Inequity and Seat Lean in the Detection of Partisan Gerrymanders

Abstract

In this article we propose a simple method for detecting problematic partisan gerrymanders. We begin by defining a new standard for determining a party's equitable seat share given its vote share. We provide intuitive, theoretical, and empirical justifications for our definition, and we compare it to previous standards such as the one implied by the efficiency gap. Our measure for the inequity present in a district map is defined in terms of its departure from equitability. Next we define seat lean, which assesses the relative advantage to each party that a map provides for the next election. We base the notion of seat lean on the estimated likelihood of a seat changing parties, and we show that, after a slight adjustment, seat lean is a good predictor for when the inequity in a map is likely to persist. Finally, we propose a standard for the detection of problematic maps: those whose inequity is both too large and too likely to persist. We show that the standard gives intuitive results on several theoretical examples, including competitive sweeps, as well as on a database of past U.S. House elections. We also demonstrate that the measure neither requires nor forbids proportionality.