The Fairness of Redistricting Ghost

We explore the fairness of a redistricting game introduced by Mixon and Villar, which provides a two-party protocol for dividing a state into electoral districts, without the participation of an impartial independent authority. We analyze the game in an abstract setting that ignores the geographic distribution of voters and assumes that voter preferences are fixed and known. We first show that the minority player can always win at least $p-1$ districts, where $p$ is proportional to the percentage of minority voters, and that when the minority is large they can win more than $p$ districts. We also show that a "cracking" strategy by the majority party limits the number of districts the minority player can win as a function of the size of the minority.