15 December 2020

Competitive Gerrymandering and the Popular Vote

When siblings argue about how to divide a cake, one of them should cut it and the other sibling should be the first to choose his/her own piece. Under the ruling system in the United States, the voter map is divided up by the ruling party for its own benefit (“gerrymandering”). The new game theory system presented here involves both parties in order to create a fair voter map.

Key Issue

In the US, legislatures are elected using plurality rule in single-member districts. After each decennial US census, the current state legislature selects a new district map that governs elections for the following decade. This redistricting process is often abused for “gerrymandering”, i.e., creatively drawing district lines in often absurd shapes in order to generate a map that favors the party currently in power. Gerrymandering subverts democracy because the party that was in charge of redistricting often wins a majority in the legislature even if a majority of voters now favors the other party. For example, in the 2018 elections in Pennsylvania, Democratic state house candidates received about 55% of all votes, yet Republicans won 110 out of 203 seats in the legislature.

Approach and Methodology

Our paper proposes a novel mechanism to prevent gerrymandering that does not rely on any “objective” fairness measure imposed as a constraint on the party in control, but rather sets up a game-theoretic system in which both parties participate. Even though each of them tries to “cheat” in this process (in the sense of creating a map that is more favorable to them), the “cheating” of the two parties negate each other. In the equilibrium map, each party wins a majority of districts in the legislature if and only if it wins a majority of the popular vote.

Key Findings and Conclusions

In an abstract sense, the system is similar to the one that solves the problem of a fair division of a cake between two siblings: We first ask the sister to cut the cake into two pieces, and then allow the brother to choose one of the two pieces for himself, leaving the other piece for the sister. The brother’s participation keeps the sister fair when cutting the cake. While this cake-cutting mechanism serves as inspiration, it cannot be directly applied to the gerrymandering problem because the district map is not a private good like the cake. Rather, the optimal mechanism consists of both parties sequentially distributing voters to districts over many rounds.