Utility Ghost: Gamified redistricting with partisan symmetry

Abstract

Inspired by the word game Ghost, we propose a new protocol for bipartisan redistricting in which partisan players take turns assigning precincts to districts. We prove that in an idealized setting, if both parties have the same number votes, then under optimal play in our protocol, both parties win the same number of seats. We also evaluate our protocol in more realistic settings that show how our game nearly eliminates the first-player advantage exhibited in other redistricting protocols.

A Cut-And-Choose Mechanism to Prevent Gerrymandering

“…Mixon and Villar [10] propose a map drawing game loosely based on the word game Ghost. It allows for exogenously determined units of terrain called atoms which cannot be subdivided.…”

“…Every voter has a strict preference over the two parties, and will vote according to their preference. These preferences are common knowledge (this is a standard assumption, and is also used in [9], [11], and [10]). In total, party A holds a v A fraction of the total voter population, and party B holds a v B = 1 − v A fraction.…”

“…Thus, when v B = 1 2 , the rotational symmetry criterion enforces fairness by requiring that there exist districts perfectly stacked with voters for the majority party, reducing any unfair advantage they would otherwise have. This is what makes the mechanism more fair than those presented in [11] or [10], in which the majority party inevitably has extra power.…”