A Relative Efficiency Gap formula for measuring Political Gerrymandering

TL;DR

This paper introduces a new relative efficiency gap formula for measuring political gerrymandering, addressing mathematical issues in the original by comparing proportions of wasted votes rather than absolute differences.

Contribution

It proposes a novel relative efficiency gap formula that retains desirable properties while fixing mathematical problems of the original measure.

Findings

The new formula better captures proportional differences in wasted votes.

It addresses mathematical issues identified in previous efficiency gap measures.

The approach is relevant for legal and political analysis of gerrymandering.

Abstract

The efficiency gap formula was introduced in to measure political gerrymandering. It played a key role in the Gill v. Whitford case whose appeal is currently before the Supreme Court, but it was very recently shown by Bernstein and Duchin to have some problematic mathematical properties. We propose a new relative version of the efficiency gap formula that inherits its desirable but not its undesirable features. Instead of measuring the difference between the number of votes wasted by the two parties, we measure the difference between the proportions of their votes that the two parties wasted.