Game theory paper unveils Vote-Left strategy that triples Faithful win rate

Vince Knight’s new paper on arXiv (cs.GT, May 2026) tackles the foundational problem in social deduction games: how an uninformed majority (the Faithful) can vote without being exploited by a coordinated minority (the Traitors). The author proposes a deterministic “Vote-Left” protocol: every player votes for the next surviving player in a fixed cyclic ordering. Because the votes are deterministic functions of public information, any deviation from the protocol is immediately identifiable. Combined with a simple punishment rule, this strategy constitutes a Perfect Bayesian Equilibrium for any game state where n_t > 2m_t + 2 (where n_t is surviving Faithful and m_t surviving Traitors). This region covers every configuration seen in televised seasons of The Traitors.

In late-game phases (n_t ≤ 2m_t + 2) the Faithful lose the ability to guarantee punishment, so Traitors can deviate via collusion and break the equilibrium. Crucially, across all televised configurations, Knight shows that Vote-Left raises the Faithful’s winning probability by a factor of approximately three over random voting when Traitors collude. The result bridges game theory and practical strategy: a simple, enforceable coordination protocol that outperforms random voting without requiring any private signals. The work has implications beyond the show, including decentralized consensus protocols and adversarial voting systems.