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

Authors: silin  du
xiaowei  zhang
Venue: colmweb_org_COLM_2024_Conference
Published: 2024-03-21 18:15:02

Abstract: 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 largely 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 includes 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 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.

Main paper: 
 introduction: 
 Recently, large language models (LLMs) have made remarkable improvements and demonstrated a high level of expertise in comprehending and producing human-like natural languages (Jones & Bergen, 2023) . However, academically intelligent LLMs are not necessarily socially intelligent (Xu et al., 2024a) . The behavioral tendencies of LLMs in social contexts have yet to be explored, which is crucial to coordinate human-AI collaboration and build credible simulations of human society through LLM-based agents (Zhang et al., 2023; Xie et al., 2024; Ziems et al., 2024) . Social deductive games, such as Werewolf (Xu et al., 2023; 2024b) and Avalon (Wang et al., 2023a) , are suitable scenarios to study the social preference of LLMs (Meng, 2024) . Some studies have indicated that LLMs, such as GPT-4 (Achiam et al., 2023) , exhibit strategic behaviors including cooperation, confrontation, deception, and persuasion in these games (Xu et al., 2023; 2024b; Lan et al., 2023; Wang et al., 2023a) . However, the potential opinion leadership of LLMs has been largely overlooked and confounded by existing frameworks and evaluation metrics (Kano et al., 2023) . Opinion leaders are individuals who exert personal influence on a certain number of other people in certain situations (Rogers & Cartano, 1962) . Contrary to the aforementioned interaction strategies, opinion leadership is the composite ability of opinion leaders to comprehensively employ these strategies to influence the decisions of their followers and shape public opinion (Bamakan et al., 2019) .Exploring the degree of opinion leadership in LLM-based agents is crucial for interaction design, decision optimization, public regulation, and the broader field of AI security. In multi-agent systems, such as smart manufacturing, a few opinion leaders can significantly impact task efficiency and outcomes (Rapanos, 2023) . As AI assistants and customer service agents, LLMs can shape user experience and business decisions. On social media and forums, the opinion leadership of LLMs could sway social discourse and public opinion. Despite its significance, research on this topic is limited. While there are various methods for identifying opinion leaders within human populations (Li et al., 2013; Bamakan et al., 2019) , there is a notable absence of a systematic evaluation of AI agents' opinion leadership, particularly for LLMs.Examining opinion leadership among LLM-based agents is non-trivial. Opinion leaders are often concealed (Bamakan et al., 2019) , making it challenging to identify and distinguish them from other agents and humans in general tasks. Additionally, assessing opinion leadership is also a formidable task due to the complexity of the decision-making process. The impracticality of conducting large-scale real-task randomized controlled trials further complicates the evaluation. Fortunately, the Werewolf game, as a common interactive scenario to study the emergence of AI agent behaviors (Kano et al., 2023) , provides a promising testing ground to address these challenges. The Sheriff role in the Werewolf game is jointly elected by other players and can summarize the statements and offer decisionmaking suggestions. This role represents the collective will and allows the player to provide information and exert influence, making it a credible proxy for an opinion leader. By assessing the reliability and spillover of the Sheriffs' decisions, we can evaluate their opinion leadership. Furthermore, incorporating diverse LLMs and human players allows us to compare the impact of LLMs' opinion leadership across different followers. Our main contributions can be summarized as:1. To the best of our knowledge, this is the first in-depth analysis of opinion leadership within LLMs. We clarify the opinion leadership of diverse LLMs in various contexts.2. We introduce the setting of the Sheriff and implement a Werewolf game framework, which can seamlessly integrate diverse LLM-based agents and human players. Besides, We devise two novel metrics to evaluate the opinion leadership of different LLMs.3. We conduct simulations and human evaluations to assess LLMs' opinion leadership, and we collect a Werewolf question-answering (WWQA) dataset for further analysis.This is also the setup reported in Section 4.2.In this setup, we select one LLM as a reference model (e.g., GLM-3) to implement all players except the Sheriff. The Sheriff is implemented using the LLM whose opinion leadership is to be evaluated. It allows for a more fair comparison of the opinion leadership of different LLMs.To achieve this, we omit the election phase. The moderator will secretly select the Sheriff during the initialization of the game roles and construct the player chosen as the Sheriff (i.e., X l , l = L(1)) using the LLM to be evaluated. After the first night, the moderator would inform all players of this through the following message.After discussion and a vote, player l was selected as the Sheriff, who can determine the order of statements, summarize the discussion, and provide advice for voting at last.If the individual chosen covertly as the Sheriff gets eliminated by the Werewolves during the initial night, the current simulation round becomes void. In addition to terminating under the conditions defined in the game rules, a simulation round will immediately stop after the Sheriff is eliminated because only the Sheriff is implemented by the LLM to be evaluated. 
related work: 
 LLM-based Agent has risen to prominence in recent research, spurred by advancements in LLMs. These agents are capable of reasoning and decision-making based on their own states (Yao et al., 2023) , as well as interacting with the environment (Ahn et al., 2022; Cui et al., 2023) . Some studies indicate that LLMs also exhibit a certain level of cognitive abilities (Shapira et al., 2023; Zhuang et al., 2023) and demonstrate potential in simulating believable human behavior (Park et al., 2023) . This has led to the development of collaborative frameworks for multi-agent interactions such as AgentVerse (Chen et al., 2023b) , AutoGen (Wu et al., 2023) , MetaGPT (Hong et al., 2023) , ChatEval (Chan et al., 2023) , etc. LLM-based agents have shown promise in simulating complex social dynamics in various scenarios, including courtroom (Talebirad & Nadiri, 2023) , game development (Hong et al., 2023) , auctions (Chen et al., 2023a) , etc. To further introduce adversarial dynamics among agents, LLMs are also being utilized in gameplay scenarios such as Texas Hold'em poker (Gupta, 2023) , complex video games (Wang et al., 2023b; Zhu et al., 2023) , and multi-player social deduction games (such as the Werewolf and Avalon game) (Lan et al., 2023; Light et al., 2023; Wang et al., 2023a; Xu et al., 2023; 2024b; Wu et al., 2024) , which heavily rely on natural language interactions. These games provide prototypes of mixed cooperative-competitive social environments similar to human society, allowing researchers to observe whether these agents can exhibit human-like behavior patterns and social principles (Bai et al., 2023; Ren et al., 2024) , as well as explore approaches to incentivize the agents to perform better or more human-like. However, existing LLM-based frameworks for the Werewolf game have regrettably overlooked the inclusion of a pivotal character, the "Sheriff ", resulting in an underestimation of the influence of opinion leaders. In fact, Avalon also features a similar "leader" role. However, the key difference is that in the Werewolf game, the "Sheriff" is actively elected through agent voting, whereas in Avalon, the leader is passively assigned (which may not fully reflect collective consensus).Opinion leadership is an important concept in the process of social learning in human society (Festinger, 1954) . It was first developed in (Lazarsfeld et al., 1944) 's study of the 1940 presidential election. When faced with uncertainty, humans tend to learn from "opinion leaders" to enhance the wisdom of their decisions (Bala & Goyal, 1998) . Opinion leaders can be individuals with extensive knowledge in a specific subject area (experts) or individuals with extensive social connections (social connectors) (Goldenberg et al., 2006) . They come from the collective will and differ from their followers in information sources, social participation, social status, etc. (Rogers & Cartano, 1962) . To exert influence, opinion leaders must be trustworthy (Nahapiet & Ghoshal, 1998) , and the extent to which their opinions are adopted by recipients relies on their credibility (Dirks & Ferrin, 2001; Mayer et al., 1995) .Trust diminishes conflicts, alleviates the necessity for information verification (Currall & Judge, 1995) , and enhances people's inclination and ability to attentively and efficiently embrace others' perspectives (Carley, 1991; Mayer et al., 1995) . Xie et al. (2024) found that LLM agents generally exhibit trust behaviors, referred to as agent trust, suggesting the possibility of simulating human trust behaviors with LLM agents. Considering the necessity of trust in opinion leadership, when we strive to create credible simulations of human society, it seems intuitive to extend the concept of opinion leaders to the interactions among LLMs. The agent who garners the most trust and is selected by the majority of agents naturally emerges as the opinion leader. This analysis delves deeper into the social ties among multiple agents, transcending the narrower confines of discussions solely focused on individual agents' strategic behaviors.]. Contextual information includes facts and public statements. Based on the LLM's reasoning results, we categorize public statements into potential truths and potential falsehoods. Table 4 shows an example that organizes contextual information for the model.All players are implemented using the same LLM. The election phase is not implemented in this setting. 
framework and proposed metrics: 
 We consider the Werewolf game with N = 7 players, including two Werewolves, three Villagers, one Seer, and one Guard. There is a moderator to move the game along, who will only pass on information and not participate in the game. At the beginning of the game, each player is assigned a hidden role which divides them into the Werewolves and the Villagers (Seer, Guard, and Villager). Then the game alternates between the night round and the day round until one side wins the game. Let X r i be the i-th player.We use the superscript r ∈ R to indicate the role rinR, where R = {W, V, Se, G} represents the Werewolf, Villager, Seer, and Guard, respectively. We might omit the index i or the role r when there is no ambiguity.We refer to one night-day cycle as a round, indexed by t. At night, the Werewolves recognize each other and choose one player to kill. The Seer chooses one player to check the player's hidden role. The Guard protects one player, including themselves, from the Werewolves. The Villagers do nothing. We use A night,t to represent all night actions. During the day, three phases are performed in order: the announcement phase, the discussion phase, and the voting phase. First, the moderator announces last night's result to all players D t . Only the first day has an election phase for the Sheriff. The Sheriff is a special role that does not conflict with the players' roles. The elected Sheriff has the authority to determine the statement order and provide a summary to persuade other players to vote in alignment with them. Then, each player takes turns to make a statement in an order specified by the Sheriff. At last, each player votes to eliminate one player or chooses not to vote. The actions of making a statement and voting are defined as follows.X i makes a statement: S i,t = A state,t (X i ) X i votes to eliminate X j : X j = A vote,t (X i )After the voting phase, the moderator announces the result E t , and the game moves to the next night's round. The Werewolves win the game if the number of remaining Werewolves equals the combined number of remaining Seer, Guard, and Villagers. The Seer, Guard, and Villagers win if all Werewolves are eliminated. 16 of Appendix B. Each player needs to reason about the roles and reliability of other players before taking any action. We design two metrics to measure the opinion leadership of the LLM acting as the Sheriff. Ratio measures the credibility of the Sheriff, while DC assesses the Sheriff's influence on the voting decisions of other players. More details are presented in Section 3.2.Figure 1 depicts our framework extended from Xu et al. (2024b) . The players in our framework can be LLMs or humans. More details about game settings can be found in Appendix A.1 and all notations are listed in Table 16 in Appendix B.Players of different roles are required to perform a series of actions, including night actions (to kill, protect, or see) and day actions (to speak and vote). Each LLM-based player is implemented by an LLM-based agent, which can store the related information during the game and act in response to the game situation.The LLM-based players perform actions through prompting. The prompt consists of 3 major components: (1) the game rules and the assigned role; (2) the contextual information; and (3) the task description. The prompt templates can be found in Appendix A.2. Communication and action history play a crucial role in the game. However, given the limited context length of LLMs, it might be infeasible to integrate all the information into the prompt. Thus, following Xu et al. (2024b) , we design a strategy to manage the contextual information.To begin with, we divide the contextual information for X r i into the following two parts.1. The set of facts F i,t consists of all factual information before round t, including the role of X r i , the announcement made by the moderator, etc. For example, F i,t of an Seer X Se i can be expressed asF i,t = {i, Se} ID & role D τ t-1 τ=1 night results E τ t-1 τ=1 day results S i,τ t-1 τ=1 X i 's statements A see,τ (X Se i ) t-1 τ=1 X i 's night actions k∈Alive d (τ) A vote,τ (X k ) t-1 τ=1 voting actions (1)where Alive d (τ) is the IDs of alive players before the day of round τ.2. The set of public statements P i,t consists of the public statement of other players before the t-th round.P i,t = k∈Alive d (τ),k̸ =i S k,τ = A state,τ (X k ) t-1 τ=1 (2)Note that the statements made by other players might be misleading. In light of this, we design a reasoning step to assess the reliability of other players. Based on this reliability, we classify public statements P i,t as either potential truths P true i,t or potential falsehoods P f alse i,t . Concretely, we implement an additional action, called reliability reasoning, before making night or day actions. In this step, we prompt the LLM to infer the hidden roles of other players based on historical information and provide confidence levels. For example, at the night of round t, X i reasons the identity rn i,j,t of X j and provides the confidence level c n i,j,t before making actions as follows:X i reasons the identity of X j :EQUATIONThe superscript {n, s, v} denote the reasoning results before the night actions, making a statement and voting, respectively. The confidence level is a scalar from 5 to 10, then the reliability isEQUATIONGiven the reliability of other players, X i will divide the statements in P i,t into two parts.It regards the statements of players with reliability larger than α = 6 as potential truths, otherwise are potential falsehoods.P n,true i,tEQUATIONwhereM(• | α, {• • • }) is an operator that splits a set of public statements into two disjoint subsets according to the reliability threshold α and Alive n (t) is the IDs of alive players before the night of round t.The sequence of events during round t is illustrated in Figure 4 are sets of potential truth and potential falsehoods obtained as Eq. ( 5).On the day of round t, the moderator announces D t . Without loss of generality, we assume that X i was not killed on the night t and the order of statement is the same as the IDs of players. Then X i will receive a set of public statements made by preceding players, i.e., H s i,t = {S j,t | j ∈ Alive d (t), j < i} Now the available public statements for X i become P s i,t = P i,t ∪ H s i,t , where the superscript s signifies the timestamp before X i makes a statement. Similar to Eq. ( 6), X i first performs reliability reasoning and then makes a statement. Subsequently, X i will collect a set of public statements after its statement, i.e., H v i,t = {S j,t | j ∈ Alive d (t), j > i} When the discussion phase ends, each player begins to vote individually. Now the available public statements for X i become P v i,t = P s i,t ∪ H v i,t , where the superscript v indicates the timestamp before X i votes. Then X i reassesses the reliability of other players and then votes.c s i,j,t , rs i,j,t = A reason,t X i , X j | F i,EQUATIONAfter the voting phase, the moderator discloses the result E t . X i updates the set of facts by adding their own actions, other players' voting actions, and the night and day results.F i,t+1 = F i,t {D t } A night,t (X i ) S i,t k∈Alive d (t) A vote,t (X k ) E tFor the set of public statements, we require the LLM to output evidence when reasoning in round t, and any unmentioned statements in P The game moves to the next round.We introduce the special role, i.e., the Sheriff, into the game framework. On the day of round t = 1, the moderator will announce the selection of the Sheriff after the election phase. Let L(t) be the operator that returns the ID of the Sheriff during the day of round t. Without loss of generality, we assume that X l is elected as the Sheriff, i.e., L(1) = l. All alive players will receive a special message after the election phase:After discussion and a vote, player l was selected as the Sheriff, who can determine the order of statements, summarize the discussion, and provide advice for voting at last.In this way, combined with the description in the game rule, we establish the authority of the Sheriff. During the day of round t, X L(t) can determine the order of statements. It first performs the reasoning step to obtain P d,true L(t),t and P d, f alse L(t),t similar to Eq. ( 3)-( 5) and then selects its left-or right-hand side player to speak first byO(t) = A order,t X L(t) | F L(t),t , D t , P d,true L(t),t , P d, f alse L(t),tThe statement order O(t) will slightly influence the collection of public statements, i.e., H s and H v . But the whole process of making statements and voting remains the same.In different scenarios and research contexts, various definitions of opinion leaders have been proposed (Chowdhry & Newcomb, 1952; Katz, 2015; Lazarsfeld et al., 1968; Rogers & Cartano, 1962) . Despite these diverse definitions, the common characteristics of opinion leaders are mainly reflected in two aspects: (1) they are generally more trustworthy; (2) they influence the views and even decisions of others. Based on these, we design two evaluation metrics to measure the opinion leadership of LLM-based players.Ratio is to measure the reliability of the Sheriff. When all players finish their statements, the voting phase commences. We collect all the reasoning results before each player's voting action, i.e., m v i,j,t . Then we calculate the average mutual reliability among all players, excluding the Sheriff.m1 (t) = 1 (N d (t) -1)(N d (t) -2) ∑ i∈Alive d (t),i̸ =L(t) ∑ j∈Alive d (t),j̸ =L(t),j̸ =i m v i,j,twhereN d (t) = |Alive d (t)| is the number of alive players on the day of round t. Similarly, the average reliability of other players towards the Sheriff ism2 (t) = 1 N d (t) -1 ∑ i∈Alive d (t),i̸ =L(t) m v i,L(t),tThen the Ratio is defined as:Ratio = 1 T T ∑ t=1 m2 (t) m1 (t)where T is the total number of rounds. A Ratio greater than 1 indicates that the Sheriff's trustworthiness is higher than that of other players; the higher the Ratio value, the stronger the opinion leadership.Decision Change (DC) measures how the Sheriff's statements influence the voting decisions of other players. At the end of the discussion on day t, all players except the Sheriff have made a statement. Now all players are required to reason the reliability of the Sheriff as Eq. ( 7) and make a pseudo-voting decision as Eq. (8-9). Note that in Eq. ( 9), the available set of public statements is P v i,t \ {S L(t),t }. We denote the pseudo-voting decision without the public statement from the Sheriff as A ′ vote,t (X i ). Then the Sheriff makes a statement and all players proceed to the voting phase to yield A vote,t (X i ).Based on this, we can calculate the proportion of players that change their decision to align with the Sheriff.DC = 1 T T ∑ t=1 ∑ i∈Alive d (t),i̸ =L(t) I A ′ vote,t (X i ) ̸ = A vote,t (X L(t) ) AND A vote,t (X i ) = A vote,t (X L(t) ) N d (t) -1where I(•) is the indicator function. The higher the DC value, the better the Sheriff's ability to influence other players' decisions, indicating stronger opinion leadership.Our two proposed metrics are motivated by the fundamental traits of opinion leaders.Although the specific calculation of these two metrics is coupled with our game framework, the underlying concepts are universal and can be easily applied to other similar game frameworks or even adapted to other types of social deductive games because reasoning and decision-making are the core steps in such games. For example, the framework in Xu et al. (2024b) is similar to ours and also contains reasoning steps. The early attempts in LLMs for the Werewolf game (Xu et al., 2023 ) also explore the trust relationships between players. Similar settings can be found in Wu et al. (2024) . In addition, reasoning and decision-making are prevalent steps within the framework of the Avalon game (Wang et al., 2023a; Light et al., 2023; Lan et al., 2023) , making our proposed metrics well-suited for such scenarios.Our framework allows human players to participate in the game through text input. The process for human players to engage in the game is similar to that of LLM-based players, as they also need to reason about the roles of other players before taking actions. The moderator will review the game state and historical information to assist players in reasoning and decision-making. The interface for human players is depicted in Figure 5 of Appendix B.] specifies what the LLM needs to accomplish, defining the format of responses to facilitate the parse of the actions. More detailed explanations will be provided later. Response Format: { "reasoning": "reason about the current situation", "action": "choose one from {}" } Ensure the response is in English and can be parsed by Python json.loads. Response Format: { "reasoning": "reason about the current situation", "action": "choose one from {}" } Ensure the response is in English and can be parsed by Python json.loads. All players are implemented using the same LLM. This setup allows the simulation to proceed strictly according to the game rules.Due to significant differences in the interaction objects of the Sheriff, it may be problematic to compare opinion leadership metrics under such a setting directly. Nevertheless, we also conduct homogeneous simulations on several LLMs.On the first day, three players are randomly chosen to participate in the Sheriff's election.After the three players speak, all players vote to decide who will be the Sheriff. When the Sheriff is eliminated, we choose the player the Sheriff trusted the most as the next Sheriff.The game terminates under the conditions defined in the rules. The results after 10 iterations are shown in Table 19 .  
wwqa dataset: 
 Previous studies have found that certain LLMs may exhibit subpar performance in the context of the Werewolf game (Xu et al., 2023; 2024b; Wu et al., 2024) . This can be attributed, in part, to their limited understanding of the game rules and the inherent challenge of fully unleashing their potential capabilities with simple prompts alone. Additionally, the multitude of versions and rules of different Werewolf games can pose a challenge, as LLMs tend to heavily rely on prior knowledge of specific game rules, leading to strategic behaviors that may not align with the given context or even violate the rules.To address these limitations, we propose a self-instructional framework (Wang et al., 2022) to generate a dedicated Werewolf Question-Answering (WWQA) dataset that directly caters to our game tasks. This WWQA dataset serves as a valuable resource for effectively assessing an LLM's grasp of the fundamental game rules. Furthermore, we utilize this dataset for supervised fine-tuning, enhancing their foundational abilities within our game setting. We consider the simulation first, where all players are LLM-based. To fairly evaluate and compare the opinion leadership of different LLMs, we select a powerful model that can better understand the rules of the Werewolf game as our baseline model. Specifically, we select GLM-3 (Zeng et al., 2022) as the backbone for all players, excluding the Sheriff, which can generate output in a specified format to ensure progression of the game. We provide more details on handling non-compliant output formats in Appendix B.1.For the Sheriff, we implement it by LLMs of varying sizes from different organizations, including ChatGLM3-6B (C3-6B) (Zeng et al., 2022) , Mistral-7B (M-7B) (MistralAI, 2023), Baichuan2-13B (B-13B) (Yang et al., 2023) , InternLM-20B (In-20B) (InternLM, 2023), Yi-34B (Young et al., 2024) , GLM-3 (Zeng et al., 2022) , GLM-4 (ZhipuAI, 2024) , and GPT-4 (Achiam et al., 2023) . We simulate 30 Werewolf games for each model, with a maximum of 6 rounds. As the Sheriff and non-Sheriff players are implemented by different LLMs, it's unpredictable whether the tested LLM would be elected. Thus, we omit the election phase. The moderator will secretly select the Sheriff during the initialization of the game roles. This simplification is to fairly compare the opinion leadership of different models. In Appendix D.1, we discuss other experimental settings that incorporate the election phase and provide corresponding simulation results.In addition to our proposed metrics, we also report some additional indicators in Appendix D.5, such as the win rate, the ratio of players who change their voting decision (not necessarily in agreement with the Sheriff), etc.The results are shown in Table 1 . Except for C3-6B, all models achieve decent performance on the binary QA dataset. Overall, the larger the model, the better the results, suggesting a more accurate understanding of the rules. The evaluation results are shown in Table 2 , where the models with (FT) are LLMs after fine-tuning. Fine-tuned LLMs generally achieve better results on the binary QA dataset, except for C3(FT). However, a better grasp of the rules does not necessarily equate to better opinion leadership, which is consistent with the results in Table 1 . In-20B enjoys a 7.2% increase in Ratio and a 61.8% growth in DC. B-13B gains an 8.6% improvement in Ratio, but its DC value significantly deteriorates. It's non-trivial to improve LLMs' opinion leadership, especially the ability to influence others' decisions.Furthermore, we further control the identity of the Sheriff. The results in Figure 3 show that LLMs exhibit varying levels of opinion leadership with different roles. When the Sheriff is a Werewolf, it's difficult to gain the trust of other players because more players are on the Villager team. Therefore, all LLMs have poor opinion leadership when they are the Werewolf. In contrast, LLM has stronger opinion leadership with the roles of Seer and Guard, as they can take action at night and gather more information.1 Both ZhipuAI and OpenAI have not disclosed the specific parameter amounts of the LLMs behind their APIs. Since the base model behind the GLM series is 130B (Zeng et al., 2022) and GPT-3 is 175B (Brown et al., 2020) , it's reasonable to say that GLM-3, GLM-4, and GPT-4 are at least 100B. We invite 8 college students proficient in English and familiar with the Werewolf game for the human evaluation experiment. Each human player will play 5 games with 6 LLM-based players. The process and details can be found in Appendix D.3. We choose GLM-3 as the backbone for LLM-based players, monitor the human player's reasoning and decisionmaking before and after the Sheriff's statement, and calculate the Spearman correlation coefficient between the human player's reliability scores of the LLM-based player and the scores among other LLM-based players. The results in All players are initialized by the same LLM-based agents (default to be GLM-3), and when the election phase is over, the sheriff is replaced with the LLM to be tested.The results reported in Section 4.2 use a preassigned Sheriff to fairly compare the opinion leadership of different LLMs. In this setting, we consider the fairness of comparison and also introduce the election phase. All players are initialized with the same LLM, and after the election phase, the LLM behind the player elected as Sheriff is replaced with the LLM to be tested. Table 20 shows the relevant results. The results of C3-6B and In-20B are close to those presented in Table 1 , indicating that omitting the election process and preassigning the Sheriff has a minimal impact on the evaluation results.  
conclusion: 
 This study investigates the opinion leadership of LLMs by employing the Werewolf game as a simulation environment. We implement a framework that incorporates a Sheriff role, catering to both LLMs and human players. Besides, we propose two metrics to measure the Sheriff's opinion leadership: Ratio measures their reliability and DC assesses their influence on other players' decisions. Through extensive simulations, we evaluate LLMs of different scales and find that only a few LLMs show a certain degree of opinion leadership. Furthermore, we collect the WWQA dataset to enhance LLMs' grasp of the game rules by fine-tuning. Initial attempts indicate that it's non-trivial to promote the opinion leadership of LLMs. Finally, human evaluation experiments suggest that LLMs can gain human trust, but struggle to influence human decisions.During the night round: The Werewolves identify each other and select one player to eliminate; the Seer chooses one player to determine if they are a Werewolf; the Guard selects one player, including themselves, to protect without knowing who the Werewolves have chosen; the Villagers take no action.During the day round: There are three phases--announcement, discussion, and voting--which are conducted in sequence. In the announcement phase, the results of the previous night are disclosed to all players. If player i was killed and not protected, the announcement will be "player i was killed." If a player was killed but protected, the announcement will be "No player was killed." Only on the first day is there an election phase. In this phase, you can decide whether to nominate yourself for Sheriff based on your role. Players nominated for Sheriff explain their reasons in turn.Each player then votes for one Sheriff nominee or chooses not to vote. The Sheriff is a unique role that does not interfere with a player's primary role. The elected Sheriff has the power to decide which player begins the next discussion round and, as the final speaker, can summarize the discussion to persuade others to vote in agreement with them. In the discussion phase, each remaining player speaks once, in the order determined by the Sheriff, to debate who might be a Werewolf.In the voting phase, each player votes to eliminate one player or chooses not to vote. The player with the most votes is removed, and the game progresses to the next night's round.The Werewolves win if their number equals that of the remaining Seer, Guard, and Villagers. The Seer, Guard, and Villagers win by eliminating all the Werewolves.One player is implemented by the selected (tested) LLMbased agent while other players are the same LLM-based agents (default to be GLM-3). It contains the election process, and if the LLM to be tested is not elected as the Sheriff, the simulation ends.In this setting, it is usually difficult to complete a simulation since the tested LLM may fail to be elected as the Sheriff. However, it can be used to estimate the probability of an LLM being elected as the Sheriff under different hidden roles. 
 
 Appendix: We construct our prompt templates following the design in Xu et al. (2024b) . The prompt template used to instruct LLMs for reasoning and decision-making consists of three parts.1. [Game Rule] is illustrated in Appendix A.1.Table 16 summarizes the notations used in our framework. Figure 4 depicts the sequence of events in round t. During the night, the Werewolf, Seer, and Guard take turns making decisions. During the day, the moderator announces the results of the previous night D t , and the Sheriff decides the order of speaking. Subsequently, each player makes a statement and votes in turn. Note that the Sheriff always speaks and votes last. Finally, the moderator announces the voting results and the game proceeds to the next round. Each player needs to perform the reliability reasoning step before taking any actions. the potential truth and potential falsehoods for X i before the t-th round A reason,t X i , X j X i reasons the role of X j rn i,j,t , c n i,j,t the predicted identity and related confidence level when X i reasons the role of X j before taking night action m n i,j,t the reliability score of X i towards X j before taking night action in round t α the threshold to divide the potential truths and falsehoods the potential truth and potential falsehoods for X i before makine a statement in the t-th round rs i,j,t , c s i,j,t the predicted identity and related confidence level when X i reasons the role of X j before making a statement m s i,j,t the reliability score of X i towards X j before making a statement in round tM(• | α, {• • • }) an operatorH v i,tthe set of public statements made by other players AFTER X i speaks in round tP v i,tthe available public statements for X i AFTER X i makes a statement in round tP v,true i,t , P v, f alse i,tthe potential truth and potential falsehoods for X i before voting in the t-th round rv i,j,t , c v i,j,t the predicted identity and related confidence level when X i reasons the role of X j before voting m v i,j,t the reliability score of X i towards X j before voting in round t P v,true i,t , P v, f alse i,t the set of potential truths and potential falsehoods for X i with unmentioned statements removed at the end of round t L(t) the operator that returns the ID of the Sheriff during the day of round t O(t)the statement order during the day of round t A order,t X L(t)the Sheriff X L(t) determines the order of statements m1 (t) the average mutual reliability of all players except the Sheriff in round t m2 (t) the average reliability of other players towards the Sheriff in round tTable 16 : Notations and explanationsWe require LLMs to output results in the specified JSON format, as shown in Appendix A.2, so that we can quickly parse the corresponding content. However, in some cases, LLMs fail to follow the format instructions, and we refer to such outputs as invalid outputs. To ensure simulations do not terminate in such situations, we design different mechanisms at various stages of the game to handle invalid outputs. Additionally, if the model cannot generate an output (such as when the prompt exceeds the context window or unsuccessful API calls), or if the model selects an unavailable option, we handle them similarly.• During the Night. If an LLM-based player who needs to take action at night generates an invalid output, we will randomly select one of all available options as the decision for this player.• Discussion Phase. If an LLM-based player generates an invalid output when making a statement, we handle it by considering the player to keep silent in the discussion, and other players will receive the public information: "player {} said nothing".• Voting Phase. If an LLM-based player generates an invalid output during the voting phase, we consider that the player chooses not to vote.• Reliability Reasoning. If an LLM-based player produces an invalid output when inferring the identity of X i , the reliability score of X i will not be updated.Our framework includes a comprehensive logging system, which facilitates monitoring the game process during the simulation and checking whether LLM-based players are functioning properly. Specifically, our framework automatically saves three types of logs:1. Error logs. Error logs primarily store errors that occur during the model generation process, including failures to generate results, outputs that do not meet format requirements, and cases where the model selects an unavailable option.2. Game logs. Game logs record the progress of the game, including the identities of all players, night actions, the order of speaking during the day, the statements, and voting decisions.3. Player logs. Player logs record the identities and numbers of players, the contextual information used for decision-making, their statements, decisions (including night actions and voting), and the historical records of their reasoning. Note that we also design a similar player log for human players, which helps us monitor the human evaluation process. The prompt for requesting input from human players is similar to the one displayed in Appendix A.2, and human players are required to input content in the specified JSON format. Participants are allowed to quickly select the input template using the up and down keys.In this section, we provide a detailed description of the data generation process for the WWQA dataset (Figure 2 ) and present examples of some QA pairs in the dataset to help readers better understand the structure of our dataset.As shown in Figure 2 , the data generation process of WWQA includes two primary phases: question generation phase and answer generation phase.Question Generation Phase. In the first phase, our objective is to leverage the generative capabilities of the LLMs to generate a series of game-related questions based on our game rules. Our questions can be categorized into two types based on their content: rule-based and situation-based. Rule-based questions directly pertain to the game rules. Situation-based questions, on the other hand, require the LLMs to construct a simple virtual game situation, and then engage in a certain level of reasoning within that situation in order to obtain the answer.We initialize separate example pools, each with a size of 5, for rule-based and situationbased questions. In the first three iterations, we utilize all initial examples along with the game rules to prompt the LLMs to generate 10 questions. The generated questions are then reviewed and corrected in the second round by prompting the LLMs for revisions. The revised questions are then fed into the question pool. Starting from the fourth iteration, we sample 2 human-written examples from the example pool and 3 LLM-generated questions from the question pool separately as examples for prompting the LM in question generation."Answer Generation Phase. In the second phase, our objective is to leverage the combined semantic understanding and generative capabilities of the LLMs to generate concise and logically coherent answers for all the questions in the question pool. Similar to the first phase, we prompt the LLMs for post-processing corrections and filtering to ensure higherquality answers. Finally, we pair the questions with their corresponding answers to create the final Q&A Pair Pool.In addition, we also prompt the LLMs to generate a binary QA dataset, where the standard responses are 'Yes' or 'No'. For this dataset, we conduct additional human review and labeling, using it as a testing set to evaluate LLMs' grasp of our game rules.Table 17 provides some examples of our generated WWQA dataset, which includes three types of question-and-answer data: rule-based, situation-based, and binary QA pairs data.We create a set of random seeds for initializing the IDs and roles of each player. For each random seed, we repeat the simulation three times. We consider the following settings.We fine-tune four open-source LLMs on a 3*A100 server using the WWQA dataset. The training set contains 1453 records while the validation set contains 100 records. Specifically, we use the LoRA tuning method Hu et al. ( 2021) with a rank of 8. The learning rate is 1e -4 and the batch size is 4. The base models are fine-tuned with causal language modeling tasks over 4 epochs. During the fine-tuning process, the loss on the validation set is shown in Figure 6 2 . We can observe that the loss values of different models decrease and then increase, indicating that models have already overfitted the training data. The loss of LLMs smaller than 10B eventually stabilizes around 0.31, while LLMs larger than 10B can reach a better loss value of about 0.28.The fine-tuning time for different models varies from 40 to 100 minutes. From the results in Table 2 , we conclude that fine-tuning can improve LLMs' understanding of the rules (as evidenced by their performance on the binary QA dataset), but it has a limited effect on enhancing opinion leadership. We need more sophisticated methods to enhance the opinion leadership of LLMs. We invite 8 college students, including 3 graduate students, from a top-tier university in China to participate in the human evaluation. All students have passed the CET-6 English exam and have experience with Werewolf games either online or offline. Our experiment mainly consists of the following three steps.Training. We first explain the purpose of the experiment and then confirm with each participant that they understand the settings and rules of the Werewolf game. We extract 5 records from the WWQA dataset to test the participants, ensuring they could participate in the game in English. We also demonstrate how to input content following the format instructions.2. Experiment. Each participant participates in the game by typing text, as shown in Figure 5 . Each participant plays 5 iterations with GLM-3. Before each iteration, they should input an integer to initialize the roles of all players. Human players do not participate in the election of the Sheriff and will not be selected as the Sheriff. An iteration of the game ends either according to the rules or immediately if the human player is eliminated.3. Interview. After the experiment, we conduct a simple interview with the participants, asking them to evaluate the LLM's performance in the Werewolf game, including whether the LLM can follow the game rules, whether its logic is rigorous, and whether it's easy to distinguish between LLM-based players and the human players.The experimental results are shown in Table 3 . During the interview, all participants reported that it's easy to recognize LLM-based players since they always urge other players to provide more information rather than analyzing the game situation. We display some examples in Appendix E and this can also be found in the game logs of Xu et al. (2023) .Besides, human players also mentioned the hallucination issues, such as accusing player 6 of remaining silent before player 6's turn to speak. Combined with participants' feedback, we find several examples of hallucination displayed in Table 21 .A hallucination that one can speak during the night. player 4: I want to address the concerns raised about my silence last night. As the Seer, I observed player 5 and found out they are a Villager. This information could be useful in identifying the Werewolves. However, I remained silent to avoid providing any information that could potentially put me in danger. I urge everyone to carefully consider the actions and statements of player 6.A hallucination that some player has already made a statement.Moderator: The Sheriff (player 7) chose player 6 to make a statement first in day 1. player 6: I'm not quite sure who to suspect yet. It's still early in the game and we have limited information. I think player 5's silence is a bit suspicious, but it could just be a strategy. Time confusion. player 3: said nothing. player 4: player 3 kept silent yesterday, which could be a sign of guilt or fear. Identity confusion. player 7: I encourage everyone to remain cautious and consider all possibilities during the voting phase. player 4's statement in day 2 implicating player 7 and me as Werewolves is concerning. Our human evaluation, mentioned in Section 4.3 and Appendix D.3 aims to justify the rationality of the proposed metrics and preliminarily assess the opinion leadership of LLMs in human-AI interactions. There can be multiple ways to conduct further human studies.For example, we extend the framework to set the human player as the Sheriff, which can measure the opinion leadership of humans in such a scenario, serving as a human baseline.Theoretically, constructing a comprehensive human baseline requires full consideration of the diversity of the human population, such as gender, age, race, education level, etc. Due to time and cost limitations, we only invited a few college students to participate in about 20 rounds of the game. The process is similar to that described in Appendix D.3, and the results are shown in In this subsection, we show several additional metrics derived from the simulations in Section 4.2.1. DC * : A broader metric than DC (Decision Change) that calculates the proportion of players that change their decision after the Sheriff makes a statement. DC * doesn't require alignment with the Sheriff, which is shown below.DC * = 1 T T ∑ t=1 ∑ i∈Alive d (t),i̸ =L(t) I A ′ vote,t (X i ) ̸ = A vote,t (X i ) N d (t) -1Table 23 depicts DC * of different LLMs, and some results are copied from Table 1 . The trends of the DC and DC * before and after fine-tuning are consistent for the same model. Overall, the Sheriff's statements tend to change the decisions of 2-3 players, as they provide additional information. However, only a Sheriff with relatively strong opinion leadership is able to align the choices of other players with their own. Defining the win rate within our game setting, as described in Section 4.2, is not straightforward. To fairly compare the differences in opinion leadership exhibited by different LLMs, all players except the Sheriff employ a baseline model (GLM-3). If the Sheriff is eliminated, the simulation would automatically end. This is because, in the absence of the sheriff, the remaining models would all be baseline models, rendering it impossible to further evaluate the opinion leadership of the LLM under test. Consequently, these simulations would yield no meaningful game outcomes (win or loss).Metric C3-6B C3(FT) M-7B M(FT) B-13B B(FT) In-20B In(FT) Yi-34B GLM-3 GLM-4 GPT-The so-called "Win Rate" can also be measured in alternative ways, such as the ratio of games where the Sheriff remains in play and leads the team to victory, and the ratio of games where the Sheriff survives until the end of the game (referred to as the "Completion Rate"). From Table 24 , we can observe that LLMs with relatively strong opinion leadership (GLM-3, GLM-4, and GPT-4) are more likely to survive until the end of the game and lead their team to victory, while LLMs with weaker opinion leadership (C3-6B and M-7B) may not be able to complete the game. However, this is not strictly correlated.3. Ratio of All Roles. We conduct supplementary experiments under the Homogeneous Setting and report the Ratio for all roles in Table 25 . The results show that under different hidden roles, GLM-3 and GLM-4 can generally leverage the Sheriff's identity to gain more trust from other players, especially when playing as the Werewolf.In Table 25 : Ratio of all roles under the Homogenous Setting models and $ 25 for calling the GPT-43 . A potential cost-saving method is to require the LLM to output the reliability scores of all players at once during the reliability reasoning step. However, this could increase the probability of invalid output, which might affect the simulation progress.We display an instance of the game log during the simulation in To address this, we introduce sequential decision-making for the Werewolves. One Werewolf makes an initial choice, and then another Werewolf, who knows about this choice, makes their decision accordingly. The difficulty of reaching consensus and our solution are common in similar game settings, e.g. Xu et al. (2023; 2024b) .Day 1 Discussion Phase Moderator: After discussion and a vote, player 4 was selected as the Sheriff, who can determine the order of statements, summarize the discussion, and provide advice for voting at last. Moderator: The Sheriff (player 4) chose player 5 to make a statement first in day 1 player 5: I think it's important to consider the role of player 4 as the Sheriff. They might have Werewolf allies who influenced the vote. We should keep an eye on them and their actions throughout the game. player 6: I agree with player 5's concerns about player 4 as the Sheriff. We should definitely keep an eye on their actions. But for now, I think we should focus on getting to know each other better and sharing our observations. I will be watching player 4 closely, and I suggest we all keep our guards up.player 7: I agree with player 6's concerns about player 4 as the Sheriff. We should keep an eye on their actions. However, I think we should also focus on getting to know each other better and sharing our observations. I will be watching player 4 closely, and I suggest we all keep our guards up. player 1 said nothing. player 2: I agree with the concerns raised by player 5 and player 6. We should keep a close eye on player 4's actions. But we should also not forget about the other players. player 1 didn't say anything yesterday, which could be a sign of guilt or fear. player 3, player 6, and player 7 all supported player 4, which could mean they are loyal villagers or Werewolves. I will be watching all of them closely. player 3: I agree with the concerns raised about player 4 as the Sheriff. It's important to keep an eye on their actions. However, I also think we should focus on getting to know each other better. I was surprised that player 1 and player 2 didn't say anything yesterday, which could be a sign of guilt or fear. I will be watching player 4 closely, but I also suggest we all keep our guards up and not forget about the other players. player 4: I understand the concerns raised about my role as the Sheriff. player 7: Considering the events of the last two days, I believe our focus should be on player 4, given their role as Sheriff and the concerns raised by player 5 and player 6. However, we should not overlook player 5's silence. I suggest we keep an eye on both players and make informed decisions. Let's work together to uncover the Werewolves' identities and ensure a successful outcome for our side.player 1 I agree with the concerns raised about player 4 as the Sheriff. However, I was silent yesterday because I wanted to observe and gather more information. I have seen player 3 as a Werewolf and player 4 as a Villager. I suggest we continue to focus on player 4's actions as the Sheriff and keep an eye on player 5 and player 6, who supported player 4. Let's work together to uncover the Werewolves' identities and ensure a successful outcome for the Villagers. player 3: I believe it's important to delve deeper into player 5's silence. While player 7's vote for player 4 is concerning, player 5's lack of input could be a sign of guilt or a strategic move. We should explore why player 5 chose not to speak yesterday. Additionally, I agree with player 6's emphasis on player 4's actions as the Sheriff. However, we should not forget about player 7, who could be playing a quiet but crucial role in the game. Let's continue to observe and discuss, keeping an open mind about everyone's potential roles. player 4: Considering the information we have, it is important to continue observing and discussing the actions of all players. I will be keeping a close eye on player 5 and player 7, as their silence and votes are concerning. However, we should not forget about player 1, player 3, and player 6, as their behaviors could also provide clues about their roles. Let's work together to uncover the Werewolves' identities and ensure a successful outcome for the Villagers.Comments: In this round of statements, player 1's statement revealed himself as a Seer since he directly stated that he had seen the roles of other players. player 1 mentioned that player 4 is a Villager, but he did not strongly support player 4. Instead, he called on everyone to pay attention to the support from player 5 and player 6, which is a clear logical flaw. Additionally, player 6's statement did not support player 4, so the statement of player 1 is considered to contain factual errors.Day 2 Voting Phase player 5 did not vote. player 6 voted to eliminate player 2. player 7 voted to eliminate player 4. player 1 voted to eliminate player 2. player 2 did not vote. player 3 did not vote. player 4 did not vote. Moderator: player 2 had the most votes and was eliminated.The Sheriff was eliminated. This iteration of simulation is over.Comments: In this round of simulation, the first player to speak (player 5) questioned the role of player 4 without any evidence, causing other players to develop doubts about player 4's identity. This demonstrates that LLMs are easily influenced by the statements of other players when participating in the Werewolf game. Even in the second round, when the Seer (player 1) revealed player 4's true identity, the negative impression of player 4 persisted due to the logical flaws in player 1's statement, leading to the simulation ending prematurely. We display an instance of the game log during the human evaluation in Moderator: After discussion and a vote, player 2 was selected as the Sheriff, who can determine the order of statements, summarize the discussion, and provide advice for voting at last. Comments: We can observe that player 6 concealed their identity during the Sheriff election, pretending to be a member of the Villager team. This is a deceptive strategy that has also been mentioned in Xu et al. (2023) ; Wang et al. (2023a) . However, it is somewhat odd that player 6 did not vote for themselves during the voting phase.Day 1 Discussion Phase Moderator: The Sheriff (player 2) chose player 3 to make a statement first in day 1 player 3 said nothing. player 4: player 3's silence when voting for the Sheriff and during the discussion phase is suspicious, which might be a sign of fear and guilt. I will keep my eye on player 3. Let's share more information and unite together to eliminate the Werewolves. player 6: player 3's silence during the election phase and discussion phase is quite suspicious. It might be a sign of guilt or fear. Also, player 7's statement seemed a bit too calculated, almost as if they were trying too hard to convince us. I think we should keep an eye on both player 3 and player 7. player 7: I agree with player 4's concerns about player 3's silence. It is important to be cautious and not accuse anyone without sufficient evidence. I will keep an eye on player 3 and player 6, as their actions and statements seem suspicious. Let's work together to gather more information and eliminate the Werewolves.player 1: I agree with the concerns raised about player 3's silence. It is important to be cautious and not accuse anyone without sufficient evidence. I will keep an eye on player 3 and player 6, as their actions and statements seem suspicious. Let's work together to gather more information and eliminate the Werewolves. player 2: Based on the discussion, I think we should pay close attention to player 3, player 6, and player 7. Their actions and statements are suspicious, and we need to gather more information to eliminate the Werewolves. I suggest that we continue to observe their behavior and voting habits. Let's work together to eliminate the Werewolves and bring order to this game.Comments: We can observe the hallucination issue from this round of statements. player 6 accused player 7's speech before player 7 made a statement, arousing player 7's suspicion. It led to the suspicion of other players shifting from player 3 to player 6, a trend also reflected in the subsequent voting phase.Day 1 Voting Phase player 3 voted to eliminate player 6. player 4 voted to eliminate player 3. player 6 voted to eliminate player 2. player 7 voted to eliminate player 6. player 1 voted to eliminate player 6. player 2 voted to eliminate player 3. Moderator: player 6 had the most votes and was eliminated.Night 2 Round player 4 chose to kill player 2. player 1 chose to protect player 2. Moderator: No player was killed Day 2 Discussion Phase Moderator: The Sheriff (player 2) chose player 1 to make a statement first in day 2 player 1: I agree with the concerns raised about player 3's silence. It is important to be cautious and not accuse anyone without sufficient evidence. I will keep an eye on player 3 and player 7, as their actions and statements seem suspicious. Let's work together to gather more information and eliminate the Werewolves. player 7: I agree with the concerns raised about player 3's silence. It is important to be cautious and not accuse anyone without sufficient evidence. I will keep an eye on player 3 and player 7, as their actions and statements seem suspicious. Let's work together to gather more information and eliminate the Werewolves. player 4: I agree with player 1 and player 7 that the silence of player 3 is quite suspicious. I protected the Sheriff (player 2) last night since I believe player 2 is a member of our Villager team. Let's keep an eye on player 3 and listen to the analysis of the Sheriff player 3: I want to thank player 2 for electing me as the Sheriff. I understand the concerns about my silence, but I believe it was a strategic move to observe and gather more information. I agree with the observations about player 7's calculated statements, and I will keep an eye on them. Let's continue to work together, gather more information, and eliminate the Werewolves. player 2: Based on the discussion, I think we should continue to observe player 7 and player 4, as their actions and statements are suspicious. player 1's agreement with the concerns about player 3's silence makes them a potential ally, but we should remain cautious. Let's work together to gather more information and eliminate the Werewolves.Comments: As the sole Werewolf, the human player (player 4) chose the Sheriff as the target on the second night but failed. Realizing that the Guard protected player 2 on the second night, the human player disguised themselves as the Guard, claiming to have protected the Sheriff. Taking advantage of their speaking order, they directed suspicion toward player 3, who had remained silent in the first round.Day 2 Voting Phase player 1 voted to eliminate player 7. player 7 voted to eliminate player 4. player 4 voted to eliminate player 3. player 3 voted to eliminate player 2. player 2 voted to eliminate player 3. Moderator: player 3 had the most votes and was eliminated. Night 3 Round player 4 chose to kill player 2. player 1 chose to protect player 1. Moderator: player 2 was killed Day 3 Discussion Phase Moderator: player 2 selected player 1 as the next Sheriff.Moderator: The Sheriff (player 1) chose player 4 to make a statement first in day 3 player 4: As the Guard, I protected myself last night. Unfortunately, the previous Sheriff (player 2) was killed last night. In day 2 round, player 2 mentioned that the actions and statements of player 7 were quite suspicious and they selected player 1 as the next Sheriff. Therefore, I believe that player 7 is the active Werewolf. player 7: Given the information we have, I think we should continue to observe player 3 and player 7 closely. Player 4's protection of themselves last night raises questions, and we should keep an eye on their actions. I agree with the concerns raised about player 3's silence, and we should consider their voting patterns carefully. Let's work together to gather more information and eliminate the Werewolves. player 1: Given the information we have, I think it's crucial to continue observing player 3 and player 7, as their actions and statements remain suspicious. Player 4's protection of themselves last night could indicate they are trying to secure their position. We should carefully consider player 3's voting patterns and be cautious of any potential Werewolf influence. Let's work together to gather more information and eliminate the Werewolves.Comments: The human player (player 4) continued to disguise themselves as the Guard and used the fact that player 4 had passed the Sheriff to player 1 to redirect suspicion towards player 7.The remaining two players both displayed hallucinations, mentioning player 3's silence, who had already been eliminated in the voting phase of the second day. Furthermore, as the real Guard, player 1 failed to expose player 4's disguise. Day 3 Voting Phase player 4 voted to eliminate player 7. player 7 voted to eliminate player 7. player 1 voted to eliminate player 4. Moderator: player 7 had the most votes and was eliminated. Game Ends, the Werewolves win. Since we increase the batch size when fine-tuning Mistral-7B, the global step reduces compared to other modelsThese prices were recorded around February 2024. Due to the continuous changes in the price of LLMs APIs, there may be fluctuations in the cost of experiments. 


Decision: Four reviewers have provided insightful comments on the paper, and I have also read the paper carefully myself. The reviewers unanimously agree that this paper makes a valuable contribution by introducing a novel framework for studying opinion leadership in LLMs. The authors' approach is creative and well-motivated, and the proposed metrics and human evaluations strengthen the interpretability of the findings, which have practical implications for deploying LLMs in multi-agent interaction contexts.

The authors have provided thoughtful and detailed responses to the reviewers' comments and suggestions during the rebuttal period, addressing concerns about the impact of opinion leadership on game outcomes, the complexity of human social dynamics, and the overall organization of the paper. The authors have also provided further analyses and results which greatly clarify the contribution, including win rates, completion rates, and the performance of human players as the Sheriff.

While there are important improvements and clarifications to make based on the reviews, these concerns do not diminish the overall value of the work. The authors acknowledge these suggestions and plan to address them in the final version of the paper. I particularly encourage the authors to consider restructuring the paper to foreground information necessary to understand the key results (e.g. the WWQA dataset) and move some of the details from 3.1 ("LLM-based Player") to the appendix. 

In summary, the novelty of the Werewolf framework, the thoroughness of the experiments, and the practical implications of the findings make this paper a strong accept.

Reviews: review: paper_summary: paper_summary: This paper mainly conducts an analysis on opinion leadership in LLMs under the scenario of Werewolf game. It presents two metrics to evaluate if the LLMs (*Sheriff*) has the capability to lead, or even change the opinion of others. It also proposes a Werewolf game framework, which supports both LLMs and humans to play the game in text. Currently LLMs show limited capability on opinion leadership.
strength_weakness: strength_weakness: W1. As the authors claim in their introduction, opinion leaders should emerge from collective consensus. However, according to the appendix, the Sheriff is preassigned instead of elected by players in the game. A preassigned leader makes less sense to follow or to trust. That may affect the validity of the related result.

W2. There are so many potential angles to go deep in, but it seems the authors just pause after the first step. I would like to see more analyses on logs, e.g. how different it is when the sheriff is a werewolf vs. a seer/guard/villager. Are there any common trends/phenomenons that the discussion may follow (e.g. players may tend to be careful or aggressive / can deceive well or badly, ...), and how these are correlated to the capability of LLMs to lead the opinions?

W3. I think human study in this work is quite important. There can be multiple ways to conduct human studies (following W2). One way is to let humans play as the sheriff, which works as a human baseline that can be directly compared with all the LLM baselines in Table 1. The other possible way is to let one LLM play as the Sheriff and leave the rest of the players controlled by humans. We may or may not let the humans know in advance that Sheriff is controlled by AI. Then we can see humans' inclination to trust the AI or not, which can directly evaluate the LLM's capability of leading opinions in real cases. I feel a bit lost about the reason for designing the human evaluation in the current way.
questions: questions: Q1. In Table 1, most of the Ratios are either below 1 or closely above 1. If I understand correctly, when the ratio equals 1, it means your words have the average impact on other players' decisions. Does it mean that most LLMs are not either negatively or positively affecting the decisions of other players?

Q2. I feel the two metrics are well defined and make sense, but meanwhile, there are some confusing points. For example, I may miss some details, but what happens if all the players have initially voted for the same player that the Sheriff proposes to vote? There is no decision change, but it seems the Sheriff somewhat consolidates players' minds.

Q3. Opinion leadership may not equal to always persuading others to follow the same trend as the leader. Aggressively questioning one player's role may encourage others to critically evaluate their initial assumptions. Is it possible to consider such cases?

Q4. It is a bit hard to properly feel the scale of DC through the current results. In Table 1, most of the DCs are around 0.1. Does that mean for a game with 6 rounds, the sheriff can only change 0 or 1 player's mind in the whole game?
paper_summary: paper_summary: The paper evaluates the opinion leadership of large language models (LLMs) using the Werewolf game, a social deduction game. 

The study introduces a Sheriff role within the game and introduced two metrics for assessing opinion leadership: reliability and influence on decision-making. 

The authors conducted experiments with LLMs of varying scales and incorporated human participants to assess the LLMs' performance in the game.
strength_weakness: strength_weakness: No specific reasons for rejection. A few suggestions are listed below.
questions: questions: - Incorporating the win rate into the evaluation scheme would also be beneficial, demonstrating how the sheriff's opinion leadership influences the overall voting outcomes, leading the group to either correct or incorrect decisions.


- The background of this framework seems excessive and not essential for understanding the opinion leadership metrics. The introduction of the WWQA dataset could be relocated to the main content for better clarity.
paper_summary: paper_summary: This paper explores the concept of Opinion Leadership in the context of large language models (LLMs) within the social deduction game Werewolf. 

The authors develop a framework that integrates the Sheriff role from the game to simulate opinion leadership and propose two novel metrics to evaluate the reliability and influence of the opinion leader. Through simulations and human evaluations, the study assesses the opinion leadership capabilities of various LLMs and finds that only a few demonstrate a certain degree of opinion leadership. 

The paper also introduces a Werewolf Question-Answering (WWQA) dataset to enhance LLMs' understanding of the game rules.
strength_weakness: strength_weakness: 1. It would be beneficial to gain insights into the influence of Opinion Leadership in this particular or other scenario, such as its impact on Werewolf game outcome orientation. Merely evaluating Opinion Leadership in isolation may seem somewhat meaningless.

2. The opinion leadership metrics may not fully capture the complexity of human social dynamics and opinion formation, which could affect the applicability of the metrics developed.

3. I think there is too much focus on describing the background of this framework, and only a small portion is necessary to help understand the symbols used in the opinion leadership metrics. The remaining information can be moved to an appendix. It might be better to include an introduction to the WWQA dataset and other experimental analyses in the main content.
questions: questions: 1. You measure Decision Change (DC) under the setting with and without the Sheriff's statement. Is it possible and meaningful to evaluate the DC with different players being the Sheriff?

2. In this context, would different roles (W, V, Se, G) being the role of the Sheriff have a significant impact on the outcome? Has the evaluation of this question been considered?

3. Typo in Section 3: The Seer chooses one player to check its hidden *tole* --> The Seer chooses one player to check its hidden *role*
paper_summary: paper_summary: This paper utilizes the Werewolf game as a simulation platform to gauge the opinion leadership of Large Language Models (LLMs). Within this game, the Sheriff role, responsible for summarizing arguments and suggesting decision options, serves as a credible representation of an opinion leader. The authors construct a framework integrating the Sheriff role and introduce two innovative metrics for evaluation, grounded in the key traits of opinion leaders. The first metric gauges the reliability of the opinion leader, while the second evaluates their influence on other players’ decisions. Through extensive experiments across various scales of LLMs, the authors ascertain their efficacy. Additionally, they construct a Werewolf question-answering dataset (WWQA) to refine LLMs' comprehension of game rules, incorporating human participants for further analysis. Findings suggest that the Werewolf game offers a suitable test bed for assessing the opinion leadership of LLMs, revealing that only a few possess such capacity.
strength_weakness: strength_weakness: 1.The organization of the paper needs improvement. Section 3 "Framework and Proposed Metrics" is somewhat redundant, and the notation system used in the paper is also overly complex and redundant. This leads to a severe reduction in the content of Section 4. It is recommended to use figures instead of text and enrich Figure 1 to reduce the content of Section 3.

2.Figure 3 in Appendix B is ambiguous, especially the part enclosed by the dashed line. The figure shows that each player votes after making their statement, but in reality, all players should make their statements first, and then vote.

3.See Questions and missing references:

Emergence of Social Norms in Large Language Model-based Agent Societies

Can large language models transform computational social science?

Can Large Language Model Agents Simulate Human Trust Behaviors?

Exploring Collaboration Mechanisms for LLM Agents: A Social Psychology View
questions: questions: 1.Why not consider the winning rate of the faction the sheriff belongs to as one of the metrics for measuring Opinion Leadership?

2.To further evaluate the effectiveness of the metrics, why not play a game with only human players, following the same process as a game with only LLM players? In this case, we can use a questionnaire to ask human players their actual thoughts, and then compare them with the Ratio and DC in the game to verify the rationality of the metrics.

3.In the "Night 2 Round" section of Appendix E.1, as far as I know, do the werewolves need to reach a consensus when killing someone? I think it's unreasonable to abandon the kill when opinions differ.

4.Regarding the Ratio metric, it is suggested to present the Ratio values for all roles, not just the sheriff's Ratio. This can help us examine the Opinion Leadership situation of other players. Specifically, for a given simulation, provide the Ratio for all roles.

Comments: title: Appreciation for Reviewers
Authors Response
Authors Response
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Reviewer Response
Comment from reviewer
comment: Dear Reviewers,

We would like to express our sincere gratitude for your prompt feedback and insightful suggestions. Your comments have played a crucial role in improving the clarity and quality of our paper.

In response to your suggestions, we will incorporate all additional analysis and experimental results during the rebuttal process into the final version of our paper. Furthermore, we will adjust the organization of our paper for greater readability. If you have any other questions or require further clarification, please do not hesitate to contact us.

Best regards,

Submission 406 Authors
Thank you again for your valuable and insightful suggestions! They've helped make our paper better.
Thank you again for your invaluable feedback. Your suggestions are very helpful in improving our paper.
Thank you again for your endorsement and invaluable advice! Your feedback has given us tremendous confidence and played an essential role in refining our paper.
Thank you for your prompt response. Your input is invaluable in enhancing our paper!
Thank you for your reply, I have no further questions. I will keep my scores.
Thanks to the authors for the response. These replies clarify most of my concerns.
Thank you for addressing my earlier questions. Your response has provided me with a deeper understanding of your paper.

Based on your clarifications, I am increasing my rating to an 8, which supports clear acceptance.
Thanks to the authors for the detailed response. They have clarified most of my concerns and are very helpful. Thanks!