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Group Perspective Matters: Regulating Debate Relationships Can Mitigate Blind Conformity in Multi-Agent Debate
Hao Wu, Shoucheng Song, Chang Yao, Haoyu Wang, Huaiyu Wan, Youfang Lin, Kai Lv
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 89%
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Summary
The paper introduces DEAR (Dynamically rEgulating debAte Relationships), a framework to mitigate blind conformity in Multi-Agent Debate (MAD) systems. DEAR shifts focus from individual LLM evaluation to group interaction by regulating debate relationships. It uses group evidence (consensus and divergence) to drive three stages: perceiving consultation tendency (What), selecting reference peers via a Selection RL-Agent (Who), and adjusting generation behaviors via a Behavior RL-Agent (How). The agents are jointly optimized using HAPPO.
Entities (10)
Relation Signals (8)
DEAR → mitigates → Blind Conformity
confidence 95% · DEAR... effectively mitigating blind conformity in Multi-Agent Debate.
DEAR → uses → Selection RL-Agent
confidence 92% · introducing a Selection RL-Agent to dynamically select reference peers
DEAR → uses → Behavior RL-Agent
confidence 92% · adopting a Behavior RL-Agent to adaptively adjust generation behaviors
DEAR → optimizes → HAPPO
confidence 90% · we innovatively employ the Heterogeneous-Agent Proximal Policy Optimization (HAPPO) algorithm [29] for end-to-end joint training.
Behavior RL-Agent → adjusts → Generation Behaviors
confidence 88% · How: adopting a Behavior RL-Agent to adaptively adjust generation behaviors
Selection RL-Agent → regulates → Debate Relationships
confidence 88% · regulating the debate relationships through three stages... Who: introducing a Selection RL-Agent to dynamically select reference peers
Subjective Logic → decouples → Group Evidence
confidence 85% · we employ Subjective Logic (SL) [28] to decouple the group evidence into consultation tendency and uncertainty
Group Evidence → derivedfrom → Consensus and Divergence
confidence 85% · DEAR quantifies consensus and divergence as group evidence to capture the debate state.
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Abstract
Abstract:Multi-Agent Debate (MAD) improves the reasoning performance of Large Language Models (LLMs) through multi-round interaction. However, LLMs in MAD are highly susceptible to blind conformity. Existing individual evaluation methods, typically based on confidence or perplexity, fail to reflect the correctness of reasoning and may even exacerbate blind conformity. To address this, we shift the perspective from individual evaluation to group interaction. We define mutual referencing among LLMs as \textbf{Debate Relationships} and recognize that regulating these relationships is the key to mitigating blind conformity. In this paper, we propose a novel framework for \textbf{D}ynamically r\textbf{E}gulating deb\textbf{A}te \textbf{R}elationships (DEAR) from the group perspective. At first, DEAR quantifies consensus and divergence as \textit{group evidence} to capture the debate state. Then, DEAR operates through three stages: 1) What: perceiving group consultation tendency and uncertainty; 2) Who: introducing a Selection RL-Agent to dynamically select reference peers; and 3) How: adopting a Behavior RL-Agent to adaptively adjust generation behaviors. Notably, we formulate the execution of the two RL-Agents as a sequential decision-making process, jointly optimizing via multi-agent reinforcement learning. Extensive experiments demonstrate that DEAR achieves superior performance while significantly reducing token consumption.
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- Source: https://arxiv.org/abs/2608.03648v1
- Canonical: https://arxiv.org/abs/2608.03648v1
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Group Perspective Matters: Regulating Debate Relationships Can Mitigate Blind Conformity in Multi-Agent Debate Hao Wu1,2, Shoucheng Song1,2, Chang Yao1,2, Haoyu Wang1,2, Huaiyu Wan1,2, Youfang Lin1,2, Kai Lv1,2 1School of Computer Science & Technology, Beijing Jiaotong University, Beijing, China 2Beijing Key Laboratory of Traffic Data Mining and Embodied Intelligence, Beijing, China insis_wh,insis_songsc,yaochang,kassawang,hywan,yflin,lvkai@bjtu.edu.cn Corresponding author. Abstract Multi-Agent Debate (MAD) improves the reasoning performance of Large Language Models (LLMs) through multi-round interaction. However, LLMs in MAD are highly susceptible to blind conformity. Existing individual evaluation methods, typically based on confidence or perplexity, fail to reflect the correctness of reasoning and may even exacerbate blind conformity. To address this, we shift the perspective from individual evaluation to group interaction. We define mutual referencing among LLMs as Debate Relationships and recognize that regulating these relationships is the key to mitigating blind conformity. In this paper, we propose a novel framework for Dynamically rEgulating debAte Relationships (DEAR) from the group perspective. At first, DEAR quantifies consensus and divergence as group evidence to capture the debate state. Then, DEAR operates through three stages: 1) What: perceiving group consultation tendency and uncertainty; 2) Who: introducing a Selection RL-Agent to dynamically select reference peers; and 3) How: adopting a Behavior RL-Agent to adaptively adjust generation behaviors. Notably, we formulate the execution of the two RL-Agents as a sequential decision-making process, jointly optimizing via multi-agent reinforcement learning. Extensive experiments demonstrate that DEAR achieves superior performance while significantly reducing token consumption. 1 Introduction In recent years, Multi-Agent Debate (MAD) has gained widespread attention as an effective paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs) [12, 3, 24]. Compared to the independent reasoning of a single model, MAD effectively mitigates hallucinations [35, 44, 54] by organizing multiple LLMs to debate around a common problem. However, in MAD, LLMs are highly susceptible to blind conformity—the minority often abandons their independent reasoning to align with the majority [5, 61, 76]. Current methods evaluate individual LLM reasoning’ reliability using confidence [55, 1, 77, 67] or perplexity [58]. By restricting the propagation of uncertain reasoning, these approaches moderately improve debate quality [1]. However, both confidence and perplexity suffer from inherent flaws. For confidence-based methods, they prompt LLMs to output confidence scores alongside their responses. Yet LLMs exhibit “overconfidence” [68], frequently assigning high confidence to incorrect reasoning even with confidence calibration [55, 77]. For perplexity-based methods, they calculate the token-level negative log-probability of the reasoning to quantify LLMs’ uncertainty. Yet perplexity measures textual fluency rather than reasoning correctness, meaning LLMs may easily generate incorrect responses with low perplexity [59, 23]. Moreover, the above methods apply fixed thresholds to propagate only high-confidence or low-perplexity responses. However, such unreliable individual evaluation may amplify the influence of incorrect reasoning and exacerbate blind conformity [46]. The limitations of evaluation methods motivate us to rethink the nature of blind conformity: rather than a single reasoning error, blind conformity is a group phenomenon driven by majority dominance. As this phenomenon emerges from group interactions, static individual evaluations are insufficient to capture the evolving group dynamics. Therefore, to mitigate blind conformity, we need to shift our perspective from individual evaluation to group interactions. In group interactions, we argue that debate is a dynamic process of viewpoint collision and integration. During this process, LLMs continuously update their reasoning by referencing peer opinions. We define the above mutual referencing as Debate Relationship. This relationship spans the entire group interaction and serves as the medium for viewpoint exchange. A beneficial debate relationship facilitates the reasonable adoption of peer responses, enabling LLMs to enhance their reasoning. Therefore, effectively regulating the debate relationships at the group level offers a viable pathway to mitigate the phenomenon of blind conformity. Building on the above insight, we propose a novel framework for Dynamically rEgulating debAte Relationships (DEAR) from the group perspective. To capture the debate state after each round, DEAR initially quantifies the group consensus and divergence as group evidence. Leveraging this evidence, DEAR regulates the debate relationships through three stages: perceiving consultation tendency and uncertainty (What), selecting reference peers (Who), and guiding generation behaviors (How). Specifically, in the first stage, we employ Subjective Logic (SL) [28] to decouple the group evidence into consultation tendency and uncertainty among LLMs. In the second stage, we introduce a Selection RL-Agent to learn an adaptive peer selection policy to determine which peers each LLM should reference. Finally, based on the established debate relationships, a Behavior RL-Agent is adopted to adjust the generation behaviors of individual LLMs. Furthermore, we formulate the ordered execution of the above RL-Agents as a sequential decision-making process. To guarantee the coordinated optimization of these policies, we innovatively employ the Heterogeneous-Agent Proximal Policy Optimization (HAPPO) algorithm [29] for end-to-end joint training. Extensive experiments on four mathematical reasoning tasks and four question-answering (QA) tasks demonstrate the effectiveness of our proposed method. Our main contributions are summarized as follows: • We shift the perspective from individual evaluation to group interactions centered on debate relationships, effectively mitigating blind conformity in Multi-Agent Debate. • We propose DEAR, a novel framework that employs group evidence to dynamically regulate debate relationships through: What–Who–How stages. • We conduct extensive experiments to demonstrate that DEAR achieves superior performance while significantly reducing token consumption. 2 Related Works 2.1 Single-Agent Reasoning. Several works propose various single-agent reasoning policies to augment the reasoning capabilities of LLMs [65, 63, 72, 2, 78, 52]. However, constrained by the intrinsic knowledge boundaries of an individual model, these methods struggle to correct hallucinations and reasoning errors. 2.2 Multi-Agent Debate. Multi-Agent Debate (MAD) leverages multi-round LLM interactions to improve reasoning performance [12, 3, 30, 73], yet LLMs frequently exhibit blind conformity during debate [5, 61]. Existing methods filter responses using confidence or perplexity to improve debate quality [55, 1, 58, 67], but the inherent unreliability of these metrics may instead exacerbate blind conformity [46]. Free-MAD [8] attempts to address the error propagation caused by incorrect majority responses through heuristic scoring of LLMs’ reasoning trajectories. However, evaluating the correctness of individual reasoning is fundamentally infeasible during the debate process without ground truth. More detailed related works and discussion can be seen in Appendix A. 3 Problem Definition We aim to mitigate blind conformity in the Multi-Agent Debate (MAD) system by regulating debate relationships from the group perspective, without fine-tuning any internal parameters of Large Language Models (LLMs). In this setting, we formulate this regulation process as a Partially Observable Markov Decision Process (POMDP) defined by the tuple ⟨,,,Ω,,ℐ,,,ℛ,γ⟩ ,V,S, ,O,I,A,T,R,γ , where =1,2N=\1,2\ represents the set of the Selection RL-Agent (with policy ρ) and the Behavior RL-Agent (with policy π); =1,…,VV=\1,…,V\ denotes the set of debating LLMs, with V representing their number; S denotes the state space; Ω represents the observation space; O is the observation function; ℐI and A denote the respective action spaces for the Selection and Behavior RL-Agents; T is the state transition function; ℛR is the reward function that assigns an environmental reward RdebateR_debate based on the correctness of the final answer at the terminal round T; and γ is the discount factor. Within this formulation, the Selection RL-Agent receives an observation oρ∈Ωo^ρ∈ derived from the group evidence, and outputs selection actions ∈ℐ ids to regulate which peer opinions each LLM should reference. The Behavior RL-Agent takes the observation and action of the Selection RL-Agent as conditional inputs, i.e., oπ=(oρ,)∈Ω×ℐo^π=(o^ρ, ids)∈ ×I, and outputs generation behaviors ∈ a , where ai=[Ti,Top_pi]a_i=[T_i,Top\_p_i], to adjust the temperature and nucleus sampling parameters for each LLM. According to the probability chain rule, the joint policy of the two RL-Agents can be defined as: (,∣s)=ρ(∣oρ)⋅π(∣oπ). π^all( ids, a s)=ρ( ids o^ρ)·π( a o^π). (1) 4 Method To mitigate blind conformity in MAD, our core idea is to dynamically regulate debate relationships from the group perspective. As illustrated in Figure 1, after each generation round, DEAR first quantifies the group consensus and divergence as group evidence to capture the debate state (⊳ Section 4.1). Driven by this, DEAR operates through three stages: (1) What (⊳ Section 4.2): We apply Subjective Logic (SL) [28] to decouple the group evidence into consultation tendency and uncertainty, providing the foundation for regulating debate relationships. (2) Who (⊳ Section 4.3): A Selection RL-Agent is introduced to select which peer responses each LLM should reference, dynamically regulating the debate relationships. (3) How (⊳ Section 4.4): A Behavior RL-Agent is adopted to adjust the generation behaviors of LLMs within the established debate relationships. Finally, we employ the Heterogeneous-Agent Proximal Policy Optimization (HAPPO) algorithm [29] for joint training of the above RL-Agents (⊳ Section 4.5). 4.1 Group Evidence Extraction To dynamically regulate debate relationships, we should first realize the current debate state. During the debate, the consensus and divergence among LLMs directly represent the collision and integration of viewpoints, objectively reflecting the current group dynamics. Therefore, we quantify the above two critical indicators as group evidence to capture the debate state. Specifically, we extract group evidence from paired LLM responses (AnsiAns_i, AnsjAns_j). Inherently, the final answers serve as the most direct indication of LLMs’ viewpoint. The alignment between two answers directly signifies whether they are in consensus or in divergence. However, standard outputs (e.g., a number or option) yield excessively sparse semantics for meaningful comparison. To address this, we prompt each LLM to summarize its reasoning process into a conclusion. Subsequently, we quantify the consensus and divergence across two dimensions. Conclusion Similarity. Conclusions represent the LLMs’ most direct judgments. To quantify conclusion similarity, we project the conclusions into a latent space hi∈ℝdh_i ^d using a pre-trained text encoder ξ(⋅)ξ(·) and calculate their scaled cosine similarity: eij(con)=12(1+hi⊤hj‖hi‖2‖hj‖2).e_ij^(con)= 12 (1+ h_i h_j\|h_i\|_2\|h_j\|_2 ). (2) Reasoning Similarity. Conclusion similarity only captures the alignment of final judgments, but fails to reveal the underlying logical reasoning process. To address this, we further quantify reasoning similarity. Following the same procedure as conclusion similarity, we map the reasoning processes of LLMs into latent representations ci∈ℝdc_i ^d. We then quantify the reasoning similarity with scaled cosine similarity: eij(rea)=12(1+ci⊤cj|ci|2|cj|2).e_ij^(rea)= 12 (1+ c_i c_j|c_i|_2|c_j|_2 ). (3) The above two similarities satisfy eij(con),eij(rea)∈[0,1]e_ij^(con),e_ij^(rea)∈[0,1]. We adopt the arithmetic mean to compute the scalar evidence score eije_ij (where we set eii=0e_i=0). To capture the debate state, we aggregate all pairwise scores to formulate the overall group evidence matrix agentE_agent. By measuring inter-LLM similarity independent of task-specific semantics, this evidence matrix is inherently task-agnostic and generalizes well across diverse reasoning tasks. Figure 1: The overall framework of DEAR. We employ a two-round debate as an example to detail it. In this framework, the debate perception represents group evidence extraction and What; the selection policy corresponds to Who; the behavior policy denotes How. 4.2 Group Evidence Decouple (What) While group evidence objectively captures consensus and divergence, it fails to reflect an LLM’s subjective consultation tendency toward its peers. Moreover, when facing conflicting opinions, LLMs inevitably experience uncertainty regarding peer credibility. This uncertainty is the key to perceiving whether they will abandon independent reasoning and blindly conform. Therefore, perceiving both the consultation tendency and the uncertainty is essential to effectively regulate debate relationships. To realize this, we employ Subjective Logic (SL) [28]. SL provides a theoretical framework that translates evidence into a distribution of belief masses across multiple targets, accompanied by an overall uncertainty mass. Accordingly, we decouple LLM i’s evidence into two components: the consultation tendency (the belief mass) bijb_ij toward peer j, and the corresponding uncertainty uiu_i. These variables satisfy the following zero-sum constraint: ui+∑j∈bij=1,bij≥0,ui≥0.u_i+ _j b_ij=1, b_ij≥ 0, u_i≥ 0. (4) In SL, transforming evidence into the belief mass requires a base weight to represent the initial total uncertainty (i.e., when no evidence has been collected). We set this base weight to the number of LLMs V. Defining the total accumulated evidence as Ei=∑j∈eijE_i= _j e_ij, the overall evidence strength of LLM i is Si=Ei+VS_i=E_i+V. The belief mass bijb_ij and the uncertainty uiu_i can be derived as: bij=eijSi,ui=VSi.b_ij= e_ijS_i, u_i= VS_i. (5) Based on this formulation, we perceive the LLMs’ subjective consultation tendencies and uncertainties to serve the subsequent regulation. 4.3 Adaptive Debater Selection (Who) With the consultation tendencies and uncertainties, we adopt them to regulate the debate relationships by determining the specific peers each LLM should reference. However, relying on static heuristic rules to make decisions is inadequate for the evolving dynamics of debate. Thus, we introduce a Selection RL-Agent to learn an adaptive peer selection policy ρ for group-level regulation. To achieve this, we construct a group observation oρo^ρ by concatenating the consultation tendency bib_i, uncertainty uiu_i, and a one-hot identity embedding IDi∈0,1ID_i∈\0,1\ of all LLMs: oρ=[b1‖u1‖ID1‖…‖bV‖uV‖IDV].o^ρ= [b_1 u_1 _1 … b_V u_V _V ]. (6) Then, we learn a mapping network fρ:ℝV(2V+1)→[0,1]V×(V−1)f_ρ:R^V(2V+1)→[0,1]^V×(V-1) that maps oρo^ρ to a preference matrix =[pi←j]i≠jP=[p_i← j]_i≠ j. Fundamentally, regulating debate relationships is a binary decision-making process: an LLM either references a peer’s response or does not. To realize this, we formulate the discrete peer selection action ∈ℐ ids as a set of independent Bernoulli variables parameterized by P. Accordingly, each binary action idsi←j∈0,1ids_i← j∈\0,1\, indicating whether LLM i references peer j, is sampled from the following joint policy distribution: ∼ρ(∣oρ)=∏i=1V∏j=1,j≠iV(pi←j)idsi←j(1−pi←j)1−idsi←j. ids ρ( ids o^ρ)= _i=1^V _ subarraycj=1,\ j≠ i subarray^V(p_i← j)^ids_i← j(1-p_i← j)^1-ids_i← j. (7) The action ids serves as the interaction mask for the subsequent debate round. By achieving group-level regulation of debate relationships, the RL-Agent selectively severs the transmission of harmful responses while preserving beneficial reasoning exchange, thereby mitigating blind conformity. 4.4 Generation Behavior Adjustment (How) After selecting a distinct subset of reference peers, each LLM should integrate the selected peers’ evidence into its own decisions. Traditional mean aggregation fails to distinguish between consensus and divergence, which are essential for determining whether an LLM should converge on existing opinions or explore breakthroughs. Instead, we employ the Dempster-Shafer Evidence Theory (DST) combination rule to fuse evidence. Definition 4.4.1 (Dempster’s Combination Rule). Given two independent belief sets ℳ1=(b1kk=1V,u1)M_1=(\b_1k\_k=1^V,u_1) and ℳ2=(b2kk=1V,u2)M_2=(\b_2k\_k=1^V,u_2), their fused joint belief ℳ=ℳ1⊕ℳ2=(bkk=1V,u)M=M_1 _2=(\b_k\_k=1^V,u) is computed as: bk=11−C(b1kb2k+b1ku2+b2ku1),u=11−Cu1u2,b_k= 11-C(b_1kb_2k+b_1ku_2+b_2ku_1), u= 11-Cu_1u_2, where C=∑p≠qb1pb2qC= _p≠ qb_1pb_2q quantifies the degree of conflict between the two beliefs, and 11−C 11-C is the normalization factor. Based on this, LLM i fuses its own belief set ℳiM_i with peers from the selected subset i=j∈∣j≠i,idsi←j=1X_i=\j j≠ i,ids_i← j=1\ by the subsequent rule: ℳ=ℳ1⊕ℳ2⊕…ℳV.M=M_1 _2 …M_V. (8) Once we have determined the fused belief ℳ^i=(b^i,u^i) M_i= ( b_i, u_i ), the evidence E^i E_i can be derived as: S^i=Vu^i,E^i=b^i×S^i S_i= V u_i, E_i= b_i× S_i. Taking E^i E_i as input, we sample the continuous variable zi=[zi,T,zi,P]⊤z_i=[z_i,T,z_i,P] from a diagonal Gaussian distribution parameterized by the Behavior RL-Agent policy π: zi∼π(⋅∣E^i)=((E^i),diag((E^i)2)).z_i π(· E_i)=N ( μ( E_i),diag( ν( E_i)^2) ). (9) To ensure the generation behaviors fall within the valid ranges [Tmin,Tmax][T_min,T_max] and [Pmin,Pmax][P_min,P_max], we apply a scaling mapping to the sampled variable ziz_i: Ti=Tmin+(Tmax−Tmin)⋅σ(zi,T),T_i=T_min+(T_max-T_min)·σ(z_i,T), (10) Top_pi=Pmin+(Pmax−Pmin)⋅σ(zi,P),Top\_p_i=P_min+(P_max-P_min)·σ(z_i,P), (11) where σ(⋅)σ(·) denotes the Sigmoid function. Finally, the Behavior RL-Agent outputs the continuous generation behavior ai=[Ti,Top_pi]a_i=[T_i,Top\_p_i], effectively adjusting the LLM’s generation behavior in the subsequent debate round. 4.5 Optimization Scheme Within DEAR, the Selection RL-Agent first generates the peer selection action ids. Subsequently, the Behavior RL-Agent dynamically adjusts the LLM’s generation behavior based on ids. This ordered execution constitutes an explicit sequential decision-making process. To ensure coordinated optimization, we employ the Heterogeneous-Agent Proximal Policy Optimization (HAPPO) algorithm [29] for end-to-end joint training. The Selection RL-Agent Optimization. Given that the Selection RL-Agent acts first in each iteration, we prioritize its optimization. Taking oρo^ρ as its input, this RL-Agent outputs a binary action ids for all LLMs. Its policy update ratio is defined as rϕρ,t=ρϕ(∣oρ)ρϕold(∣oρ)r_φ^ρ,t= _φ( ids^t o^ρ) _ _old( ids^t o^ρ). The Selection RL-Agent is optimized based on the advantage function A^t A^t, with the objective formulated as: ℒρ(ϕ)=[−min(rϕρ,tA^t,clip(rϕρ,t,1±ϵ)A^t)].L_ρ(φ)=E [- (r_φ^ρ,t A^t,clip(r_φ^ρ,t,1±ε) A^t ) ]. (12) Here, A^t A^t represents the Generalized Advantage Estimation (GAE), which is computed via the Temporal Difference (TD) error δtδ^t: A^t=∑l=0T−t(γλ)lδt+l,δt=ℛt+γVψ(st+1)−Vψ(st),ℛt=Rdebate,t=T0,t<T, A^t= _l=0^T-t(γλ)^lδ^t+l, δ^t=R^t+γ V_ψ(s^t+1)-V_ψ(s^t), ^t= casesR_debate,&t=T\\ 0,&t<T cases, (13) where RdebateR_debate denotes the environmental reward, T denotes the round of debate. The Behavior RL-Agent Optimization. Following the update of the Selection RL-Agent, we proceed to optimize the Behavior RL-Agent. Specifically, the sequential surrogate advantage for the Behavior RL-Agent is defined as: Mπ,t=rϕρ,tA^t,M^π,t=r_φ^ρ,t A^t, where rϕρ,tr_φ^ρ,t is the importance sampling ratio previously computed by the Selection RL-Agent. This term strictly conditions the Behavior RL-Agent’s optimization on the Selection RL-Agent’s policy updating, thereby guaranteeing the monotonic improvement of the joint policy. Since the Sigmoid mapping is a deterministic transformation, the essence of updating the Behavior RL-Agent is to optimize the parameterized distribution of the variable t z^t. Therefore, the corresponding policy update ratio is computed as rθπ,t=πθ(t∣E^t)πθold(t∣E^t)r_θ^π,t= _θ( z^t E^t) _ _old( z^t E^t). The optimization objective is defined as: ℒπ(θ)=[−min(rθπ,tMπ,t,clip(rθπ,t,1±ϵ)Mπ,t)].L_π(θ)=E [- (r_θ^π,tM^π,t,clip(r_θ^π,t,1±ε)M^π,t ) ]. (14) The Global Critic Optimization. To support the advantage estimation for the above RL-Agents, the centralized critic Vψ(s)V_ψ(s) precisely fits the expected return r^t=A^t+Vψold(st) r^t= A^t+V_ _old(s^t), employs a clipping operation similar to RL-Agents. The objective is expressed as: ℒcritic(ψ)=[max((Vψ(st)−r^t)2,(clip(Vψ(st),Vψold(st)±ϵ)−r^t)2)].L_critic(ψ)=E [ ((V_ψ(s^t)- r^t)^2, (clip(V_ψ(s^t),V_ _old(s^t)±ε)- r^t )^2 ) ]. (15) The pseudo-code for DEAR is given in Appendix F. Through the end-to-end training, we obtain the coordinated pair of Selection RL-Agent and Behavior RL-Agent for subsequent evaluation. Table 1: Performance comparison on GPT-4o-mini. We highlight the optimal and suboptimal results. Acc. (%) denotes accuracy, and T. (K) represents the average tokens per task. Math Reasoning Tasks GSM8K AIME24 GSM-Hard MATH-500 Avg. (Math) Architecture Method Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Single-Agent CoT 93.0 0.5 13.3 1.1 56.5 0.5 65.8 0.8 57.2 0.7 CoT-SC 96.3 6.0 10.0 17.3 59.3 8.5 73.3 12.5 59.7 11.1 Multi-Agent Majority Voting 94.5 1.2 6.7 3.3 57.3 1.4 63.3 2.2 55.5 2.0 MAD 94.5 13.3 13.3 36.1 54.8 15.3 64.8 24.2 56.9 22.2 DMAD 93.8 17.5 10.0 37.0 55.3 19.3 72.3 27.6 57.9 25.4 CortexDebate 93.5 22.6 6.7 34.4 56.3 25.6 69.3 36.6 56.5 29.8 MAD-M2(S) 94.0 9.0 10.0 32.3 53.5 9.7 71.0 21.1 57.1 18.0 ECON 91.5 8.1 - - 52.0 9.0 65.0 12.9 - - DEAR (Ours) 95.0 6.3 16.7 18.7 68.8 7.4 79.8 12.0 65.1 11.1 QA Tasks ARC-C MMLU (Pro.H.) TruthfulQA GPQA Dia. Avg. (QA) Architecture Method Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Single-Agent CoT 91.0 0.3 71.0 0.3 68.5 0.3 38.7 1.0 67.3 0.5 CoT-SC 93.0 6.6 73.5 7.2 70.5 7.3 44.0 16.2 70.3 9.3 Multi-Agent Majority Voting 93.8 1.2 73.0 1.3 68.0 1.4 40.7 3.0 68.9 1.7 MAD 93.0 12.5 73.5 19.4 72.0 14.0 40.0 32.1 69.6 19.5 DMAD 92.0 17.7 71.3 25.5 77.8 19.2 35.3 31.8 69.1 23.6 CortexDebate 92.0 12.0 70.3 15.5 74.5 11.3 42.0 42.7 69.7 20.4 MAD-M2(S) 93.8 6.1 73.0 10.4 62.5 7.3 42.7 20.2 68.0 11.0 ECON 92.5 9.5 71.0 10.0 73.0 8.8 42.0 14.8 69.6 10.8 DEAR (Ours) 94.5 5.6 74.0 8.5 83.5 5.2 48.0 14.3 75.0 8.4 5 Experiments In this section, we design extensive experiments to answer: (RQ1) How does DEAR perform against existing Multi-Agent Debate methods in terms of both accuracy and token consumption? (RQ2) What is the scalability of the DEAR scale across varying foundation models and debate configurations? (RQ3) What is the specific contribution of key components to the performance of DEAR? 5.1 Experimental Settings Datasets and Benchmarks. To evaluate the effectiveness of DEAR, we employ four math reasoning datasets (i.e., GSM8K [7], AIME24, GSM-Hard [16], and MATH-500 [36]) and four question answering (QA) datasets (i.e., ARC-C [6], MMLU_Pro (Health) [64], TruthfulQA [37], and GPQA Diamond [48]). Among these, AIME24 and GPQA Diamond are challenging tasks. Baselines. For single-agent baselines, we adopt Chain-of-Thought (CoT) [65] and Self-Consistency Chain-of-Thoughts (CoT-SC) [63] with 16 independent reasoning paths. For multi-agent baselines, we employ Majority Voting, Multi-Agent Debate (MAD) [12], Diverse Multi-Agent Debate (DMAD) [41], and CortexDebate [55]. We employ MAD-M²(O) [58] for open-source LLMs, and regarding the MAD-M2(O) for perplexity calculation, we adopt its variant, MAD-M2(S) [58] for closed-source LLMs. Additionally, for training-based reinforcement learning methods, we select ECON [73] as our baseline. Notably, we refrain from fine-tuning any internal parameters of LLMs and exclusively train the Selection RL-Agent and the Behavior RL-Agent. Detailed descriptions of the benchmarks and baselines are provided in Appendix B. Implementation Details. Only divergent viewpoints are worthy of debate. The diverse responses of LLMs can introduce multidimensional perspectives into MAD [69, 45, 77, 33]. Therefore, for the homogeneous debate system, we assign a distinct persona to each LLM following [69]. To ensure fair comparison, all baselines are initialized with the same personas as DEAR. For single-agent baselines, we compute the average accuracy across different personas. The pre-trained text encoder ξ(⋅)ξ(·) uses BGE-M3 [4]. Since DEAR is task-agnostic, our experiments primarily focus on zero-shot settings. Specifically, for math reasoning tasks, we train the DEAR on the GSM8K training set and evaluate it on the all math test set. For QA tasks, training is conducted on the ARC-C training set, followed by evaluation across all QA test sets. Comprehensive LLM persona configurations and additional implementation details are provided in Appendix B.3. 5.2 Main Results (RQ1) We evaluate the performance of DEAR using both an open-source model (Qwen3-8B) [57] and a closed-source model (GPT-4o-mini). Table 1 presents the evaluation results, with additional results provided in Appendix Table 3. Our key observations are summarized as follows: Observation 1: DEAR achieves the optimal or suboptimal results across diverse task domains. As shown in Table 1, 3, DEAR significantly outperforms baseline methods in average accuracy for both math reasoning and QA tasks. Even in challenging datasets, AIME24 and GPQA Diamond, DEAR yields substantial performance gains. These results present that MAD’s fully-connected topology tends to amplify erroneous reasoning. Meanwhile, individual evaluation methods such as CortexDebate and MAD-M2(S) rely on unreliable confidence or perplexity, which exacerbate blind conformity and compromise overall performance. In contrast, DEAR regulates debate relationships based on objective group evidence rather than flawed metrics. Using this evidence, the Selection RL-Agent dynamically selects which peers to reference to shield reasonable minority reasoning. Meanwhile, the Behavior RL-Agent utilizes DST-fused evidence to adaptively balance exploration and convergence, guiding the LLMs toward a valid consensus. Observation 2: DEAR significantly reduces token consumption during the debate. Current methods typically rely on massive token expenditure to improve accuracy. This reliance is especially obvious in debate methods such as DMAD and individual LLM policies like CoT-SC. In contrast, DEAR’s efficiency stems from the dynamic peer selection driven by the Selection RL-Agent. By perceiving the consultation tendency and uncertainty, the RL-Agent adaptively severs valueless peer references, preserving the beneficial reasoning exchanges, thereby reducing token consumption. Table 2: Performance and token consumption comparison on advanced closed-source models. AIME24 IMO AnswerBench MedXpertQA (Text) GPQA Dia. Avg. LLM Method Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Claude-4.5- Sonnet MAD 60.0 40.7 23.0 39.9 35.0 29.1 76.0 32.2 48.5 35.5 CortexDebate 53.3 57.6 21.0 57.3 29.0 48.4 74.0 50.4 44.3 53.4 MAD-M2(S) 63.3 44.8 25.0 40.0 31.0 30.7 78.0 36.5 49.3 38.0 DEAR (Ours) 76.7 26.6 35.0 31.7 40.0 23.2 82.0 24.0 58.4 26.4 Gemini-3.1- Flash-Lite MAD 63.3 35.4 22.0 34.1 54.0 25.3 73.0 28.0 53.1 30.7 CortexDebate 66.7 36.0 21.0 50.4 44.0 31.2 80.0 38.8 52.9 39.1 MAD-M2(S) 66.7 33.1 24.0 33.3 55.0 23.2 81.0 27.9 56.7 29.4 DEAR (Ours) 73.3 19.6 27.0 19.1 59.0 10.6 84.0 13.6 60.8 15.7 Figure 2: Effect of scaling the number of agents in the case of Qwen3-8B and GPT-4o-mini. 5.3 Scalability Analysis (RQ2) This section evaluates the DEAR across three dimensions: (1) adaptability across open- and closed-source models, (2) vertical scalability regarding the number of debate rounds, and (3) horizontal scalability concerning the number of LLMs. Different Model Adaptability. To verify compatibility, we test DEAR on advanced closed-source models Claude-4.5-Sonnet and Gemini-3.1-Flash-Lite. We also incorporate exceptionally challenging datasets, IMOAnswerBench [42], and MedXpertQA (Text) [79]. Several existing MAD methods rely on extracting token-level probabilities to calculate perplexity [47, 58]. However, closed-source models restrict access to these probability distributions, severely limiting their applicability. DEAR eliminates this reliance by utilizing group evidence, which quantifies inter-LLM similarity based solely on semantic outputs, thereby decoupling debate regulation from internal token distributions and specific tasks. Therefore, DEAR seamlessly adapts to diverse foundational models while consistently achieving superior performance on complex tasks, as shown in Table 2. Figure 3: Effect of scaling the number of debate rounds in the case of Qwen3-8B and GPT-4o-mini. Figure 4: Ablation study of the proposed DEAR on four datasets. Scaling of Debate Rounds & Number of LLMs. In this section, we evaluate the scalability of our framework. When scaling the number of LLMs, we fix the debate at three rounds. We also assign specific personas to each LLM following the configuration in [69]. Conversely, when scaling the debate rounds, we fix the LLM count at three. As illustrated in Figures 2 and 3, the performance of DEAR consistently improves as the number of LLMs increases. This demonstrates that the Selection RL-Agent effectively identifies reliable peers. In terms of scaling the debate rounds, DEAR converges to near-optimal performance within fewer rounds. This is attributed to the Behavior RL-Agent’s adjustment of generation behaviors, which facilitates valid consensus formation in the early rounds. 5.4 Ablation Study (RQ3) To validate the effectiveness of each components within DEAR, we design several ablated variants. Specifically, we remove diverse personas (w/o Personas). For the Behavior RL-Agent, we either completely remove it (w/o Behav. Policy) or substitute the DST fusion rule with simple mean-pooling (w/o Behav. Policy (Mean)). As for the Selection RL-Agent, we introduce two variants: a fully connected setting where all debaters are involved (w/o Selec. Policy (Full)), and a fully disconnected setting where selection is disabled (w/o Selec. Policy (Zero)). Figure 4 presents the results of these variants across four datasets using Qwen3-8B and GPT-4o-mini. The results confirm that removing any individual module degrades overall performance. Among all components, the Selection RL-Agent demonstrates the most substantial impact, particularly on complex reasoning tasks, indicating that regulating which peer should be referenced is the primary driver of debate quality. Disabling the Behavior RL-Agent also degrades, and replacing DST fusion with mean-pooling leads to performance decay, demonstrating that mean aggregation fails to distinguish between consensus and divergence among selected peers. Finally, while diverse personas contribute positively, their impact is relatively smaller compared to the RL-Agents. We investigate the performance of various diversity configurations and present the results in Appendix E. 6 Conclusion and Future Works In this paper, we propose DEAR, a novel framework that mitigates blind conformity by dynamically regulating debate relationships from the group perspective. Operating through the What-Who-How stages, DEAR utilizes group evidence to drive two RL-Agents for adaptive peer selection and behavior adjustment. To guarantee coordinated optimization, DEAR employs a multi-agent reinforcement learning algorithm for end-to-end joint training. 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Ding, and B. Zhou (2025) MedXpertQA: benchmarking expert-level medical reasoning and understanding. In International Conference on Machine Learning, p. 80961–80990. Cited by: 10th item, §5.3. Appendix A Detailed Related Works A.1 Single-Agent Reasoning. Large Language Models (LLMs) have shown formidable reasoning capabilities by independently executing complete reasoning processes. However, direct answer generation often fails on complex tasks because it forces models to jump to conclusions without intermediate logical deduction. To address this, some methods [65, 63, 52] have proposed various prompt-based internal reasoning policies. The most representative paradigm is Chain-of-Thought (CoT) [65], which guides models to decompose complex problems into sequential steps through few-shot exemplars or zero-shot instructions such as “Let’s think step by step” [65]. To further enhance robustness and leverage the diversity of generation paths, Self-Consistency Chain-of-Thought (CoT-SC) [63] samples multiple reasoning trajectories for the same problem and extracts the final answer via majority voting. As research progressed, single-agent reasoning evolved beyond linear paradigms to explore more complex logical topologies. For instance, Tab-CoT [78] introduces highly structured reasoning. Tree-of-Thoughts (ToT) [72] constructs a tree topology by generating multiple candidate answers at each step, facilitating multi-path exploration and self-evaluation. Graph-of-Thoughts (GoT) [2] further models the reasoning process as a flexible graph structure to handle non-linear reasoning tasks. A.2 Multi-Agent Debate. Multi-Agent Debate (MAD) [12] scales conventional reasoning paradigms by allowing multiple LLMs to engage in multi-round interactions, ultimately reaching a consensus through majority voting. AgentsCourt [21] improves answer quality via adversarial debate, while ChatEval [3] and Debatrix [34] introduce judge panels and multi-dimensional evaluation criteria for collaborative assessment, respectively. MLC [30] employs reinforcement learning for task-specific role differentiation. ECON [73] reformulates the collaborative process as an incomplete information game, seeking Bayesian Nash Equilibrium (BNE) through hierarchical reinforcement learning. CortexDebate [55] and ConfidenceCal [1] attempt to select opinions using explicit confidence as soft weights. MAD-M² [58] adopts a dual-component policy for memory filtering. The subjective component involves agents labeling historical records manually. The objective component utilizes model perplexity as the primary screening criterion. Sparse MAD (S-MAD) [32] and Selective Sparse MAD (S2-MAD) [75] achieve interaction sparsification by pruning redundant information flows. RUMAD [60] introduces a reinforcement learning-based controller to generate dynamic debate topologies. Regarding interaction constraints, Group Debate (GD) [40] simplifies global broadcast relationships into localized group debates, while DOWN [13] and iMAD [14] control debate rounds along the temporal dimension through adaptive triggers. [70] investigates sycophancy, revealing how LLM agents may prematurely abandon independent reasoning under peer answers, leading to debate collapse. Closely related to our work, Free-MAD [8] addresses conformity-driven error propagation using heuristic scoring to evaluate individual reasoning trajectories. However, assessing reasoning correctness without ground truth during inference is inherently unreliable. Returning to the essence of debate, our DEAR framework bypasses flawed individual evaluations by dynamically regulating debate relationships at the group interaction, effectively protecting the valid reasoning of the minority. A.3 The Dempster-Shafer Evidence Theory (DST). DST is a theory of belief functions established by Dempster [9]. It allows for combining multi-source beliefs through various fusion operators, thereby generating a new belief distribution that integrates all available evidence [50, 27]. In early research, DST was primarily utilized to model epistemic uncertainty in classification tasks [15, 10, 43, 11, 56, 20]. With the development of LLM, this theory has been extended to identify feature-level multimodal conflicts for hallucination detection in large vision-language models (LVLMs) [26, 31, 51, 25]. Furthermore, in retrieval-augmented generation (RAG), DST is primarily applied to resolve conflicts among multi-source retrieved evidence [62]. In LLM-as-a-Judge, it is effectively employed to fuse the evaluation opinions of multiple agents [39]. In this work, we use DST combination rules to fuse the evidence of the LLMs and their selected peers, thereby guiding the adaptation of generation behaviors. Appendix B Experimental Details B.1 Datasets Descriptions. In this section, we describe the datasets used in our experiments: • GSM8K [7] comprises grade-school math word problems designed to evaluate a model’s proficiency in multi-step arithmetic operations and foundational logical reasoning. We randomly sample 400 questions to assess basic mathematical performance. • AIME24 consists of official problems from the 2024 American Invitational Mathematics Examination, designed to probe the boundaries of profound and rigorous mathematical reasoning. We utilize the entire set of 30 problems for comprehensive evaluation. • GSM-Hard [16] is a difficulty-enhanced variant of GSM8K featuring larger or more complex numerical values. It investigates the robustness of reasoning trajectories under high computational complexity, from which we randomly sample 400 questions. • MATH-500 [36] is curated from the challenging MATH benchmark, broadly encompassing advanced domains like algebra, geometry, and number theory across multiple difficulty levels. We randomly sample 400 questions from this dataset. • ARC-C [6] (Challenge Set) comprises difficult multiple-choice questions from primary-level science exams, evaluating commonsense comprehension and scientific logical reasoning beyond superficial text retrieval. We randomly sample 400 questions for performance assessment. • MMLU_Pro (Health) [64] is a highly challenging subset focused exclusively on health and medicine, designed to quantify the internalization of professional medical knowledge and domain-specific reasoning accuracy. We randomly sample 400 questions for this study. • TruthfulQA [37] rigorously evaluates a model’s ability to generate objective, factual responses and mitigate hallucinations when confronted with empirical human misconceptions. We randomly sample 400 questions from this dataset. • GPQA Diamond [48] is an expert-level benchmark featuring graduate-level questions in physics, biology, and chemistry, measuring the capacity for in-depth, domain-specific reasoning. We randomly select 150 questions for our experiments. • IMOAnswerBench [42] aggregates top-tier International Mathematical Olympiad (IMO) problems, representing a rigorous standard for evaluating complex formal mathematical reasoning capabilities. We randomly sample 100 questions to explore the limits of extreme reasoning. • MedXpertQA [79] is a dataset focused on complex clinical medical scenarios. In our experimental setup, we use text-modal clinical data and randomly sample 100 questions for evaluation. Table 3: Performance comparison on Qwen3-8B. We highlight the optimal and suboptimal results. Acc. (%) denotes accuracy, and T. (K) represents the average tokens per task. Math Reasoning Tasks GSM8K AIME24 GSM-Hard MATH-500 Avg. (Math) Architecture Method Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Single-Agent CoT 91.5 0.4 30.0 4.1 57.0 0.4 70.8 1.2 62.3 1.5 CoT-SC 93.5 5.4 36.7 64.2 60.3 8.4 75.8 16.9 66.6 23.7 Multi-Agent Majority Voting 93.0 1.1 33.3 11.7 60.5 1.7 74.0 3.4 65.2 4.5 MAD 93.5 11.1 30.0 75.7 61.5 16.3 76.3 30.8 65.3 33.5 DMAD 91.5 17.5 33.3 98.2 61.8 23.4 78.8 41.0 66.4 45.0 CortexDebate 94.0 15.9 30.0 100.0 60.5 21.3 69.3 35.6 63.5 43.2 MAD-M2(O) 92.0 8.7 30.0 47.9 61.5 10.0 77.0 20.8 65.1 21.9 ECON 91.0 8.0 - - 61.0 9.3 72.0 13.3 - - DEAR (Ours) 94.0 7.6 36.7 21.2 73.5 6.2 85.0 8.4 72.3 10.9 QA Tasks ARC-C MMLU (Pro.H.) TruthfulQA GPQA Dia. Avg. (QA) Architecture Method Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Single-Agent CoT 90.0 0.4 56.8 0.4 63.3 0.5 36.7 2.0 61.7 0.8 CoT-SC 95.0 8.1 61.5 6.2 70.5 7.5 40.7 25.6 66.9 11.9 Multi-Agent Majority Voting 91.0 1.5 66.5 2.1 74.0 1.9 41.3 6.5 68.2 3.0 MAD 90.0 15.7 62.5 30.8 68.8 20.2 40.7 30.4 65.5 24.3 DMAD 91.5 22.6 64.0 39.2 72.0 27.7 38.0 64.1 66.4 38.4 CortexDebate 91.8 11.8 60.0 19.8 70.8 12.6 46.0 61.8 67.2 26.5 MAD-M2(O) 90.0 4.7 65.0 14.5 73.0 6.8 42.7 29.8 67.7 14.0 ECON 90.5 13.3 64.8 10.9 64.5 9.2 31.3 16.4 62.8 12.5 DEAR (Ours) 93.3 4.6 68.5 6.9 80.8 4.8 52.0 13.9 73.7 7.6 B.2 Baselines Descriptions In this section, we provide detailed descriptions of each baseline used in our comparison: • CoT (Chain-of-Thought) [65]: Guides large language models to generate intermediate step-by-step reasoning processes before producing the final output, serving as the foundational single-agent prompting method in this study. • CoT-SC (Self-Consistency Chain-of-Thought) [63]: Builds upon CoT by performing independent sampling to generate multiple distinct reasoning paths (set to 16 in our experiments) and using Majority Voting to determine the final answer. • Majority Voting: Aggregates the initial outputs from multiple independent agents, directly selecting the most frequently occurring answer as the final group decision. • MAD (Multi-Agent Debate) [12]: Allows multiple agents to read and evaluate each other’s reasoning processes across multiple interaction rounds, attempting to reach a group consensus through an iterative feedback mechanism. • DMAD (Diverse Multi-Agent Debate) [41]: Assigns diverse perspectives to agents within the traditional debate framework to mitigate the formation of mental sets during multi-agent interactions. • CortexDebate [55]: Utilizes the internal confidence of the models as a filtering metric to dynamically construct a sparse communication topology, thereby organizing information exchange pathways among agents. • MAD-M² [58]: Incorporates subjective (S) and objective (O) methods to filter historical memory. The subjective approach (S) requires agents to autonomously evaluate and label records (e.g., “YES,” “NO,” or “NOT SURE”), whereas the objective approach (O) utilizes model perplexity to screen responses. • ECON [73]: A multi-agent reinforcement learning-based debate method that strictly freezes the internal parameters of LLMs, training only external networks to adjust and optimize the generation behavior used during LLM API calls. B.3 Implementation Details Our pre-trained text encoder, ξ(⋅)ξ(·), employs BGE-M3, which outputs feature embeddings with a dimensionality of 1024. To instantiate the diverse homogeneous debate system introduced in the main text, we assign a distinct persona to each LLM. Specifically, for math reasoning tasks, the designated personas are Rigorous_Formalist, Creative_Explorer, and Systematic_Decomposer; for question-answering (QA) tasks, they are Consensus_Fact_Checker, Elimination_Reasoner, and Careful_Reader. To guarantee a fair comparison, all baseline methods are initialized with identical persona configurations. The explicit prompt templates corresponding to each persona are detailed in Appendix H. The core reinforcement learning hyperparameters and the debate environment parameters adopted during the training process are summarized in Table 4. Table 4: Key hyperparameters in the training process of DEAR. Parameter Explanation Value HAPPO Optimization Parameters γ Discount factor 1.01.0 λ GAE parameter 0.950.95 ϵε HAPPO clip range 0.20.2 lrlr Learning rate 5×10−45× 10^-4 λv _v Value loss coefficient 0.50.5 −- Optimizer type Adam NbatchN_batch Mini-batch size 11 NepochN_epoch PPO epochs 55 Buffer_size Buffer size in HAPPO 128 Debate Environment & Behavior Parameters V Number of LLM 33 T Maximum debate rounds 33 RdebateR_debate Reward for correct consensus +1.0+1.0 Tmin/TmaxT_min/T_max Temperature action boundaries 0/1.00/1.0 Pmin/PmaxP_min/P_max Top_p action boundaries 0/1.00/1.0 Appendix C Analysis for HAPPO with Reward Sharing C.1 Selection of HAPPO We consider a cooperative Multi-Agent Debate (MAD) system, where all LLMs collaboratively strive to maximize the accuracy of the group answer. In our proposed DEAR, the Selection RL-Agent and the Behavior RL-Agent form an explicit sequential decision: the Behavior RL-Agent’s input is strictly conditioned on the action output of the Selection RL-Agent. Moreover, the two RL-Agents operate over heterogeneous action spaces—the former outputs discrete binary masks, while the latter produces continuous generation behavior. Standard algorithms such as Independent PPO (IPPO) [49] update each RL-Agent in isolation, entirely ignoring inter-agent coordination. To address these limitations, we adopt Heterogeneous-Agent Proximal Policy Optimization (HAPPO) [29]. HAPPO naturally accommodates heterogeneous action spaces and, critically, guarantees the monotonic improvement of the joint policy through sequential advantage decomposition. Specifically, the Behavior RL-Agent’s surrogate advantage is explicitly scaled by the Selection RL-Agent’s policy update via importance sampling ratios. This mechanism precisely encapsulates the sequential causal dependency between the two RL-Agents, providing a theoretically grounded framework for joint optimization. C.2 Reward Sharing Reward sharing is a standard paradigm in cooperative Multi-Agent Reinforcement Learning (MARL) [74, 66, 53, 71], premised on the assumption that all agents pursue a unified optimization objective. Our framework DEAR intrinsically satisfies this assumption. The Selection RL-Agent and the Behavior RL-Agent jointly regulate the debate relationships through peer selection and behavior generation to maximize the final accuracy. This collective outcome is inherently inseparable, as it arises from the coupled interplay of peer selection and behavior generation, and cannot be meaningfully attributed to either RL-Agent individually. Furthermore, reward sharing is not merely a heuristic choice, but a necessity for HAPPO’s sequential advantage decomposition to function correctly. The generalized advantage A^t A^t, derived from a shared reward and a global critic, provides the base signal that is scaled by the Selection RL-Agent’s importance sampling ratio to guide the Behavior RL-Agent’s update. Without a shared reward, this sequential propagation of policy dependencies would be ill-defined. Therefore, employing reward sharing is both logically sound and theoretically indispensable for the coordinated optimization of our heterogeneous RL-Agents. Appendix D Analysis of Computational Efficiency and Training Overhead All experiments in this work are conducted on a workstation equipped with an AMD Ryzen 9 9950X 16-Core Processor and a single NVIDIA GeForce RTX 5090 GPU. To accelerate the empirical data collection process, we deploy 16 parallel interaction environments. The results demonstrate that the total training time for the DEAR framework is approximately 4.6 hours on the GSM8K dataset and 4.0 hours on the ARC-Challenge dataset. Furthermore, the peak GPU memory consumption during training is recorded at 20,112 MB (approximately 20 GB). This memory overhead is primarily due to the computational requirements of the BGE-M3 [4] embedding model during feature extraction. These metrics clearly indicate that both the computational and storage overheads of our framework are maintained within a highly reasonable range, demonstrating exceptional training efficiency and practical deployment feasibility. Appendix E Additional Experiments E.1 Analysis of Different Diversity Configurations To evaluate the impact of diversity and decouple its benefits from our proposed DEAR, we structure LLM heterogeneity into four progressive levels based on [69]. This approach systematically isolates each diversity source: • L1 (No Diversity): Identical base models and identical default prompts. • L2 (Persona Diversity Only): Identical base models equipped with the persona prompts specified in Section B.3. • L3 (Model Diversity Only): Distinct base models with identical default prompts. • L4 (Full Diversity): Distinct base models equipped with the persona prompts specified in Section B.3. In our specific setup, the heterogeneous small-scale LLM group utilizes LLaMA-3.1-8B-Instruct [18], GLM-4-9B-0414 [17], and Qwen3-8B [57]. The heterogeneous large-scale LLM group employs DeepSeek-V3.2 [38], GPT-5.4, and Claude-Sonnet-4.5. For the homogeneous setting, we use Qwen3-8B and Claude-Sonnet-4.5. Table 5: Performance comparison under different diversity configurations for small-scale LLMs. Config. Method GSM8K GSM-Hard ARC-C GPQA Dia. Acc. (%) Acc. (%) Acc. (%) Acc. (%) MAD 92.3 60.0 88.5 40.0 L1 DEAR 92.5 72.0 91.5 49.0 MAD 93.5 61.5 90.0 40.7 L2 DEAR 94.0 73.5 93.3 52.0 MAD 94.0 66.0 92.3 57.0 L3 DEAR 95.0 77.3 94.5 67.3 MAD 94.5 66.3 93.3 62.0 L4 DEAR 95.8 78.0 95.5 68.0 Table 6: Performance comparison under different diversity configurations for large-scale LLMs. Config. Method AIME24 IMO AnswerBench MedXpertQA (Text) GPQA Dia. Acc. (%) Acc. (%) Acc. (%) Acc. (%) MAD 53.3 21.0 30.0 74.0 L1 DEAR 70.0 32.0 37.0 80.0 MAD 60.0 23.0 35.0 76.0 L2 DEAR 76.7 35.0 40.0 82.0 MAD 86.7 37.0 38.0 82.0 L3 DEAR 93.3 42.0 42.0 85.0 MAD 90.0 40.0 39.0 83.0 L4 DEAR 96.7 44.0 45.0 87.0 The results are presented in Tables 5 and 6. Based on this, we draw the following observations: Observation 1: Introducing diversity yields progressive performance gains. From L1 to L4, debate performance improves steadily. Model-level differentiation (L3) serves as the primary driver, while persona prompts (L2/L4) provide only marginal additional gains. Observation 2: DEAR consistently outperforms the MAD baseline across all configurations. In both homogeneous and heterogeneous settings, DEAR surpasses MAD. This indicates that the performance of DEAR stems from the regulation of debate relationships by the two heterogeneous RL-Agents, rather than from a specific diversity configuration. In summary, diversity configuration and debate relationship regulation are two orthogonal dimensions for improving debate performance. The core innovation of the DEAR lies in the dynamic regulation of debate relationships rather than the introduction of diversity. Moreover, DEAR is compatible with various diversity settings and delivers consistent performance gains under each configuration. E.2 Comparison with Sparse Multi-Agent Debate To assess DEAR’s performance and token efficiency, we compare it with static sparse debate (S-MAD [32], S2-MAD [75]) and an RL-based dynamic topology generation method (RUMAD) [60]. Ensuring a fair comparison, we strictly adopt RUMAD’s configuration: a 6-round debate involving 6 LLMs. These LLMs are uniformly instantiated from three base models (LLaMA-3.1-8B-Instruct [18], ChatGLM-4 9B [17], and Deepseek-Math-7B-Instruct [19]), utilizing two agents per model. Performance is assessed on GSM8K [7], MMLU [22], and GPQA [48]. • MMLU: A comprehensive benchmark evaluating multi-domain reasoning capabilities in LLMs, spanning diverse fields such as STEM, humanities, and social sciences. • GPQA: A highly challenging, graduate-level QA dataset designed to test advanced scientific reasoning across disciplines like physics, biology, and chemistry. Table 7: Comparison of accuracy and token consumption with sparse debate methods. Acc. (%) denotes accuracy, and T. (K) represents the average tokens per task. S-MAD∗ and S-MADo represent S-MAD configured with star and ring topologies, respectively. Best results are bolded and the second-best are underlined. Method GSM8K MMLU GPQA Avg. Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ Acc. ↑ T. ↓ S-MAD∗ 83.0 39.4 61.0 33.3 30.0 36.4 58.0 36.4 S-MADo 70.0 37.8 54.0 31.7 34.0 38.6 52.7 36.0 S2-MAD 70.0 30.5 46.0 25.4 28.0 23.3 48.0 26.4 RUMAD 89.0 17.3 68.0 22.5 35.0 33.4 64.0 24.4 DEAR 94.0 16.7 74.0 21.8 42.0 31.3 70.0 23.3 Table 7 show that static sparse methods (S-MAD and S2-MAD) reduce token costs by restricting communication, yet typically sacrifice accuracy. RUMAD improves this accuracy-cost balance via RL-driven dynamic topologies, though it solely optimizes peer selection. DEAR outperforms these methods by delivering higher accuracy at lower token costs across all benchmarks. This confirms that the synergistic regulation of both Selection and Behavior RL-Agents offers a far more efficient performance boost than static or single-dimensional dynamic topologies. E.3 Analyzing Cross-Domain Zero-Shot Transfer The task-agnostic of DEAR stems from deriving RL-Agents inputs from objective cosine similarity. Beyond validating cross-task generalization within single domains in our primary experiments, we further conduct zero-shot cross-domain transfer experiments (Math ↔ QA). Specifically, for the Math → QA transfer, we train the RL-Agents on GSM8K and evaluate their zero-shot performance on TruthfulQA and GPQA Diamond. Conversely, in the QA → Math transfer, the RL-Agents are trained on ARC-C and tested on unseen reasoning tasks, including GSM-Hard and MATH-500. Table 8: Cross-domain transfer performance of DEAR between Math and QA on GPT-4o-mini. Best results are bolded and the second-best are underlined. Math → QA Method GSM8K TruthfulQA GPQA Diamond Acc. (%) Acc. (%) Acc. (%) MAD 94.5 72.0 40.0 DEAR (in domain) 95.0 83.5 48.0 DEAR (out of domain) - 76.0 45.0 QA → Math Method ARC-C GSM-Hard MATH-500 Acc. (%) Acc. (%) Acc. (%) MAD 93.0 54.8 64.8 DEAR (in domain) 94.5 68.8 79.8 DEAR (out of domain) - 64.5 76.0 Table 8 demonstrates that DEAR outperforms the standard MAD across all target datasets, proving that the RL-Agents rely on task-agnostic features to form a universal regulation policy. The slight performance decay in cross-domain transfer is primarily caused by the natural distribution shift of the input features. Even with a constant cosine similarity, the fundamental differences in the statistical distributions of these scores across domains (e.g., Math vs. QA) perturb the RL-Agents’ inputs, leading to suboptimal decision-making. E.4 Ablation on SL and DST Fusion To validate the effectiveness of Subjective Logic (SL) and the DST fusion in debate relationship regulation, we design two ablation variants: (1) DEAR-EviMean, which directly feeds group evidence into the Selection RL-Agent and applies mean-pooling for evidence fusion; and (2) DEAR-EviDST, which retains the same input but employs Dempster-Shafer Evidence Theory (DST) to fuse the received evidence. The experiments are conducted using GPT-4o-mini. Table 9: Performance comparison of DEAR with different regulation bases and fusion strategies. GSM8K GSM-Hard ARC-C GPQA Diamond Method Acc. (%) Acc. (%) Acc. (%) Acc. (%) DEAR-EviMean 92.0 64.0 91.0 42.0 DEAR-EviDST 93.3 65.5 92.3 42.7 DEAR 95.0 68.8 94.5 48.0 The results in Table 9 indicate performance degradation in both variants. Notably, DEAR-EviDST underperforms the full DEAR framework despite both using the DST mechanism. This gap proves the effectiveness of identifying LLMs’ consultation tendencies and quantifying individual consultation uncertainty. Consequently, they provide a reliable basis for group-level debate regulation. Furthermore, the steeper decline in DEAR-EviMean shows that DST fuses conflicting evidence more rationally than simple mean-pooling. Appendix F The Pseudocode of Training Process of DEAR The training pseudocode for DEAR is presented in Algorithm 1. Algorithm 1 DEAR Input: LLMs =1,…,VV=\1,…,V\, Debate rounds T, Text encoder ξ(⋅)ξ(·), Problem Q Initialize: Selection RL-Agent ρϕ _φ, Behavior RL-Agent πθ _θ, Critic VψV_ψ, Replay buffer D Set: learning rate lrlr, hyperparameters γ,λ,ϵγ,λ,ε 1: for episode =1,…,E=1,…,E do 2: for round t=1t=1 to T do 3: 1. Multi-Agent Debate Execution: 4: for each LLM i∈i do 5: Generate response AnsitAns_i^t based on problem Q with parameters (Tit,Top_pit)(T_i^t,Top\_p_i^t) 6: end for 7: 2. Group Evidence Extraction and Decouple (What): 8: Extract group evidence eije_ij from pairwise responses via ξ(⋅)ξ(·) 9: Decouple eije_ij into belief mass bijb_ij and uncertainty uiu_i via Subjective Logic 10: Construct group observation oρo^ρ from bi,ui,IDii=1V\b_i,u_i,ID_i\_i=1^V 11: 3. Adaptive Debater Selection (Who) & Generation Behavior Adjustment (How): 12: Sample peer selection mask t∼ρϕ(⋅∣oρ) ids^t _φ(· o^ρ) via independent Bernoulli distributions 13: for each LLM i∈i do 14: Filter reference peers it=j∣idsi←jt=1X_i^t=\j ids_i← j^t=1\ 15: Construct next debate context using problem Q and peer responses Ansjt∣j∈it\Ans_j^t j _i^t\ 16: Fuse evidence of LLM i with selected peers itX_i^t by DST combination rule 17: Derive fused evidence E^i E_i via inverse SL mapping 18: Sample continuous latent variable zit∼πθ(⋅∣E^i)z_i^t _θ(· E_i) from diagonal Gaussian 19: Map zitz_i^t to generation behavior ait+1=[Tit+1,Top_pit+1]a_i^t+1=[T_i^t+1,Top\_p_i^t+1] via Sigmoid 20: end for 21: end for 22: Obtain terminal reward RdebateR_debate based on final consensus; Store trajectory in D 23: Sample a minibatch of trajectories from D 24: 4. End-to-End Joint Optimization: 25: Compute Generalized Advantage Estimation (GAE) A^t A^t 26: Compute sequential surrogate advantage Mπ,t=rϕρ,tA^tM^π,t=r_φ^ρ,t A^t 27: Update Selection RL-Agent ρϕ _φ by minimizing objective ℒρL_ρ (Eq. 12) 28: Update Behavior RL-Agent πθ _θ by minimizing objective ℒπL_π (Eq. 14) 29: Update Critic VψV_ψ by minimizing objective ℒcriticL_critic (Eq. 15) 30: end for 31: return Trained ρϕ _φ and πθ _θ Appendix G Case Study To intuitively demonstrate how DEAR prevents to mitigate blind conformity in MAD, we extract a real debate trajectory from the challenging GPQA Diamond [48]. Example of Debate Trajectory in GPQA Diamond • Initial question Q: - Your colleague has devised a new quantum field theory on four-dimensional spacetime, and is exploring the regularization of certain higher-order loop diagrams in that theory. On their desk you spy a scribbled note: a Feynman diagram, and next to it, the words “size estimate” followed by a string of physical constants, numbers, and ratios between what appear to be energy scales. The symbols read: α3⋅g22⋅8⋅1(4π)6⋅(QM)2α^3· g^2 2· 8· 1(4π)^6· ( QM )^2. The diagram, unfortunately, has been rendered unreadable by a spilled coffee. How many loops did it contain? (A) 1 (B) 2 (C) 6 (D) 3 • Ground Truth: (D) 3 • Initial Round: - [Agent 1] Persona: Consensus_Fact_Checker Reasoning process: In quantum electrodynamics (QED), the size estimate of a Feynman diagram typically scales with αnα^n, where n is the number of loops. In this case, the expression includes α3α^3, suggesting a three-loop diagram. Conclusion: The most consistent interpretation with well-established quantum field theory is a three-loop diagram. D ✓ - [Agent 2] Persona: Eliminative_Reasoner Reasoning process: The presence of a factor of 1/(4π)61/(4π)^6 is a strong indicator of six-loop diagrams. Evaluating options: (A) 1 loop gives 1/(4π)21/(4π)^2. (B) 2 loops give 1/(4π)41/(4π)^4. (C) 6 loops matches the 1/(4π)61/(4π)^6 factor. (D) 3 loops would give 1/(4π)61/(4π)^6 only in non-standard schemes. Conclusion: By elimination, 6 is the best-supported choice. C ✗ - [Agent 3] Persona: Careful_Reader Reasoning process: In dimensional regularization, the divergence is proportional to 1/(4π)d−41/(4π)^d-4. For four-dimensional regularization, we get a factor of 1/(4π)61/(4π)^6, which implies six loops. Conclusion: The factor 1/(4π)61/(4π)^6 strongly suggests six loops. C ✗ • Round 1: - [Agent 1] Persona: Consensus_Fact_Checker (← Isolated) Reasoning process: Independently re-checking the reasoning. In quantum field theory, particularly in dimensional regularization, the divergence of a Feynman diagram is often expressed with a factor of the form 1/(4π)2n1/(4π)^2n, where n is the number of loops. Given the factor 1/(4π)61/(4π)^6, we deduce that n=3n=3, since (4π)2⋅3=(4π)6(4π)^2· 3=(4π)^6. Conclusion: The presence of α3α^3 also supports this. Therefore, the diagram contains three loops. D ✓ - [Agent 2] Persona: Eliminative_Reasoner (← Refers to Agents 1 & 3) Reasoning process: Scanning peers (Agent 1, Agent 3). Agent 1 misinterprets the scaling of the coupling constants, suggesting α3α^3 implies three loops. Agent 3 correctly identifies the 1/(4π)61/(4π)^6 factor as a strong indicator of six loops based on the exponent mapping. Conclusion: While 1/(4π)61/(4π)^6 could be interpreted as three loops in some contexts, the standard convention corresponds to six loops. By elimination, 6 remains the logical choice. C ✗ - [Agent 3] Persona: Careful_Reader (← Refers to Agents 1 & 2) Reasoning process: Scanning peers (Agent 1, Agent 2). Agent 2 maintains 6 loops. However, Agent 1 correctly identifies that in dimensional regularization, the divergence of a Feynman diagram is proportional to 1/(4π)2L1/(4π)^2L, where L is the number of loops. The exponent is 6, so 2L=6⇒L=32L=6 L=3. Conclusion: While some might misinterpret the factor 1/(4π)61/(4π)^6 as indicating six loops, the correct interpretation is that it represents three loops. D ✓ • Round 2: - [Agent 1] Persona: Consensus_Fact_Checker (← Refers to Agent 2) Reasoning process: Scanning peer (Agent 2). Agent 2 still argues that the 1/(4π)61/(4π)^6 factor is a strong indicator of six-loop diagrams. However, independently confirming the derivation, the standard convention is that the exponent is 2n2n. Thus 2n=6⇒n=32n=6 n=3. Conclusion: The peer’s reasoning remains flawed. Mathematical derivation clearly indicates three inherent loops. D ✓ - [Agent 2] Persona: Eliminative_Reasoner (← Refers to Agents 1 & 3) Reasoning process: Scanning peers (Agent 1, Agent 3). Both peers now point out the specific dimensional regularization formula 1/(4π)2L1/(4π)^2L. This means the exponent is twice the number of loops, so 2L=6⇒L=32L=6 L=3. Let’s systematically eliminate: (A) 1 gives 1/(4π)21/(4π)^2. (B) 2 gives 1/(4π)41/(4π)^4. (C) 6 would correspond to 1/(4π)121/(4π)^12. (D) 3 matches the 1/(4π)61/(4π)^6 factor. Conclusion: By eliminating the incorrect exponent mappings based on the proper 2L2L rule, 3 loops is the only defensible answer. D ✓ - [Agent 3] Persona: Careful_Reader (← Refers to Agent 2) Reasoning process: Scanning peer (Agent 2). While Agent 2 still argues that 1/(4π)61/(4π)^6 implies six loops by elimination, they are missing the 2L2L formula detail. Having carefully corrected this exact trap myself in the previous round, the correct QFT convention dictates the exponent is twice the number of loops. Conclusion: I will not regress. The correct interpretation of the dimensional regularization standard convention confirms three loops. D ✓ • Final Vote: - D. ✓ Appendix H Prompt Set In our framework, each LLM is assigned a distinct persona prompt. Each persona defines a unique reasoning style, guiding the LLM to approach problems from a differentiated perspective. The detailed persona prompts are presented below. H.1 Math Reasoning Tasks For math reasoning tasks, we assign the following three personas from [69]: Persona 1: Rigorous_Formalist You are a rigorous mathematician who formalizes problems precisely. Your approach: - Define all variables and terms clearly at the start. - State any assumptions explicitly. - Justify each step with mathematical principles or rules. - Use precise mathematical notation and language. - Ensure logical completeness in your reasoning. Persona 2: Creative_Explorer You are an innovative problem solver who looks for elegant and creative solutions. Your approach: - Look for patterns, shortcuts, and elegant solutions. - Try multiple approaches and compare them. - Think about the problem from different angles. - Don’t be afraid to try unconventional methods. - Value insight and elegance alongside correctness. Persona 3: Systematic_Decomposer You are an expert at breaking complex problems into manageable parts. Your approach: - Identify the core components of the problem. - Break the problem into smaller, independent sub-problems. - Solve each sub-problem systematically. - Carefully combine the results, checking for consistency. - Review the overall solution for completeness. H.2 Question Answering Tasks For QA tasks, we assign the following three personas from [69]: Persona 1: Consensus_Fact_Checker You select the option most consistent with well-established consensus knowledge. Your approach: - Prefer mainstream scientific/medical/historical understanding when relevant. - Penalize claims that conflict with widely accepted facts. - Choose the option whose core claim best matches reliable background knowledge. Persona 2: Eliminative_Reasoner You are an expert at process of elimination reasoning. Your approach: - Systematically evaluate each option. - Find clear reasons to eliminate wrong answers. - Use contradictions and impossibilities. - Narrow down to the most defensible answer. - Verify the remaining answer makes sense. Persona 3: Careful_Reader You are a careful reader who avoids traps in questions. Your approach: - Pay attention to qualifiers (most likely, best, depends, always/never). - Identify what the question is REALLY asking (definition vs application). - Prefer simple textbook truths over tricky interpretations. H.3 Debate Prompt Templates In addition to persona prompts, we design prompt templates for the initial round and subsequent debate rounds. H.3.1 Initial Round Prompt Template In the initial round, each LLM independently solves the problem without peer interaction: Initial Round Prompt Persona Prompt Problem: Question Instruction: 1. Provide your reasoning process. 2. Summarize your reasoning into a conclusion that includes the final answer. Output Instruction Where the output instructions are: • Math: “Output the final result inside . Example: 42.” • QA: “Output the final choice selection using the format: X where X is the exact option letter. Example: C.” H.3.2 Debate Round Prompt Template In subsequent debate rounds, each LLM receives its own previous response along with peers’ responses. Depending on whether peer responses are available, two prompt variants are used. Case 1: With Peer Responses Debate Round Prompt (With Peer Responses) Persona Prompt Problem: Question Previous Thought: Self Memory Peer Responses: Peer Context REVIEW PROTOCOL: 1. BEFORE reading peers, rederive the key steps independently. 2. THEN scan peers. Only consider an objection if it identifies a SPECIFIC step where a particular number, formula, or factual claim is wrong. Instruction: 1. Provide your reasoning process. 2. Summarize your reasoning into a conclusion that includes the final answer. Output Instruction Case 2: Without Peer Responses Note that when no peer responses are available, the peer context block is replaced with: Debate Round Prompt (No Peer Responses Available) Persona Prompt Problem: Question Previous Thought: Self Memory Task: Independently re-check the reasoning. Identify the single step least certain, re-derive it from scratch, and correct it only if a concrete error is found. Instruction: 1. Provide your reasoning process. 2. Summarize your reasoning into a conclusion that includes the final answer. Output Instruction