Helmsman of the Masses? Evaluate the Opinion Leadership of Large Language Models in the Werewolf Game

Large language models (LLMs) have exhibited memorable strategic behaviors in social deductive games. However, the significance of opinion leadership exhibited by LLM-based agents has been overlooked, which is crucial for practical applications in multi-agent and human-AI interaction settings. Opinion leaders are individuals who have a noticeable impact on the beliefs and behaviors of others within a social group. In this work, we employ the Werewolf game as a simulation platform to assess the opinion leadership of LLMs. The game features the role of the Sheriff, tasked with summarizing arguments and recommending decision options, and therefore serves as a credible proxy for an opinion leader. We develop a framework integrating the Sheriff role and devise two novel metrics for evaluation based on the critical characteristics of opinion leaders. The first metric measures the reliability of the opinion leader, and the second assesses the influence of the opinion leader on other players' decisions. We conduct extensive experiments to evaluate LLMs of different scales. In addition, we collect a Werewolf question-answering dataset (WWQA) to assess and enhance LLM's grasp of the game rules, and we also incorporate human participants for further analysis. The results suggest that the Werewolf game is a suitable test bed to evaluate the opinion leadership of LLMs and few LLMs possess the capacity for opinion leadership.