Political districting without geography

TL;DR

This paper explores political districting without geographical constraints, providing mathematical insights into proportionality, competitiveness, and critiquing the efficiency gap as a gerrymandering measure.

Contribution

It offers a theoretical analysis of districting without geography, highlighting the contrast between proportionality and competitiveness and exposing limitations of the efficiency gap.

Findings

Distinguishes between proportionality and competitiveness in districting

Identifies weaknesses in the efficiency gap as a gerrymandering metric

Provides insights to inform model construction without geographical constraints

Abstract

Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis of the problem without such constraints yields mathematical insights that can inform real-world model construction. In particular, it clarifies the sharp contrast between proportionality and competitiveness and how it might be overcome in a properly formulated objective function. It also reveals serious weaknesses of the much-discussed efficiency gap as a criterion for gerrymandering.