# The Vote-Left Equilibrium: A Deterministic Coordination Strategy for the Faithful in The Traitors

Source: [The Vote-Left Equilibrium: A Deterministic Coordination Strategy for the Faithful in The Traitors](<https://www.sota2.com/research/paper/6a02b49cdbc836b87d824e36>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-13T05:00:20.520Z

Authors: Vince Knight

Published: 2026-05-11T09:10:14.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Traitor win probability estimation on The Traitors Game Small configurations Migdał value based (n \<= 11)](<https://www.sota2.com/research/sota/traitor-win-probability-estimation-on-the-traitors-game-small-configurations-migda-value-based-n-11.md>): Traitor win probability estimation; The Traitors Game Small configurations Migdał value based (n \<= 11); Traitor Win Probability: 100.

- [Traitor win probability estimation on The Traitors Game Televised range configurations 15 \<= n \<= 25 Migdał value based](<https://www.sota2.com/research/sota/traitor-win-probability-estimation-on-the-traitors-game-televised-range-configurations-15-n-25-migda-value-based.md>): Traitor win probability estimation; The Traitors Game Televised range configurations 15 \<= n \<= 25 Migdał value based; Win Probability: 92.7.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.10233>)

[PDF](<https://arxiv.org/pdf/2605.10233.pdf>)