The Traitors is a social deduction game in which an informed minority of Traitors face an uninformed majority of Faithful, and the recurring question facing the Faithful is how to vote. Random voting is known to be optimal for the uninformed majority under simultaneous-signal protocols [Braverman, Etesami and Mossel, 2008], but when votes are cast individually, random votes are indistinguishable from strategic ones and the Faithful remain exposed to coordinated Traitor collusion. We introduce the Vote-Left protocol, a deterministic rule under which every player votes for the next surviving player in a fixed cyclic ordering. Under full compliance every surviving player receives exactly one vote, so the banishment distribution coincides with random voting; since prescribed votes are deterministic functions of public information, any deviation is immediately identifiable. Combined with a simple punishment rule, Vote-Left constitutes a Perfect Bayesian Equilibrium for every state with $n_t > 2m_t + 2$, a region that contains every televised configuration. We characterise the Traitors' best response in the late-game phase ($n_t \leq 2m_t + 2$): deviate via collusion once the Faithful no longer have enough votes to guarantee punishment. Across the configurations played on television, Vote-Left raises the Faithful's winning probability by a factor of approximately three over random voting under collusion.

翻译：《叛徒游戏》是一种社会推理游戏，其中信息占优的少数叛徒对抗信息缺失的多数忠实玩家，忠实玩家面临的反复问题是如何投票。已知在同步信号协议下，随机投票对信息缺失的多数玩家是最优策略[Braverman, Etesami and Mossel, 2008]；但当投票单独进行时，随机投票与策略性投票无法区分，忠实玩家仍面临叛徒协同勾结的风险。我们提出左倾投票协议，这是一种确定性规则，即每位玩家在固定循环顺序中投票给下一个存活的玩家。在完全遵守规则的情况下，每位存活玩家恰好获得一票，因此放逐分布与随机投票一致；由于指定投票是公共信息的确定性函数，任何偏离行为均可立即识别。结合简单的惩罚规则，左倾投票协议在$n_t > 2m_t + 2$的每个状态下构成完美贝叶斯均衡，该区域包含所有电视播出的配置。我们刻画了晚期阶段（$n_t \leq 2m_t + 2$）叛徒的最佳应对：一旦忠实玩家没有足够票数保证惩罚，便通过勾结偏离。在电视播出的所有配置中，左倾投票协议在勾结情境下将忠实玩家的获胜概率提升至随机投票的大约三倍。