Communication Shapes Collective Inference in Self-Adapting LLM Societies: Evidence from Mafia

Abstract

When does communication help a group identify hidden adversaries, and how does its value change as the group adapts? In Mafia, an informed minority hides inside an uninformed majority whose only evidence is open play. The zero-information game, where each day's vote eliminates a random player, is exactly solved and scores every society; matched-casting comparisons between protocols identify the effect of communication. Societies of 8-100 claude-haiku-4-5 agents (7,416 analyzed games, 1.9M model calls) adapt by rewriting and inheriting private strategy notes. Simultaneous broadcast improves adversary identification over silence in all nine compositions tested (8-46 players). Turn-taking removes most of this advantage; its voting landslides are as frequent as broadcast's but land on mafia near chance (1.08x versus 2.53x). At 70 players, agents reading eight statements per day identify adversaries worse than silent ones, and limited talk is worth less than at 46 players. Adaptation is fast but need not help. In their first broadcast games, citizens announce their role far more often than mafia (91% vs. 30%) and first-day votes find mafia at three times chance; within two generations citizens stop announcing and the cue fades, a change the inherited notes carry. In controlled redeployments at 16 players, societies carrying sixty generations of their own notes score below societies with none. Communication shapes both collective inference and the signals it depends on, so a protocol's value must be measured together with the adaptation that changes those signals.