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 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 show that the minority player can always win at least $p-1$ districts, where $p$ is proportional to the percentage of minority voters. We give an upper bound on the number of districts won by the minority based on a "cracking" strategy for the majority.

翻译：我们探索了由Mixon和Villar提出的一种重新划分选区博弈的公平性，该博弈提供了一种无需独立权威参与、将州划分为选举区的两党协议。我们在忽略选民地理分布且假设选民偏好固定且已知的抽象设定中分析了这一博弈。我们证明，少数派玩家总能赢得至少$p-1$个选区，其中$p$与少数派选民的比例成正比。我们基于多数派的"破解"策略给出了少数派获胜选区数量的上界。