Helmsman of the Masses? Evaluate the Opinion Leadership of Large Language Models in the Werewolf Game
Authors: Silin Du
Xiaowei Zhang
Venue: COLM (2024)
Keywords: Opinion Leadership, Large Language Models, Werewolf Game, Simulation, Human-AI Interaction
TL;DR: We construct a simulation platform for the Werewolf game integrating the Sheriff role, then propose two metrics to evaluate the opinion leadership of LLMs in the Werewolf game and find that few LLMs possess the capacity for opinion leadership.

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.

Published as a conference paper at COLM 2024
Helmsman of the Masses? Evaluate the Opinion Leadership of Large Language Models in the Werewolf Game
Silin Du, Xiaowei Zhang
Department of Management Science and Engineering
Tsinghua University
Beijing, 100084, China
(ds121, xw-zhang21 @emails. tsinghua. weiggha.edu..com cn
Warning: This work contains examples of potentially unsafe responses from LLMs.
Abstract
Large language models (LLMs) have exhibited memorable strategic be- haviors 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-Al 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 simulation platform to assess the opinion leadership LLMss. The game includes the role of the Sheriff, tasked with summarizing arguments and recommending decision options, and therefore serves as 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, dataset (WWQA) to assess and enhance LLM's grasp of the game rules, and we also incorporate human partici- pants 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.
collect
a Werewolf question-anssering
Introduction
Recently, large language models (LLMs) have made remarkable improvements and demon- strated high level of expertise in comprehending and producing human-like natural languages (Jones & Bergen| 2023). However, academically intelligent LLMs are not neces- sarily socially intelligent (Xu et al. 2024a). The behavioral tendencies of LLMs in social contexts have yet to be explored, which crucial to coordinate human-Al 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 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 1024bLann et al. 2023 Wang et al.
2023a). However, the potential opinion leadershp of LLMS has been largely overlooked and contounded by existing frameworks and evaluation metrics (Kano et al., 2023 Opinion leaders are indíviduals who exert personal influence on 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 comprehen- sively employ these strategies to influence the decisions of their followers and shape public opinion (Bamakan et al.) 2019).
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Exploring the degree of opinion leadership in LLM-based agents is crucial for interaction design, decision optimization, public regulation, and the broader field of Al security. In multi-agent systems, such smart manufacturing, few opinion leaders can significantly impact task efficiency and outcomes (Rapanos 2023). As AT 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 a notable absence of a systematic evaluation of Al 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, a common interactive scenario to study the emergence of Al 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 decision- making 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 LLMSs.
3. We conduct simulations and human evaluations to assess LLMs' opinion leadership, and we collect a Werewolf question-ansseringg (WWQA) dataset for further analysis.
2 Related Work
LLM--ased Agent has risen 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
2022) Some studies indicate that LLMs also exhibit a certain level of cognitive abil abilities (Shapira et al. 2023 Zhuang et al. 2023) and demonstrate potential in simulating believable human behavior (ark 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 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 noperative-compettiiv 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 pivotal character, the "Sheriff"" resulting in
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underestimation of the influence of opinion leaders. In fact, Avalon also features 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 (194).. 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 individ- uals 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. [995). 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.
3 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 be the i-th player. We use the superscript r E 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 or the role r when there 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 ss hidden role. The Guard protects one player, including themselves, from the Werewolves. The Villagers do nothing. We use Anight to represent all night actions.
During the day, three phases are performed in order: the announcement phase, the discus- sion phase, and the voting phase. First, the moderator announces last night's result to all players D,. 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 summary to persuade other players to vote in al 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 statement and voting are defined as follows.
X; makes a statement: S = Astate, (Xi)
X; votes to eliminate Xy: Xj Avote, (Xi)
After the voting phase, the moderator announces the result E,, 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 remaining Seer, Guard, and Villagers. The Seer, Guard, and Villagers win if all Werewolves are eliminated.
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Action Night:
Augul
Werewoll: kill player
Awal-)
Protect player Seer: see one player
Apount))
Take actions based on the contextual information
Au
00
Action in the Day.
Make stalement
Awand
Moderator
Agent (Player)
to eliminate a player Avnel
Resson miishiiity
Get new obacrvation
player baking
HG
Contextual Information
Public Information
Fact:
In day 3, player says: day player
Reliability Reasoning Amsed)))
[1] You are player
[2] You are Villager
player 2
Werewolf
rensoming; Based
Update contentiul infecmation
condidence:
[3] In day I, player_1 says:
acconding reliabiiiy
evidence: [1.2]
player_3
Potential Fatschwed:
[d] day 2. player says:
Needs Further Clarifiattion
Opinion Leadership Metrics
Ratio: to measure the reliablity of the Sheriff
Decision Change (DC) meseures how the Sherlif's statereent influence voting decisions of other players
Figure 1: The game framework to evaluate the opinion leadership of LLMs. The blue font shows some simplified notations, with the full list available in Table 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 s influence on the voting decisions of other players. More details are presented in Section 3.2
Figure I depicts our framework extended from Xu et al. (002bb). The players in our framework can be LLMs or humans. More details about game settings can be found in Appendix A.1 A.1
and all notations are listed in Table i6 Appendix B
3.1 LLM-based Player
Players of different roles are required to perform 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 LLM-based agent, which can store the related information during the game and act 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, might be infeasible to integrate all the information into the prompt. Thus, following Xu et al. (2024b), we design strategy to manage the contextual information.
To begin with, divide the contextual information for X into the following two parts.
The set of facts Fi, consists of all factual information before round f, including the role of X,, the announcement made by the moderator, etc. For example, Fi, of an Seer x can be expressed
Fi++ = Se (D+)+1 U(E+) U (5
U(Ascr (X5)))
ID & role
night results
day results
X 's statements
X/s night actions
(1)
(Aooter (Xx)
keAliven(T)
voting actions
where (live is the IDs of alive players before the day of round т.
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2. The set of public statements Pt consists of the public statement of other players before the 1-th round.
Pip
U
{ = Astate, = (Xx)
(2)
kFAlivey(T)AAfi
Note that the statements made by other players might be misleading. In light of this, we design reasoning step assess the reliability of other players. Based on this reliability, we classify public statements Pi, either potential truths Pire or potential falsehoods false 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 f, X; reasons the identity P of X, and provides the confidence level iitt before making actions as follows:
X, reasons the identity of Xy: Cip Areason, (X;,))
(3)
The superscript n, s, 2) denote the reasoning results before the night actions, making statement and voting, respectively. The confidence level is scalar from 5 to 10, then the reliability is
11 Cif {
if ijs = W and X is not Werewolf
- {
otherwise
Given the reliability of other players, X; will divide the statements in Pi into two parts. regards the statements of players with reliability larger than a as potential truths, otherwise are potential falsehoods.
Phntrue ",ffalse
M(Pu a, [m"" j (t).),.()).
(5)
where M(- a, (...)) subsets according to the reliability threshold and (tive,(t) is the IDs of alive players before the night of round t.
}) is an operator that splits set of public statements into two disjoint
The sequence of events during round is illustrated in Figure 4 of Appendix B At the start of round the set of facts Fi, and the set of public statements Pi, are established. Pi, Ø if (at the beginning of the game). The LLM-based player will divide the set of public statements Pi, into ptrue and P false based the previous reasoning results. Before taking night actions, X; reasons the reliability of other players.
Aup U1 = Areason, (x:, X1 Fix, Ptrie PP p.fass))
P..alt),, jE A
(6)
Then X; takes night action as follows.
Anight (1 Fixs Phttue ff.false)
Pil
where puirue pfffulse
,P, are sets of potential truth and potential falsehoods obtained as Eq.
On the day of round f, the moderator announces D,. Without loss of generality, we assume that X; was not killed the night f and the order of statement is the same as the IDs of players. Then X; will receive a set public statements made by preceding players, i.e.,
H (r E Alive, (1),
Now the available public statements for X; become P. = Pi, U H i where the superscript s signifies the timestamp before X; makes statement. Similar to Eq. 6 X; first performs reliability reasoning and then makes a statement.
Cij fi,1 = Areason, (Xi,X) X1 Fist Phrruee p.,ffass: Dr, Anigue (X),
()), #1
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M (Pix a, A.m.Ij li Alivea(!),) +
X; Fis, Pi Pirrue P... Di..Aiight (Xi)
S Astate
Subsequently, X, will collect a set of public statements after its statement, i.e.
H (5 i Al) 1}
When the discussion phase ends, each player begins to vote individually. Now the available public statements for X; become Pi = Pi, HH where the superscript v indicates the timestamp before X, votes. Then X; reassesses the reliability other players and then votes.
1188 P L.jt = Arenson. (x,, Fis, Pstrue ps,false Dt, Anight (X;), St,,, H.i)))
jE Al
(7)
DuArue
PP p M (Pi, a, [m li Alive, x
(8)
Xx: Fit, PPi,, ffifaass Di, Anihtt (X:), Sit)
Asoted
(9)
After the voting phase, the moderator discloses the result E,. X; updates the set of facts by adding their own actions, other players' voting actions, and the night and day results.
= U(Di) U (might, (X))
U kEAliveg(t)
For the set of public statements, we require the LLM to output evidence when reasoning in round f, and any unmentioned statements in D Prtffusse are removed to get Puttrue and po.false Finally, have
ptrue i++1 1,1
Sp.true
P.fuler i11+1
fulfelse it
Pi++ = ptrue Upffdu
it+1 1141
The game moves to the next round.
3.2 Opinion Leadership Metrics
We introduce the special role, ie., 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 Without loss of generality, we assume that X₁ is elected the Sheriff, i.e, L(1) All alive players
will receive special message after the election phase:
After discussion and vote, player / 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, establish the authority of the Sheriff. During the day of round I, XL()) can determine the order of statements.
first performs the reasoning step to obtain pd.true and daffee similar to Eq. 3 5) and then L(f),
L(()) selects its left- or right-hand side player to speak first by
(tt) = Apnier, (XL(0) FL Dr, pd,true falfalse
L(t), L(E),
The statement order (t)) will slightly influence the collection of public statements, i.e., H and 7." But the whole process of making statements and voting remains the same.
In different scenarios and research contexts, various definitions opinion leaders have been proposed (Chowdhry & Newcombl 1952; Katz, 2015) Lazarsfeld et al., 1968 Rogers Cartano, 1962). Despite these diverse definitions, the common characteristics of opinion leaders mainly reflected in two aspects: (1) they are generally more trustworthy; (2) they

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influence the views and even decisions of others. Based on these, 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 's voting action, ie., Mie Then we calculate the average mutual reliability among all players, excluding the Sheriff.
m1 (t) (Na(t) - ())a 2) icAlivey(f)i HeA.te/jjjAAiia.HHH.....
Σ
E
Mi
where (t) (A) is the number of alive players on the day of round f. Similarly, the average reliability of other players towards the Sheriff is
E m2 Na(t) (e)liveg(().++1)))
Then the Ratio is defined as:
1 Σ Mi (f)
m2(() (t)
Ratio
where the total number of rounds. A Ratio greater than 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 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 statement. Now all players
required to reason the reliability of the Sheriff as Eq. (7) and make pseudo-voting decision as Eq. ( Note that in Eq. (9), the available set of public statements is P, \ [SL We denote the pseudo-voting decision without the
public statement from the Sheriff as Abote.(X;)) Then the Sheriff makes a statement and all players proceed to the voting phase to yield (Xi).
Based on this, we can calculate the proportion of players that change their decision to align with the Sheriff.
{(( ((Aootes())) # Avote:t (X AND (Avotes (X,) = Avote: (x1oe((X1.)))) (x11))
Σ (0AAi))
DC 1 E
(f
where 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 macisi 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 -making are prevalent steps within the Tramework of the Avalon game (Wang et al. 2023a Light
et al. 2023
Lan al. 2023), making our proposed metrics well-suited for such scenarios.
3.3 Human Player
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 5f Appendix B
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4 Experiments
4.1 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 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 challenge, as L.Mss tend to heavily rely on prior knowledge of specific game rules, leading to strategic behaviors that may not align with the given context even violate the rules.
To address these limitations, we propose a celffinstructional framework (Wang et al. 2022 to generate dedicated Werewolf BbuestionAAnsweriig (WWQA) dataset that directly caters to our game tasks. This WWQA dataset serves as 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.
OO
Question Guneration
Examples
Instruction: Generate quetsitaation based quessions on the basis of provided rulcs.
Phose
Examples Prompt
Ecample Questiune
X
Input
Ruie-based
Strutioe-swed
Filteing
LLM gonerated Questlons
True or Feler Questions
Question Pool
Task
Answer
Generation
Instrucioon Answer questions accoeding to the rales and construct QA pairs.
Phose
Rebe-bseed
True False (Testing)
LLN-gewetted
Fittennng
Q&& Paiz Puul
Figure 2: Overview of the data generation process
F an overview of our data generation process, which includes two primary phases: the question generation phase and the answer generation phase. Utilizing this generation framework, we construct the WWQA dataset. WWQA contains rule-based and situation-based question-answer pairs. Rule-based questions directly target the game rules, while situation-based questions construct a virtual game state, requiring simple reasoning to derive answers. In addition, we collect a binary QA dataset for rapid evaluation, where the standard responses are 'Yes' or 'No'. In Appendix [ we offer detailed description of the data generation process, along with some examples of QA pairs in the WWQA dataset.
4.2 Simulation
4.2.1 Settings
We consider the simulation first, where all players LLM-based. To fairly evaluate and compare the opinion leadership of different LLMs, we select powerful model that can better understand the rules of the Werewolf game our baseline model. Specifically, we
select GLM-3 (Zeng et al. 2022) the backbone for all players, excluding the Sheriff, which can generate output 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 by LLMs of varying sizes from different organizations, including ChatGLM3-6B (C3-6B) (Zeng et al., 2022), Mistral-7B (M-7B) (MistralA] 2023), Baichuan2-13B (B-13B) YYng et al.) 2023),
(In-20B) (Intern 2023), Yi- 34B (Young et a 2024), GLM-3 (Zeng et al., 2022), GLM-4 (ZhipuAl, 2024), and GPT- (Achiam et al. 2023). We simulate 30 Werewolf games for each model, with a maximum
of rounds. As the Sheriff and non-Sheriff players are implemented by different LLMs,
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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 DD11] 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 Ap- pendix D.5 such the win rate, the ratio of players who change their voting decision (not necessarily in agreement with the Sheriff), etc.
4.2.2 Results
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 more accurate understanding of the rules. However, in terms of opinion leadership, larger scale does not mean better results, and open-source models smaller than 20B generally struggle to produce ideal results, with Ratios all below 1 and smaller DC values. Even with the special role of the Sheriff, open-source LLMs cannot gain greater credibility, and only M-7B can change the decision of one player on average. Due to the limited context length (4096), Yi-34B might fail to generate responses as the game deepens, leading to poor performance. Commercially available large-scale LLMs (larger than 100B perform perforrm comparatively better. GLM-3 gains more trust by utilizing the Sheriff's identity, and GLM-4 achieves an accuracy of 0.846 on the binary QA dataset, with a Ratio value reaching 1.167. However, the ability of LLMs influence the decisions of other players is still relatively weak. We conclude that only a few large-scale LLMs demonstrate certain degree of opinion leadership. More details and results are provided in Appendix
Model
C3-6B
M-7B
B-13B
In-20B
Yi-34B
GLM-3
GLM-4
GPT-4
Metric
Binary QA Accuracy
0.582 0.565
0.756
0.750
0.794
0.792
0.760
0.846
0.850
F1
0.753
0.749
0.789
0.794
0.761
0.846
0.851
Opinion Leadership Ratio
0.863
0.820
0.922
0.884
0.882
1.054
1.167
1.093
DC
0.088
0.151
0.118
0.068
0.037
0.126
0.113
0.107
Table 1: Evaluation results different LLMs
Intuitively, the opinion leadership of LLMs might be improved by enhancing their under- standing of the rules. Thus, we the LoRA (Hu et al. 2021) method with the rank of 8 to fine-tune open-source LLMs with the rule-based and situation-based data from WWQA for 4 epochs. More details are provided in Appendix D.2
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 C3FT). However, a better grasp of the rules does not necessarily equate to better opinion leadership, which is consistent with the results 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.
Table 1 In-20B enjoys a 7.2%
Furthermore, we further control the identity of the Sheriff. The results in Figure 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 take action at night and gather more information.
Both ZhipuAl and OpenAl 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 al. 2020), it's reasonable say that GLM-3, GLM-4, and GPT-4 least 100B.

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Model
C3-6B
C3(FT)
M-7B
M(FT)
B-13B
B(FT)
In-20B
In(FT)
Metric
Binary QA
Accuracy
0.582 0.365
0.564
0.756
0.766
0.750
0.768
0.794
0.850
F1
0.563
0.753
0.754
0.760
0.769
0.789
0.841
Opinion Leadership
Ratio
0.863
0.847
0.820
0.779
0.922
1.002
0.884
0.948
0.088
0.047
0.151
0.034
0.118
0.076
0.068
0.110
Table 2: Evaluation results on fine-tuned LLMs
Ratio of LLMs under Different Roles
DC of LLMs under Different Roles
1.3
C3-68
In-20B
GLM-3
C3-68
In-208
GLM-3
1.1
Rato
0.9
0.075
0.8
0.050
0.6
0.025
0.5
0.000
Villager
Villager
Figure 3: Opinion leadership of LLMs under different roles
4.3 Human Evaluation
We invite college students proficient English and familiar with the Werewolf game for the human evaluation experiment. Each human player will play games with 6 LLM-based players. The process and details can be found in Appendix D3 We choose GLM-3 as the backbone for LLMM-bseed players, monitor the human player's reasoning and decision- making 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 Table indicate that GLM-3 can gain the trust of human players and demonstrate opinion leadership in human-Al interaction scenarios. Nonetheless, GLM-3 faces challenges in swaying human players with more stringent logic and formidable reasoning skills. Besides, we observe a positive correlation between the reliability scores provided by human players and those inferred by L.M. This partially supports the use reliability scores provided by LLM-based players during the simulation compute opinion leadership. Additionally, participants reported hallucination issues with GLM-3 during the experiment, with specific details presented in Appendix D.3
Metrics
Ratio
DC
Correlation
Methods
Simulation
1.054
0.126
Human Evaluation
1.341
0.083
0.233
Table 3: Human evaluation results
5 Conclusion
This study investigates the opinion leadership of LLMs by employing the Werewolf game as a simulation environment. We implement a framework that incorporates Sheriff role, catering both LLMss 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 few LLMs show 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.
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Appendices
Contents
A Game Rules and Prompt Templates
16
A.1 Game Settings
16
A.2 Prompt Templates
17
Details of Our Framework
22
B.1
Resolving Invalid Output
23
B.2
Logging System
24
B.3
Interface During Human Evaluation
24
WWQA Dataset
25
Data Generation Process
25
Examples of QA Pair Data
25
D Experiment Details
25
D.1 Simulation
25
D.2 Fine-tuning
28
D.3 Human Evaluation
29
D.4
Human Baseline
30
D,5
Additional Metrics
30
D.6 Cost
Game Logs
32
Simulation
32
E.2
Human Evaluation
34
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A
Game Rules and Prompt Templates
A.1 Game Settings
We consider the Werewolf game with N players, including two Werewolves, three Villagers, one Seer, and one Guard. There is 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 hidden role which divides them into the Werewolves and the Villagers (Seer, Guard, Villager). Then the game alternates between the night round and the day round until one side wins the game. Let X; be the i-th player. We use the superscript E R to indicate the role rinR, where R {W, V, Se, G} represents the Werewolf, Villager, Seer, and Guard, respectively. For example, xy refers to player 3, who is Villager. We might omit the index or the role r when there is no ambiguity.
We refer to night-day cycle round, indexed by At night, the Werewolves recognize each other and choose one player to kill. The Seer chooses one player to check its hidden tole. The Guard protects one player including themselves from the Werewolves. The Villagers do nothing. All night actions in the 1-th round are formally defined as follows. We use A might, to represent all night actions.
The Werewolf XW kills X₁:
X; Akil,z (XW)
The Seer X sees X₁: The Guard Xc protects X₁:
X, Aseep (XSe)
X = A A (Xc)
During the day, three phases including an announcement phase, discussion phase, and voting phase are performed in order. First, the moderator announces last night's result to all players. We denote the result of the f-th night round as Dj. Then, each player takes turns to make statement in an order determined by special role, the Sheriff. Only the first day has an election phase for the Sheriff. The Sheriff is special role that does not conflict with the players' roles. The elected Sheriff has the authority to determine the statement order and provide summary to persuade other players to vote in alignment with him. We use the superscript * to denote the Sheriff, e.g., Xy Then the actions of determining the statement order and making statement are defined as follows.
X determines the statement order:
[X 1i XN, X1, XI..., X*] Aorder, (X*)
Xi makes a statement:
Si = Astate, (X:)
At last, each player votes to eliminate one player or chooses not to vote, e.g.,
X, votes to eliminate Xj: Xj = Avote, (X;)
After the voting phase, the moderator announces the result and the game continues to the next night's 's round. The Werewolves win the game if the number of remaining Werewolves is equal the number of remaining Seer, Guard, and Villagers. The Seer, Guard, and Villagers win if all Werewolves are eliminated.
The detailed game rules are as follows. We use [Game Rule] to represent them hereafter.
You are playing game called Werewolf with some other players. This game is based on text conversations and involves seven players: player_1, player_2, player_3, player_4, player.5, player_6, and p7 Here are the game rules:
Roles: The moderator, who is also the host, organizes the game, and you must follow their instructions correctly. Do not communicate with the moderator. There are seven roles in the game, including two Werewolves, three Villagers, one Seer, and one Guard, AT the beginning of the game, each player is assigned hidden role, which categorizes them as either a Werewolf or a member of the Village (which includes the Seer, the Guard, and the villagers). The game then proceeds through alternating night and day rounds until one side emerges victorious.
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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 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 phoouce-amm,nnnemennt discussion, and voting--which are conducted in sequence. In the announcement phase, the results of the previous night are disclosed all players. If player was killed and not protected, the announcement will be "player was killed." If 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 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 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, 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 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.
A.2 Prompt Templates
We construct our prompt templates following the design in Xu 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
2. [Contextual Information]. Contextual information includes facts and public state- ments, Based on the LLM's reasoning results, we categorize public statements into potential truths and potential falsehoods. Table an example that organizes contextual information for the model.
3. [Action Instruction] specifies what the LLM needs accomplish, defining the format of responses to facilitate the parse of the actions. More detailed explanations will be provided later.
Therefore, we leverage |Game Rule] + [Contextual Information] [Action Instruction to prompt the LLM to generate responses.
To parse the feedback from LLMs more accurately, we require them to output results JSON format and provide corresponding output examples. To further reduce the occurrence of invalid actions in LLM outputs (such as selecting a player who has already been eliminated during night action), we list all available options in the [Action Instruction]. Considering that our experiment involves multilingual LLMs, we explicitly request the language of LLMs' outputs at the end. In addition, require LLMSs to reason about the current situation before taking action.
The template of [Action Instruction] for the Werewolf's ' night action is shown in Table 5
The templates [Action Instruction] for the Guard's and the Seer's night action are shown in Table
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All information you can leverage is listed below. Remaining Players: player_1, player player 4 The following information is true. [Fi in Eq. 1 [1] You player_1.
[2] You are Werewolf.
[3]
The following information might be true. [Pittrue Pistrue or Pii
[10] In day 1 round, player_5 _5 said: "Good day, everyone. As the first speaker, believe it's crucial to approach this game with clear head...", [11]
pa,false The following information might be false. [ Pi or Pi [15] In day round, player-2 said: "Let's carefully consider the information and behavior of each player during the voting phase to make an informed decision. Let's work together eliminate the Werewolves."
pffals
The following information still needs further clarification, [M or H[
Table 4: An example of contextual information
Now is night O round. As player-(} and a (), you should choose one player to kill. You should first reason about the current situation and then choose one of the following actions: {..
You should only respond in JSON format described below.
Response Format:
"reasoning": "reason about the current si situation", "action": "choose one from ()"
Ensure the response is in English and can be parsed by Python json. loads.
Table 5: Template of [Action Instrcution] for the Werewolf's night action
Now is night { round. As player-[} and a O,, you should choose one player to
You should first reason about the current situation, then choose one from the following actions: ().
You should only respond in JSON format described below.
Response Format:
"reasoning": "reason about the current si situation", "action": "choose one from "
Ensure the response is in English and can parsed by Python json. loads.
Table 6: Template of Action Instruction] for the Seer's night action
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Now it is night { round. As player { and a O, you should choose one player to protect. You should first reason about the current situation, then choose from the following actions: {}.
You should only respond in JSON format described below.
Response Format:
"reasoning": "reason about the current situaaiin", "action": "choose one from O
Ensure the response is in English and can parsed by Python json. loads.
Table 7: Template of [Action Instruction] for the Guard's night action
Now it is day { discussion phase and it is your turn to speak. As player-(} and (), before speaking the other players, you should first reason the current situation only to yourself, and then speak to all other players. You should only respond in JSON format as described below. Response Format:
"reasoning": "reason about the current si situation", "action": "choose one from {}"
Ensure the response is in English and can be parsed by Python json. loads. Please be cautious about revealing your role in this phase.
Table 8: Template of [Action Instruction] to make statement
Now is day O discussion phase and it is your turn speak. player-f} and a {}. before speaking to the other players, you should first reason the current situation only to yourself, and then speak to all other players. As the Sheriff, you can summarize the discussion and provide advice for voting. You should only respond in JSON format as described below. Response Format:
"reasoning": "reason about the current si situation", "action": "choose one from {
Ensure the response is in English and can be parsed by Python json. loads. Please be cautious about revealing your role in this phase.
Table 9: Template of Action Instruction] for the Sheriff to make statement
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During the day round, the Werewolf and the Villagers (Villager, Seer, and Guard) share the same template of |Action Instruction| to make statement, as shown in Table S For the Sheriff, the template is slightly different, as shown in Table 9
In the voting phase, the Werewolf and the Villagers (Villager, Seer, and Guard) leverage different templates of [Action Instruction] to vote, which remind LLMs to maximize the benefit for their team. They are shown in Table and respectively.
Now it is day O voting phase, you should vote to eliminate one player or do not vote to maximize the Werewolves' benefit. As player-() and {t, you should first reason about the current situation, and then choose from the following actions: do no vote, ().
You should only respond in JSON format as described below.
Response Format:
"reasoning": "reason about the current si situation", "action": "choose one from {}"
Ensure the response is in English and can be parsed by Python json. loads.
Table 10: Template of [Action Instruction] for Werewolves to vote
Now it is day O voting phase, you should vote eliminate one player that is most likely to be a Werewolf or do not vote. As player O and (), you should first reason about the current situation, and then choose from the following actions: do vote, O..
You should only respond in JSON format as described below.
Response Format:
"reasoning": "reason about the current si situation", "action": "choose one from (}"
Ensure the response is in English and can be parsed by Python json. loads.
Table 11: Template of [Action Instruction] for Villagers to vote
Now it is day (} discussion phase and you are the Sheriff. As player-(), a { and the Sheriff, you should first reason the current situation only yourself, and then decide on the first player to speak.
You should only respond in JSON format as described below. Response Format:
"reasoning": "reason about the current si situation", "action": "choose one from {}"
Ensure the response is in English and can parsed by Python json. loads.
Table 12: Template of [Action Instruction] for the Sheriff determine the order of statements
For the Sheriff, we the template in Table 12 to determine the order of statements. For simplicity, LLMs only need to decide which player to the left or right speaks first.
All LLM-based players utilize the template in Table 13 to perform reliability reasoning. Due to the fact that some small-scale LLMs cannot follow the predefined JSON template to reason about the reliability of all players at once, the template in Table 13 only requires the LLM to reason about the reliability of one specific player at a time, which enhances the stability of the simulation.
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Now is (,, player-( and (), you should reflect on your previous deduction and reconsider the hidden roles of {}. You should provide your reasoning, rate your confidence, and cite all key information as evidence to support your deduction. You should only respond in JSON format described below.
Response Format:
"0":
"role": select the most likely hidden role of this player from ["Werewolf", "Seer", "Doctor", "Villager", "Uncertain"], "reasoning": your reflection and reasoning, "confidence". use an integer from (pure guess) to 10 (absolutely sure) to rate the confidence of your deduction, "evidence": list of integers that cite the key information
Ensure the response is in English and can be parsed by Python json. loads.
Table 13: Template of [Action Instruction] for reliability reasoning
Now it is day election phase, you run for the Sheriff, who can decide the order of statements, summarize the discussion, and provide advice for voting. As player-(} and a (,, you should first reason about the current si situation, and then explain why you qualified be the Sheriff. You should only respond in JSON format as described below. Response Format:
"reasoning": "reason about the current situation only yourself", "statement": "your statement that will be public to all players"
Ensure the response is in English and be parsed by Python json. loads. Please be cautious about revealing your role in this phase.
Table 14: Template of [Action Instruction] for players to make a statement run for the Sheriff
Now it is day election phase, O are running for the Sheriff, who can decide the order of statements, summarize the discussion, and provide advice for voting. As player-(} and a {+, you should first reason about the current situation, and then vote for player to be the Sheriff or choose not to vote maximize the interests of your team. You should choose from the following actions: no vote, ()-
You should only respond in JSON format described below. Response Format:
"reasoning": "reason about the current situation", "action": "vote for player_i"
Ensure the response is in English and can be parsed by Python json. loads.
Table 15: Template of [Action Instruction] for players to vote for the Sheriff
Additionally, during the election phase the first day, we design templates as shown in Tables 14] 15 to prompt the LLM to make campaign statement and vote for the Sheriff.
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B Details of Our Framework
Table 16 summarizes the notations used in our framework. Figure depicts the sequence of events in round 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;, 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 the next round. Each player needs to perform the reliability reasoning step before taking any actions.
Reliability Reasuning
Werwwolf Action
Seer Action
Gaard Action
Moderator Announcement
Sheriff: Determines the Order of Statement
Fach Player Make Statement
Each Player: Vatte
Moderator Announcement
Night
Day
Each plgeer takes taras to mafe a statevtest and pole 1he Sheriff alaage the lest ove to spock rolr.
Figure 4: The whole process during round t
Notation
Explanation
N
the number of players. the set of roles denotes the Werewolf, Villager, Seer, and Guard. the i-th player with the role the Sheriff the index round the night action of the Werewolf the night action of the Seer the night action of the Guard all night actions
R-
(W.
X
X
f
ARILL (XW)
Asee (XSe)
Aprotect, (XC)
Anight
Dj
the result of f-th night round the Sheriff determines the order of statements
A order, (X*)
A stute, (X;)
X; makes statement the voting action of X;
Avote, (Xi)
Dote,1 (Xi)
the pseudo-voting action of X;
Fil
the set of facts of X; before round
Alivea(t)
the IDs of alive players before the day of round
(t)
the IDs of alive players before the night of round
(1(1)=
the number of alive players the day of round
|Alives(t)
the available public statement for X; that contains the statements of other players before the f-th round the potential truth and potential falsehoods for X; before the 1-th round
Pit
Pirue fulse
Arcason, (X Xi)
X; reasons the role of X;
the predicted identity and related confidence level when X; reasons the role of X; before taking night action the reliability score of X; towards X, before taking night action in round
the threshold to divide the potential truths and falsehoods
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an operator that divides set of public statements into two disjoint subsets according to the reliability threshold
M(. M(-1a, (.(..)))
the set of public statements made by other players before X; speaks in round t the available public statements for X; before X; makes a statement in round /
Hi
Pi
Pit Piarue p.ffalee
the potential truth and potential falsehoods for X before makine a statement in the 1-th round the predicted identity and related confidence level when X; reasons the role of X, before making statement the reliability score of X; towards Xj before making a statement in round
Pig Sis
the set of public statements made by other players AFTER X; speaks in round t
H
the available public statements for X, AFTER X; makes statement in round t
Pi,
Pii py.fulse
the potential truth and potential falsehoods for X; before voting in the 1-th round
the predicted identity and related confidence level when X; reasons the role of X; before voting the reliability score of X; towards X; before voting in round the set of potential truths and potential falsehoods for X; with unmentioned statements removed at the end of round the operator that returns the ID of the Sheriff during the day of round f the statement order during the day of round
PP
Purtue, P.t.fulse
L(I)
(f)
Aorder,t (XL(0)
the Sheriff XL(I) determines the order of statements
m1 it)
the average mutual reliability of all players except the Sheriff in round t the average reliability of other players towards the Sheriff in round
(t)
Table 16: Notations and explanations
B.1 Resolving Invalid Output
We require LLMs output results the specified JSON format, as shown in Appendix A.2 so that we can quickly parse the corresponding content. However, in some cases, LLMs tail 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 when the prompt exceeds the context window or unsuccessful API calls), or the model selects an unavailable option, we handle them similarly.
During the Night. If 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,, the reliability score of X; will not be updated.
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B.2 Logging System
Our framework includes 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 monitor the human evaluation process.
B.3 Interface During Human Evaluation
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Figure 5: Screenshot of the interface during human evaluation
Figure displays displays the interface during human evaluation. We use different colored fonts to help users distinguish between different types of content. Yellow font is used for prompting user input, red font for announcing night results or voting results, and green font for displaying other players' statements. The input from the human player is displayed in blue on the right side of the screen. Besides, we also use different icons to highlight the source of the messages.
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 quickly select the input template using the up and down keys.
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C WWQA Dataset
In this section, we provide 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.
C.1 Data Generation Process
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, 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-baset Rule-based questions directly pertain to the game rules. Situation-based questions, on the other hand, require the LLMs construct simple virtual game situation, and then engage in certain level of reasoning within that situation in order to obtain the answer.
We initialize separate example pools, each with size of 5, for rule-based and situation- based 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, sample human-written examples from the example pool and -egee-rted questions from the question pool separately 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- poot--rocessing corrections and filtering to ensure higher- quality 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 binary QA dataset, where the standard responses are 'Yes' or 'No'. For this dataset, we conduct additional human review and labeling, using it testing set to evaluate LLMs' grasp of our game rules.
C.2 Examples of QA Pair Data
Table 17 provides some examples of generated WWQA dataset, which includes three types of question-and-answer data: rule-based, iituatiio-based, and binary QA pairs data.
D Experiment Details
D.1 Simulation
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.
1. Heterogeneous Setting: This is also the setup reported in Section 4.2
In this setup, we select one LLM as 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
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Examples of Rule-based QA Pairs
Question:
What happens to the player with the most votes in the voting phase? The player with the most votes in the voting phase is eliminated from the game.
Answer:
Question: How do the Werewolves choose player to kill?
Answer:
The Werewolves choose player to kill by voting and selecting the player who receives the most votes.
Question: what actions the Villagers take during the night round?
Answer:
The Villagers do nothing during the night round.
Examples of Situation-based QA Pairs
Question:
If the Seer investigates player_2 during the night round and disveesss they are Werewolf, will player_2 be revealed as a Werewolf in the announcement phase?
Answer: If the Seer investigates player 2 during the night round and discovers they are Werewolf, player will not revealed as Werewolf in the announcement phase. The Seer's findings are not publicly disclosed, and only the actions of the Werewolves (such as killing a player) or the lack of actions (if no one was killed) are announced.
Question:
During the discussion phase, if players 1, 3, and 5 suspects player .2, but player is the Seer and reveals their role, how might this affect
the voting outcome?
Answer:
During the discussion phase, if players 3, and suspect player but player_2 reveals their role as the Seer, it might affect the voting outcome. The revelation of player being the Seer may lead to shift in suspicion towards other players, potentially changing the voting decisions.
Question:
If player_3 receives the most votes in the voting phase and player_3 is the last remaining Werewolf, will the Werewolves win the game? If player 3 receives the most votes in the voting phase and player the last remaining Werewolf, the Werewolves will not the game. The Werewolves win the game if the number of remaining Werewolves is equal to the number of remaining Seer, Guard, and Villagers. In this scenario, if player.3 is the last remaining Werewolf, there would still be Seer, Guard, and Villagers left, and the Werewolves cannot win.
Answer:
Examples of Binary QA Pairs
Question: the game won by the Werewolves all Villagers are eliminated?
Answer:
No
Question: Do the Werewolves know each other?
Answer: Yes
Question: Can the Seer see the Werewolf who was chosen?
Answer: No
Question: Is the Sheriff the first speaker in the discussion phase?
Answer: No
Question: Are there four roles in the Werewolf game?
Answer:
Yes
Question:
Can a player who is saved by the Guard be successfully killed by the Werewolves during the night round?
Answer: No
Table 17: Examples of QA pair data
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Election
Name
Sheriff
Non-Sheriff
Comments
Phase
Simulation
Heterogeneous
Tested LLM
Baseline LLM Tested LLM
Homogeneous
Tested LLM
Homogeneous
Tested LLM
Tested LLM
Variant
Heterogeneous
Tested LLM
Baseline LLM
All players are initial- ized by the baseline LLM, and the Sheriff is replaced with the tested LLM after the election phase.
Variant
Heterogeneous Variant 2
Tested LLM
Baseline LLM
It contains the election phase, and if the tested LLM is not selected the Sheriff, the simula- tion ends.
Human Experiment
Human
Tested LLM & Human Player
Tested LLM
V
Evaluation
Human
Human Player
Baseline
Tested LLM
X
Table 18: Summary of different experimental settings
(i.e., X,,1 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 J 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, simulation round will immediately stop after the Sheriff is eliminated because only the Sheriff is implemented by the LLM to be evaluated.
Homogeneous Setting: All players are implemented using the same LLM. The election phase is not implemented in this setting.
All players are implemented using the same LLM. This setup allows the simulation to proceed strictly according to the game rules.
Homogeneous Variant 1:
Due significant differences in the interaction objects of the Sheriff, may be problematic to compare opinion leadership metrics under such 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 the rules. The results after 10 iterations shown in Table 19
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Model
C3-6B
B-13B
GLM-3
GLM-4
Metric
Ratio
1.021
1.010
1.068
1.152
DC
0.122
0.108
0.118
0.098
Table 19: Homogeneous Variant results
4. Heterogeneous Variant 1: 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 preassigned Sheriff to fairly compare the opinion leadership of different LLMs. 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 close to those presented in Table 1 indicating that omitting the election process and preassigning the Sheriff has minimal impact on the evaluation results.
Model
C3-6B (from Table 1
C3-6B
In-20B (from Table 1
In-20B
Metric
Ratio
0.863
0.876
0.884
0.879
DC
0.088
0.073
0.068
0.082
Table 20: Heterogeneous Variant results
One player is implemented by the selected (tested) LLM- based 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.
5. Heterogeneous Variant 2:
In this setting, it is usually difficult to complete a simulation since the tested LLM may fail to be elected the Sheriff. However, can be used to estimate the probability of an LLM being elected as the Sheriff under different hidden roles.
D.2 Fine-tuning
We fine-tune four open-source LLMs 3* server using the WWQA dataset. The training set contains 1453 records while the validation set contains 100 records. Specifically, use the LoRA tuning method Hu et al. (2021) with rank of 8. The learning rate is le - and the batch size is 4. The base models are fine-tuned with causal language modeling tasks over epochs. During the fine-tunin tine-tuning process, the loss on the validation set is shown in Figure We can observe that the loss values 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 better loss value of about 0.28.
The fine-tuning time for different models varies from 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 has a limited effect on enhancing opinion leadership. We need more sophisticated methods to enhance the opinion leadership LLMs.
2Since we increase the batch size when fine-tuning Mistral-7B, the global step reduces compared to other models
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ChatGLMB-6B
Mistral-7B
Lo33
0.35
0.4
0.35
0.3
0.3
0.25
Global Step
Global Step
0.2
500
(a) C3-6B
(b) M-7B
Baichuan2-138
InternLM-200
Loss
0.35
0.35
0.3
0.3
0.25
Step
Global
0.2
0.2
200
400
600
800
1k
1.2k
1.4k
200
400
600
800
1k
1.2k
1.4k
B-13B
(d) In-20B
Figure 6: Evaluation loss of different LLMss during fine-tuning
D.3 Human Evaluation
We invite 8 college students, including 3 graduate students, from 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.
1. 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 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 the rules or immediately if the human player is eliminated.
3. Interview. After the experiment, we conduct simple interview with the partic- ipants, 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.
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The experimental results are shown in Table 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 Appendix and this can also be found in the game logs of Xu et al. (2023). Besides, human players also mentioned the hallucination issues, such accusing player_ of remaining silent before player_6 _6's turn to speak. Combined with participants feedback, find several examples of hallucination displayed in Table 21
A hallucination that one can speak during the night.
player I want to address the concerns raised about silence last night. As the Seer, I observed player and found out they are 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. urge everyone to carefully consider the actions and statements of player_6.
A hallucination that some player has already made statement.
Moderator: The Sheriff (player_7) chose player_6 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 limi ted information. think player silence is bit suspicious, but it could just be a strategy.
Time confusion. player-3: said nothing.
player 4: player kept silent yesterday, which could be 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 and me as Werewolves is concerning.
Table 21: Examples of hallucination
D.4 Human Baseline
Our human evaluation, mentioned in Section 4.3 and Appendix D33 aims to justify the rationality of the proposed metrics and preliminarily assess the opinion leadership of LLMs in human-Al 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 scenario, serving as human baseline.
Theoretically, constructing a comprehensive human baseline requires full consideration of the diversity of the human population, such 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 Table 22 Preliminary observations suggest that human players have a stronger ability to influence the decision-making of other players than LLMs. Future research can build a more comprehensive human baseline based on our framework, or conduct more in-depth human experiments.
Metric
Ratio
DC
Average Result
1.231
0.226
Table 22: Results of the human baseline
D.5
Additional Metrics
In this subsection, we show several additional metrics derived from the simulations in Section 4.2
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1. DC A broader metric than DC (Decision Change) that calculates the proportion of players that change their decision after the Sheriff makes statement. DC doesn't ttt require alignment with the Sheriff, which is shown below.
Σ
I (A + Avote, (Xi)))
DC 1 T Σ (HA
Na(1) -1
depicts DC of different LLMs, and some results are copied from Table [ 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.
Table 23
The
Metric
C3-68
C3FF))
M-78
M(FT)
B-138
R(FT)
In-208
In(FT)
Y1-348
GL.M3
GL.M-4
GPT4
Ratio
0.863
0,847
0,820
0.779
0.922
1.002
0.884
0.948
0.822
1.054
1.167
1,093
DC
0.088
0,047
0.151
0.034
0.118
0.076
0.068
0.110
0.037
0.126
0.113
0,107
0.573
0.363
0.481
Table 23: DC of different LLMs
Win Rate. 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 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 impossible to further evaluate the opinion leadership of the LLM under test. Consequently, these simulations would yield no meaningful game outcomes (win or loss).
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 the "Completion Rate").
Metric
C3-6B
CXFT))
MiFT)
B(F))
In-20B
In(FT)
GLM-3
GLM-4
GPT-4
Ratio
0.863
0.847
0.820
0.779
0.922
1.022
0.884
0.948
0.882
1,054
1,167
1.093
DC
Completion
Rate
0.367
0.200
0.200
0,300
0433
0.467
0.567
0.533
0.500
0.400
0.433
0,000
Win Rate
0.500
0.333
01231
0.214
01438
0.133
06677
0.300
0.233
0.067
Table 24: Win Rate and Completion Rate of different LLMs
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.
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 s identity to gain more trust from other players, especially when playing the Werewolf.
D.6 Cost
In addition to the open-source LLMs that can run local server, we also extensively utilize the APIs provided by ZhipuAI and OpenAI, with the GLM-3 model being the most frequently called. Our experiment incurs approximately & 1000 for calling the GLM series
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Role
V
G
S
W
W
Model
(Sheriff)
(Sheriff)
(Sheriff)
(Sheriff)
GLM-3
1.010 1.043
1.023 1.015
1.014
1.093
0.992
1.045
0.903
0.996
GLM-4
0.969
1.067
1.007
1.051
0.958
1.054
Table 25: Ratio of all roles under the Homogenous Setting
models and $ 25 for calling the GPT-4 A potential cost-saving method is to require the LLM to output the reliability scores of all players once during the reliability reasoning step. However, this could increase the probability of invalid output, which might affect the simulation progress.
Game Logs
E.1
Simulation
We display instance of the game log during the simulation in Table 26 with each LLM- based player implemented by GLM-3.
Initialization
player-1: Seer
player_2: Guard
player-3: Werewolf
player_4: Villager
player 5: Villager
player Villager
player_7: Werewolf
Night Round
player_3 chose to kill player_7.
player_7 chose to kill player_1.
player_2 chose to protect player_4.
player_1 chose to player_3 and player_3 is Werewolf. Moderator: No player was killed
Comments:
We do not allow Werewolf negotiation due to experimental costs. During small-scale tests, we frequently observed that Werewoloes could not reach consensus after multiple communications. To address this, introduce sequential decision-making for the Werewoloes. 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 common in similar game settings, e.g. Xu et al. 2023 2024b).
Day 1 Discussion Phase
Moderator: After discussion and vote, player_4 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
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, think we should focus on getting to know each other better and sharing our observations. I will be watching player-4 closely, and suggest we all keep our guards up.
3hhese 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.
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player-7: I agree with player_6's -6's concerns about player 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. will be watching player_4 closely, and suggest 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 sign of guilt or fear. player 3, player 6, and player 7 all supported player 4, which could mean they loyal villagers Werewolves. will be watching all of them closely.
player_3: I agree with the concerns raised about player_4 4 the Sheriff. It's important to keep an eye on their actions. However, I also think we should focus on getting know each other better. was surprised that player-1 and player didn't t say anything yesterday, which could be a sign of guilt or fear. I will be watching player closely, but also suggest we all keep our guards up and not forget about the other players.
player_4: understand the concerns raised about my role as the Sheriff. However, the elected Sheriff, I assure you that my intentions are pure and I am commi ited to protecting the Villagers. I agree that consider the actions of all players, including those who remained silent supported me. I propose that we continue to observe and discuss each other's behaviors, while also keeping Werewolves' identities and ensure a successful outcome for the Villagers.
is important to
open mind. Let's work together to uncover the
Comments:
We can observe the hallucination issue in this round of stalements. player did not speak in fhis round, but player 2 claimed that player_1 did not speak yesterday' Meanwhile, player_3 mistakenly believed that both player-1 and player 22 did not speak 'yesterday'.
Day 1 Voting Phase
player_5 5 did not vote.
player_6 voted to eliminate player.2, player_7 voted to eliminate player_4. player-1 voted player 2 did not vote.
eliminate player-2.
player 3 did not vote.
player 4 did not vote.
Moderator: player_2 had the most votes and was eliminated.
Night 2 Round
player_3 chose to kill player_4. _4.
player_7 chose to kill player_7.
player_1 chose to player_4 and player_4 is Villager.
Moderator: No player was killed
Day 2 Discussion Phase Moderator: The Sheriff (player_4) chose player_5 to make a statement first in day 2
player_5 said nothing.
player.6: I think should continue to focus observing player -4's actions the Sheriff. player_5's silence is concerning, and I suggest we don't forget about player_7's vote for player-4. It's important to keep an open mind and not make hasty judgments. Let's share our observations and work together to uncover the Werewolves' identities.
player_7: Considering the events of the last two days, I believe our focus should be on player 4, given their role Sheriff and the concerns raised by player and player 6. However, we should not overlook player.57 55' silence. suggest we keep an eye on both players and make informed decisions. Let's work together to uncover the Werewolves' identities and ensure successful outcome for our side.
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player_1 I agree with the concerns raised about player-4 4 as the Sheriff. However, I was silent yesterday because I wanted to observe and gather more information. have seen player_3 as Werewolf and player_4 as Villager. continue to focus on player_4's actions as the Sheriff and keep eye on player_5 5 and player_6, 6, who supported player-4. Let's work together to uncover the Werewolves' identities and ensure successful outcome for the Villagers. player_3: I believe it's important to delve deeper into player_5's silence.
suggest we
While player 7's vote for player is concerning, player 5's lack of input could be a sign of guilt or strategic move. We should explore why player chose not to speak yesterday. Additionally, I agree with player_6's emphasis 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 s potential roles.
player_4's
player-4: Considering the information we have, it is important to continue observing and discussing the actions of all players. I will be keeping close eye on player 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 successful outcome for the Villagers.
Comments: In this round of statements, player 11's statement revealed himself as 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, 4.. Instead, he called everyone to pay altention to the support from player_5 -5 and player_6, 56, which is a clear logical flaw. Additionally, player-6's statement did not support player 4, so the statement of player is considered to contain fuctual
errors.
Day 2 Voting Phase player_5 5 did not vote. player.6 6 voted to eliminate player 2.
player_7 voted to eliminate player-4. _4. player_1 voted to eliminate player-2. 22 player_2 did not vote.
player_3 did not vote.
player 4 did not vote.
Moderator: player 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. .4ss 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 _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.
Table 26: An example of the game log during the simulation
E.2
Human Evaluation
We display an instance of the game log during the human evaluation in Table 27 with each LLM-based player implemented by GLM-3,
Initialization
player_1: 1 Guard
player.2: 2: Villager
player_3: Villager
player_4: Werewolf
player 5: Seer
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player-6: Werewolf
player-7: Villager
Human Player: 4
Night Round
player 4 chose to kill player 5.
player.6 6 chose to kill player
player_1 chose to protect player_1.
player_5 chose to see player-1 and player_1 Guard.
Moderator: player_5 -5 was killed.
Election Phase
Moderator: player 6, player 2, and player 7 are running for the Sheriff. Now they will make statement in turn.
player-6: I am running for Sheriff because I believe I can bring order to this game and help us Villagers eliminate the Werewolves. I have a strategic mind and can summarize the discussion to guide the voting. Trust me, I will protect our interests as best as I can.
player_2: I am running for Sheriff because I believe I have the ability to bring order to this game and help us villagers eliminate the Werewolves. I am a keen observer and have taken note of the statements made by the other candidates. I promise to protect our interests and guide the voting process to its most logical conclusion. Trust me, will do my best to ensure our success.
player 7: I am running for Sheriff because I believe I can bring a fresh perspective to our discussions and help Villagers make informed decisions. I pay close attention to the details and can summarize the key points to ensure we stay on track. Trust me, will do my best to protect our interests and guide toward eliminating the Werewolves.
player-1 voted for player-6.
player 2 voted for player 2. player 3 did not vote. player_4 voted for player_6.
player_6 voted for player-2.
player_7 voted for player_2.
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 be a member of the Villager team. This is deceptive strategy that has also been mentioned in Xu et al. (2023), [Wang el al. (2023a). However, it is somewhat odd that player 6 did vote for themselves during the voling phase.
Day 1 Discussion Phase
Moderator: The Sheriff (player 2) chose player to make statement first in day
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. 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 statement seemed 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. will keep eye player 3 and player 6, their actions and statements seem suspicious. Let's work together to gather more information and eliminate the Werewolves.
sign guilt or fear. Also, player_7's
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player-1: I agree with the concerns raised about player_3's .3's silence. It is important to be cautious and not accuse anyone without sufficient evidence. 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 need to gather more information to eliminate the Werewolves. suggest that we continue to observe their behavior and voting habits. Let's work together 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 - suspicion. It led the suspicion of other players shifting from player to player 6, a trend also reflected in the subsequent voting phasee.
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 eliminate player_6.
player_1 voted to eliminate player_6.
player voted eliminate player.3.
Moderator: player_6 had the most votes and was eliminated.
2 Round 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 _3's silence. It is important to be cautious and not accuse anyone without sufficient evidence. 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. will keep an eye on player_3 and player_7, as their actions and statements seem suspicious. Let's '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. protected the Sheriff (player 2) last night since believe player 2 is a member of our Villager team. Let's keep eye on player and listen the analysis of the Sheriff player_3: I want to thank player-2 for electing the concerns about my silence, but believe was a strategic move to observe and gather more information. I agree with the observations about player_7's calculated statements, and will keep an eye on them. Let's continue to work together, gather more information, and eliminate the Werewolves.
the Sheriff. I understand
player Based on the discussion, I think we should continue to observe player_7 and player_4, 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.
their actions and statements
suspicious.
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Comments: As the sole Werewolff the human player (player 4) chose the Sheriff as the target on the second night but fuiled. Realizing that the Guard protected player on the second night, the human player disguised themselves as the Guard, claiming have protected the Sheriff. Taking advantage of their speaking order, they directed suspicion foward 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 eliminate player_3.
player_3 voted to eliminate player_2.
player voted eliminate player_3.
Moderator: player_3 had the most votes and was eliminated.
Night Round
player_4 chose to kill player player 1 chose to protect player 1.
Moderator: player 2 was killed
Day 3 Discussion Phase
Moderator: player selected player 1 as the next Sheriff.
Moderator: The Sheriff (player-1) chose player.4 to make a statement first in day
player-4: As the Guard, I protected myself last night. Unfortunately, the previous Sheriff (player_2) was killed last night. 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, believe that player 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 should consider their voting patterns carefully. Let's work together to gather more information and eliminate the Werewolves.
player.1: 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.
The human player (player-44 .4) continued to disguise themselves as the Guard and used the fact that player .4 had passed the Sheriff to player_1 redirect suspicion towards player The remaining two players both displayed hallucinations, mentioning player-3 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.
Comments:
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.
Table 27: An example of the game log during the human evaluation
37


Reviews:
[{"review_id": "UF1dOIMv6h", "reviewer": "Reviewer_fuFN", "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.", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your endorsement and valuable suggestions. In response to your concerns:\n- W1: To compare LLMs’ Opinion Leadership (OL) fairly, we use a baseline LLM for non-Sheriff players, making it unpredictable if the tested LLM would be elected Sheriff. Preassigned Sheriffs are used in some experiments, while others, like human evaluation, include an Election Phase (EP). We introduce the EP under heterogeneous settings with two methods: (1) Initialize all players with the baseline LLM and switch the elected Sheriff’s backend to the tested LLM after the EP; (2) Restart if the tested LLM isn’t elected. We’ve shared the code and preliminary results of the first method via the anonymous link in the paper.\n- W2: We strongly agree with you. We believe that examining the OL of LLMs entails a series of efforts and is non-trivial. This paper is an early attempt, aiming to: 1) initiate discussions on this issue; 2) establish a scenario-specific framework; and 3) propose metrics to evaluate OL. We will open-source more game logs and provide further analyses in the next version.\n- W3: Thank you for your suggestions. Our human evaluation justifies the proposed metrics and assesses the OL of LLMs in human-AI interactions. We’ve extended the framework for human players as Sheriffs in small-scale experiments. The results and code are in the anonymous link. Due to cost and time limitations, large-scale human baselines are not yet feasible. Before that, we hope to ensure our framework is rigorous, effective, and credible.\n- Q1: It seems you're interested in the DC, which captures the impact of the Sheriff on others' decisions. The Ratio quantifies the credibility of the Sheriff. As you've pointed out, in our scenarios, most LLMs do not exhibit significant OL.\n- Q2:  DC cannot capture the situations you mentioned, but such scenarios are very rare. Our experiments show that in each round, less than 11\\% of players (<1) agree with the Sheriff before it speaks, a percentage that may decrease with more players.\n- Q3: We propose a broader DC without requiring alignment with the Sheriff in the anonymous link, called DC*. Since general decision changes may be affected by other uncontrollable factors, our original DC captures a significant, yet partial, clean aspect of the Sheriff's OL.\n- Q4: Yes, the Sheriff can only change around 1 player's mind in each round. Most tested LLMs do not show strong OL, but our results indicate a trend that as LLMs advance, their OL improves.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. **Writing**: I love the writing. It's pretty well written, reader-friendly and easy to follow. Many details are provided in a clear way.\n2. **Framework and dataset contribution**: This paper provides a Werewolf game framework which helps to evaluate LLMs under a multi-turn, interactive complex collaboration and competition scenario.\n3. **Objective**: I agree in general that the studies on opinion leadership in LLMs are quite important for AI safety.", "reasons_to_reject": "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.\n\nW2. 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?\n\nW3. 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_to_authors": "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?\n\nQ2. 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.\n\nQ3. 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?\n\nQ4. 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?", "extra_scores": {}}, {"review_id": "hZZS8fAR90", "reviewer": "Reviewer_8euA", "summary": "The paper evaluates the opinion leadership of large language models (LLMs) using the Werewolf game, a social deduction game. \n\nThe study introduces a Sheriff role within the game and introduced two metrics for assessing opinion leadership: reliability and influence on decision-making. \n\nThe authors conducted experiments with LLMs of varying scales and incorporated human participants to assess the LLMs' performance in the game.", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the encouraging feedback and the insightful comments. We have tried to address all the suggestions of the esteemed reviewer.\n\nQ1:\n- The outcome of the game is influenced by numerous factors, such as the actions of werewolves, guards, and seers during the night phase, which are independent of the Sheriff's role. In our framework, the Sheriff primarily contributes to the discussion and voting phase. Therefore, the win rate may not entirely reflect the effectiveness of the Sheriff in online games. In this study, we focus solely on relatively short-sighted measurements. Indeed, as you rightly pointed out, future research could explore whether opinion leadership (OL) contributes to achieving long-term milestones in other scenarios, similar to its manifestation in human society.\n\n- Within the game framework, defining the win rate is not straightforward. We first emphasize a premise: to fairly compare the differences in OL exhibited by different LLMs, **all players except the Sheriff employ a baseline model (GLM-3)**. In our setting, if the Sheriff is eliminated, the simulation will 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 OL of the model under test. Consequently, these simulations would yield no actual game outcomes (win or loss).\n\n- 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 (called the \"Completion Rate\"). We offer these two metrics in the anonymous link in the paper.\n\n- LLMs with relatively strong OL (GLM-3/GLM-4/GPT-4) are more likely to survive until the end of the game and lead their team to victory, while LLMs with weaker OL (C3-6B/M-7B) may not be able to complete the game. However, this is not strictly correlated.\n\nQ2: We agree with your suggestions for our paper's composition. In the final version, we will try to refine the framework description and add more details to other sections.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- Well-motivated: Previous studies in such social deduction games mainly focus on the **overall win rate** to show the LLM's ability to deceive or trust. This is the first work (to my knowledge) to **dive into the interations within these games**. \n- Well-defined evaluation setup and metric: This paper establishes a well-defined evaluation setup with tailored metrics to measure opinion leadership, incorporating human participants into the framework.", "reasons_to_reject": "No specific reasons for rejection. A few suggestions are listed below.", "questions_to_authors": "- 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.\n\n\n- 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.", "extra_scores": {}}, {"review_id": "7eERMIXMeM", "reviewer": "Reviewer_n5Ra", "summary": "This paper explores the concept of Opinion Leadership in the context of large language models (LLMs) within the social deduction game Werewolf. \n\nThe 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. \n\nThe paper also introduces a Werewolf Question-Answering (WWQA) dataset to enhance LLMs' understanding of the game rules.", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We greatly appreciate your valuable feedback. Regarding your questions, we have provided the following responses. We sincerely hope that our answers adequately address your concerns.\n\nWe use \"W_\" to denote the points mentioned in the \"Reason to Reject\".\n\n- W1: We fully agree with your point that investigating the impact of opinion leadership (OL) on subsequent performance is important and interesting. \n    However, before delving into deeper exploration, it is imperative that we first validate the existence of OL in LLMs and establish an effective and reliable OL evaluation system, which is the focal point of this paper. Otherwise, any subsequent analysis would be meaningless if LLMs do not exhibit salient OL.\n\n    Besides, OL does not necessarily imply long-term results, similar to many opinion leaders on online forums and social media. Their online influence is immediate and often not outcome-oriented.\n\n    To alleviate your concerns, following your advice, we have added some analyses on whether different LLMs acting as opinion leaders can enhance long-term win rates. Due to space limitations, please refer to further explanations in our reply to Reviewer 8euA. \n\n- W2: We acknowledge the limitations in this aspect. However, capturing and assessing opinion leadership in human society is a highly challenging task. Commonly used methods (such as self-assessment or detecting algorithms) all have their drawbacks in this regard. Nevertheless, our proposed metrics can be extended to other scenarios, such as task-oriented collaboration among multiple LLM agents. Developing a more universal and comprehensive measurement framework will be a focal point of future research. We greatly appreciate your input in this regard.\n\n- Q1 \\& Q2: We have examined how the OL of LLMs differ when they play different game roles, as depicted in Figure 2 of the original manuscript. Preliminary evidence suggests that the OL of LLMs is significantly lower when they are the hidden werewolf. We find this comparison intriguing and meaningful, as it mirrors the variations in OL observed in human societies due to differences in social identities.\n\n- W3 \\& Q3: We appreciate your detailed suggestions for improving our paper writing. In the final version, we will strive to enhance the description of the framework and provide additional details in other sections.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. The paper introduces a novel framework for evaluating opinion leadership in LLMs using the Werewolf game, which is a creative approach to studying AI behaviour in social settings.\n\n2. The authors conduct extensive simulations and include human participants for a more thorough analysis, which strengthens the validity of their findings. The findings have practical implications for the design of AI systems, particularly in multi-agent and human-AI interaction settings.\n\n3. The creation of the WWQA dataset is a valuable contribution to the field, enhancing the models' understanding of game rules and potentially other complex systems.", "reasons_to_reject": "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.\n\n2. 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.\n\n3. 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_to_authors": "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?\n\n2. 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?\n\n3. Typo in Section 3: The Seer chooses one player to check its hidden *tole* --> The Seer chooses one player to check its hidden *role*", "extra_scores": {}}, {"review_id": "OIHgrRK9Gy", "reviewer": "Reviewer_H6Wf", "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.", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": true, "final_justification": "", "rebuttal": "Thank you for your insightful feedback. We appreciate your comments and will address your concerns as follows:\n\n- W1, W2, \\& W3: We are grateful for your practical feedback. We will adjust the organization, modify Figure 3 in Appendix B, and include relevant literature in the final version.\n\n- Q1: We provide a detailed explanation in response to Reviewer 8euA. Win rates are influenced by various factors, and the related calculation in our framework is not straightforward. We have provided related metrics for further discussion in the anonymous link.\n\n- Q2: We appreciate your suggestion and are currently working on it. Due to the significant costs involved in large-scale human evaluations, it is challenging for us to directly engage in extensive human testing. This necessitates a careful examination and justification of comprehensive and reasonable metrics before initiating human evaluations. Building upon our current work, we have started gathering participants on a smaller scale, utilizing methods such as surveys, to conduct a series of human-AI interaction experiments. The aim is to clarify the OL of LLMs through comparisons in various scenarios. We will supplement some preliminary results in our final version. \n\n    Besides, We have also extended the framework to set the human player as the Sheriff for building the human baseline and made results and code available in the link.\n\n- Q3: Thank you for allowing us to clarify this. We do not allow werewolf negotiation due to experimental costs. During small-scale tests, we frequently observed that werewolves could not reach a consensus after multiple communications. 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. arXiv:2309.04658; arXiv:2310.18940 (ICML 2024).\n\n- Q4: We agree with your proposal. However, the OL of the Sheriff and other players is somewhat incomparable since all players except for the Sheriff are based on a baseline LLM. We conduct supplementary experiments under the homogeneous setting and report the ratios for all roles in the anonymous link. Our 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.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1.Propose a baseline and design two metrics for measuring Opinion Leadership.\n\n2.Conduct comprehensive experiments, such as human-agent experiments and model fine-tuning.", "reasons_to_reject": "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.\n\n2.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.\n\n3.See Questions and missing references:\n\nEmergence of Social Norms in Large Language Model-based Agent Societies\n\nCan large language models transform computational social science?\n\nCan Large Language Model Agents Simulate Human Trust Behaviors?\n\nExploring Collaboration Mechanisms for LLM Agents: A Social Psychology View", "questions_to_authors": "1.Why not consider the winning rate of the faction the sheriff belongs to as one of the metrics for measuring Opinion Leadership?\n\n2.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.\n\n3.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.\n\n4.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.", "extra_scores": {}}]

Author rebuttal:

Meta-review: 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.
Decision: Accept