Fairness in plurality systems with implications for detecting partisan gerrymandering

Abstract

For both two-party and multiparty elections we construct a baseline standard for fair seat proportions based on three intuitive assumptions about plurality voting systems. We show that such systems are inherently biased against minority parties irrespective of political geography and are thus incompatible with the ideal of proportional representation. The construction produces sensible theoretical and empirical results when applied to U.S. and Canadian elections, and it is consistent with baseline standards produced by certain simulation methods. We apply the standard to detect partisan gerrymanders in a simple way that handles edge cases appropriately and flags expected real maps as problematic.