies targeted, semi-random perturbations to existing district maps to reduce wasted votes.
• Using a greedy strategy to iteratively improve the efficiency gap by relocating precincts between adjacent districts.
• Validating the algorithm on real 2012 election data from Texas, Virginia, Wisconsin, and Pennsylvania.
• Preserving contiguity and population parity constraints during district reconfiguration.
• Evaluating performance based on normalized efficiency gap reduction and seat distribution stability.

Experimental results

Research questions

• RQ1 Can the efficiency gap be significantly reduced in real-world gerrymandered districts using a computationally efficient algorithm?
• RQ2 Does minimizing the efficiency gap alter the seat allocation between political parties in existing maps?
• RQ3 How do compactness and district shape change when the efficiency gap is minimized without explicitly optimizing for compactness?
• RQ4 To what extent do original gerrymandered maps deviate from random configurations, suggesting intentional manipulation?
• RQ5 Is the efficiency gap a practical and implementable standard for redistricting in U.S. courts?

Key findings

• The efficiency gap was reduced from 14.76% to 3.80% in Wisconsin, with no change in seat allocation (3 Democrats, 5 Republicans).
• In Texas, the efficiency gap dropped from 4.09% to 3.33%, maintaining the same 12-24 seat split.
• Virginia’s efficiency gap fell from 22.25% to 3.61%, increasing Democratic representation from 3 to 5 seats.
• Pennsylvania’s efficiency gap decreased from 23.80% to 8.64%, shifting representation from 5-13 to 6-12 seats.
• Despite no explicit compactness constraint, the new maps in Virginia showed fewer oddly shaped districts than the original gerrymandered plan.
• The algorithm achieved substantial efficiency gap reductions in under a minute per state, indicating strong practical scalability.