Beyond Solo and Consistency: Vindicating Multi-Agent Debate via Conditional Progressive Pruning

Ruosong Ye; Caiqi Zhang; Jiahao Li; Haijun Wu; Xiaolong Luo; Huiyuan Chen; Yu Wang; Ying Chen

cs.CLSep 27, 2026

Beyond Solo and Consistency: Vindicating Multi-Agent Debate via Conditional Progressive Pruning

Authors: Ruosong Ye, Caiqi Zhang, Jiahao Li, Haijun Wu, Xiaolong Luo, Huiyuan Chen, Yu Wang, Ying Chen, +4 more

Organizations: Rutgers University, New Brunswick · University of Cambridge · Tsinghua University · Harvard University · Case Western Reserve University · University of California San Diego · Carnegie Mellon University

Abstract

Large Language Model (LLM) based Multi-Agent Debate (MAD) is one of the most effective test time scaling techniques. Through multi-round communication, agents complement each other in knowledge and reasoning and solve tasks that no single member can solve. However, existing MAD frameworks fail to beat strong Single Agent and Consistency-based baselines under the same strict cost limit, which shakes the foundation of the MAD field. We propose Conditional Progressive Pruning (CPP), a lightweight pruning framework that fully exploits multi-round MAD. CPP outperforms all existing MAD frameworks on multiple dominated benchmarks. It is also the first to fully outperform consistency methods. Our code, detailed agent interaction records will be released soon.

Figures & tables

Figure 1: Overview of our CPP pipeline. FuseGLU takes the LLM behavior embedding, the query and the candidate response as input, and autoregressively decides each action by combining the available information with the candidate conditioned on previous actions.

Panel of Table 1 — Table 1: State-Variation-Aware Multi-Round Debate Reward

	MATH-Hard		GPQA-Diamond		MMLU-Pro
Method	Acc (%)	Cost	Acc (%)	Cost	Acc (%)	Cost
Grok	48.50 $\pm$ 1.38	11.17%	57.33 $\pm$ 4.27	13.50%	57.00 $\pm$ 2.90	12.05%
GPT	43.83 $\pm$ 4.79	7.56%	38.67 $\pm$ 3.78	6.78%	42.17 $\pm$ 3.43	6.49%
Mistral	46.17 $\pm$ 3.97	8.15%	45.33 $\pm$ 3.44	4.46%	57.33 $\pm$ 1.51	5.22%
Vote	55.00 $\pm$ 3.63	26.88%	58.67 $\pm$ 3.01	24.74%	60.67 $\pm$ 3.61	23.75%
IoE-Grok	56.83 $\pm$ 3.06	28.24%	65.83 $\pm$ 2.32	32.79%	58.83 $\pm$ 3.60	32.84%

Table 2: CPP Main Results: Comparison with MADs.

Panel of Figure 2 — Figure 2: Detailed Consistency Results. Full results can be found in Appendix D

	MATH-Hard		GPQA-Diamond		MMLU-Pro
Method	Acc (%)	Cost	Acc (%)	Cost	Acc (%)	Cost
Consistency-Grok	58.50 $\pm$ 1.97	101.06%	63.33 $\pm$ 1.63	91.43%	61.00 $\pm$ 1.55	77.05%
Consistency-GPT	57.67 $\pm$ 1.03	84.88%	47.83 $\pm$ 1.60	68.47%	48.50 $\pm$ 1.05	71.40%
Consistency-Mistral	57.50 $\pm$ 1.97	99.21%	45.33 $\pm$ 3.44	4.46%	58.83 $\pm$ 1.72	16.29%
Consistency-Fuse	64.00 $\pm$ 2.45	107.89%	62.67 $\pm$ 2.16	56.88%	66.17 $\pm$ 2.32	78.94%
Consistency-Best	62.83 $\pm$ 2.14	103.48%	63.17 $\pm$ 2.48	74.85%	64.17 $\pm$ 3.06	86.30%

Table 3: All Consistency Mode and MAD Struture Extension Results

Panel of Table 4 — Table 4: Accuracy (%) and Cost of single models across different numbers of CoTs on MATH-Hard

	Vanilla				Adversarial
Method	Ref	Acc (%)	Cost	Edge	Ref	Acc (%)	Cost	Edge
Grok	–	41.17 $\pm$ 3.60	13.24%	–	–	9.83 $\pm$ 2.48	9.78%	–
GPT	–	43.83 $\pm$ 4.79	3.95%	–	–	4.67 $\pm$ 2.34	1.01%	–
Mistral	–	46.17 $\pm$ 3.97	4.26%	–	–	12.67 $\pm$ 2.07	1.07%	–
Vote	–	51.17 $\pm$ 3.31	21.45%	–	–	10.17 $\pm$ 1.72	11.86%	–
IoE-Vote	–	52.83 $\pm$ 3.97	51.66%	–	–	47.17 $\pm$ 4.26	52.34%	–

Table 5: Adversarial Robustness

	Pipeline					Reward
Ablation	Ref	Acc (%)	Cost	Edge	Ablation	Ref	Acc (%)	Cost	Edge
10-Sample	0.91, 0.86, 0.86	66.00 $\pm$ 2.37	96.73%	15.77	R_ + a	0.91, 0.87, 0.86	65.17 $\pm$ 3.37	93.79%	15.83
30-Sample	0.95, 0.92, 0.90	64.67 $\pm$ 3.08	97.34%	16.61	R_0.5a	0.73, 0.7, 0.69	62.33 $\pm$ 2.25	86.91%	12.70
90-Sample	0.92, 0.88, 0.87	64.00 $\pm$ 1.10	96.27%	16.08	R_0	0.53, 0.5, 0.5	59.50 $\pm$ 2.66	81.20%	9.17
150-Sample	0.87, 0.85, 0.84	62.33 $\pm$ 3.50	94.24%	15.34	R_ - a	0.39, 0.39, 0.41	60.00 $\pm$ 2.10	77.14%	7.18
w/o Training	0.95, 0.92, 0.91	63.33 $\pm$ 2.94	96.66%	16.73	w/o Round-Var.	0.83, 0.8, 0.79	64.67 $\pm$ 1.86	92.94%	14.50

Table 6: Ablation study on Pipeline and Reward design.

Method	q5/ q5/ q5	q75/ q75/ q75	q80/ q90/ q90	q85/ q95/ q95
Full-Debate	52.83 $\pm$ 3.31 68.52%	58.83 $\pm$ 2.04 85.87%	60.00 $\pm$ 2.00 88.51%	60.67 $\pm$ 2.94 90.30%
ARG-Designer	52.67 $\pm$ 2.73 68.24%	61.83 $\pm$ 4.12 85.26%	59.00 $\pm$ 2.37 87.58%	60.33 $\pm$ 3.14 89.92%
Adv_CPP	53.83 $\pm$ 2.04 66.26%	57.00 $\pm$ 3.52 80.77%	62.17 $\pm$ 3.54 83.27%	63.00 $\pm$ 3.16 84.48%
IoE-Vote ∗	52.83 $\pm$ 3.97 78.82%
Debate-IoE	61.00 $\pm$ 2.53 87.39%
Consistency-Fuse-12	62.00 $\pm$ 1.67 68.46%

Table 7: Accuracy (%, mean

\pm

std) on the left and Cost on the right. For the first 3 lines, the columns denote the token limit configurations.

Appendix figures & tables24 assets

Supplementary material from the paper’s appendix.

Appendix

Action	Dependency
$A_{1}[0][0]$	$(A_{1}[0][0],1)$ $(A_{1}[0][1],\gamma)$ $(A_{1}[0][2],\gamma^{2})$ $(A_{2}[0][0],\beta)$ $(A_{2}[0][1],\beta\gamma)$ $(A_{2}[0][2],\beta\gamma^{2})$ $(A_{2}[1][0],\beta\gamma)$ $(A_{2}[1][2],\beta\gamma^{2})$ $(A_{2}[2][0],\beta\gamma)$ $(A_{2}[2][1],\beta\gamma^{2})$
$A_{1}[0][1]$	$(A_{1}[0][1],1)$ $(A_{1}[0][2],\gamma)$ $(A_{2}[0][0],\beta)$ $(A_{2}[0][1],\beta\gamma)$ $(A_{2}[0][2],\beta\gamma^{2})$ $(A_{2}[1][0],\beta\gamma)$ $(A_{2}[1][2],\beta\gamma^{2})$ $(A_{2}[2][0],\beta\gamma)$ $(A_{2}[2][1],\beta\gamma^{2})$
$A_{1}[0][2]$	$(A_{1}[0][2],1)$ $(A_{2}[0][0],\beta)$ $(A_{2}[0][1],\beta\gamma)$ $(A_{2}[0][2],\beta\gamma^{2})$ $(A_{2}[1][0],\beta\gamma)$ $(A_{2}[1][2],\beta\gamma^{2})$ $(A_{2}[2][0],\beta\gamma)$ $(A_{2}[2][1],\beta\gamma^{2})$
$A_{1}[1][0]$	$(A_{1}[1][0],1)$ $(A_{1}[1][2],\gamma)$ $(A_{2}[0][1],\beta\gamma)$ $(A_{2}[0][2],\beta\gamma^{2})$ $(A_{2}[1][1],\beta)$ $(A_{2}[1][0],\beta\gamma)$ $(A_{2}[1][2],\beta\gamma^{2})$ $(A_{2}[2][1],\beta\gamma^{2})$
$A_{1}[1][1]$	$(A_{1}[1][1],1)$ $(A_{1}[1][0],\gamma)$ $(A_{1}[1][2],\gamma^{2})$ $(A_{2}[0][1],\beta\gamma)$ $(A_{2}[0][2],\beta\gamma^{2})$ $(A_{2}[1][1],\beta)$ $(A_{2}[1][0],\beta\gamma)$ $(A_{2}[1][2],\beta\gamma^{2})$ $(A_{2}[2][1],\beta\gamma^{2})$
$A_{1}[1][2]$	$(A_{1}[1][2],1)$ $(A_{2}[0][1],\beta\gamma)$ $(A_{2}[0][2],\beta\gamma^{2})$ $(A_{2}[1][1],\beta)$ $(A_{2}[1][0],\beta\gamma)$ $(A_{2}[1][2],\beta\gamma^{2})$ $(A_{2}[2][1],\beta\gamma^{2})$

Appendix

Table 8: Dependency structure of

A_{1}

and

A_{2}

under

3\times 3

MAD Architecture.

	MATH-Hard		GPQA-Diamond		MMLU-Pro
Method	Ref	Edge	Ref	Edge	Ref	Edge
Full-Debate	1, 1, 1	18.00	1, 1, 1	18.00	1, 1, 1	18.00
Random	0.5, 0.51, 0.5	9.02	0.5, 0.5, 0.5	9.02	0.5, 0.5, 0.5	9.02
LLM-Self	1.67, 1.58, 1.62	29.24	1.76, 1.47, 1.51	28.48	1.77, 1.58, 1.61	29.80
Intervention	0.4, 0.77, 0.83	12.00	0.53, 0.75, 0.69	12.00	0.56, 0.72, 0.72	12.00
$S^{2}$ -MAD	0.57, 0.58, 0.57	10.31	0.52, 0.56, 0.55	9.77	0.45, 0.47, 0.46	8.24

Appendix

Table 9: Comparison of Referenced Ratio (Grok, GPT, Mistral) and Edge Number across MATH-Hard, GPQA-Diamond and MMLU-Pro.

Threshold	Grok	GPT	Mistral
q5	65	132	139
q75	157	318	432
q80	166	353	478
q85	177	393	527
q90	196	458	623
q95	233	621	872

Appendix

Table 10: Output Token limit configurations at different quantiles on MATH-Hard Validation

$n$	2	3	4	5	6	7	8	9	Cost
Grok	49.33 $\pm$ 2.34	51.17 $\pm$ 2.40	53.33 $\pm$ 3.83	55.00 $\pm$ 3.10	56.00 $\pm$ 0.63	56.83 $\pm$ 1.94	57.83 $\pm$ 1.47	58.50 $\pm$ 1.97	101.06%

Appendix

Table 11: Consistency Accuracy (%) of Grok across different sample sizes

n

on MATH-Hard-I.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	Cost
GPT	47.67 $\pm$ 2.25	49.33 $\pm$ 2.42	51.67 $\pm$ 1.51	53.33 $\pm$ 2.07	53.50 $\pm$ 2.43	54.00 $\pm$ 1.79	54.67 $\pm$ 1.03	55.83 $\pm$ 0.98	57.33 $\pm$ 2.34	57.67 $\pm$ 1.03	57.00 $\pm$ 1.55	57.17 $\pm$ 2.04	100.32%

Appendix

Table 12: Consistency Accuracy (%) of GPT across different sample sizes

n

on MATH-Hard-I.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	Cost
Mistral	49.00 $\pm$ 4.24	52.67 $\pm$ 2.16	54.50 $\pm$ 3.78	56.00 $\pm$ 2.83	55.83 $\pm$ 2.32	56.67 $\pm$ 2.25	56.33 $\pm$ 2.42	56.67 $\pm$ 1.97	57.17 $\pm$ 1.83	56.83 $\pm$ 1.72	57.50 $\pm$ 1.97	57.17 $\pm$ 1.94	107.48%

Appendix

Table 13: Consistency Accuracy (%) of Mistral across different sample sizes

n

on MATH-Hard-I.

$n$	2	3	4	5	6	7	8	9	10	11	12	Cost
Fuse-Extension	49.83 $\pm$ 1.83	52.67 $\pm$ 1.21	53.83 $\pm$ 2.64	55.50 $\pm$ 2.43	58.67 $\pm$ 1.03	59.83 $\pm$ 1.17	60.50 $\pm$ 2.59	62.33 $\pm$ 1.63	62.83 $\pm$ 2.14	63.50 $\pm$ 3.27	64.00 $\pm$ 2.45	107.89%

Appendix

Table 14: Consistency Accuracy (%) of Fuse-Extension across different sample sizes

n

on MATH-Hard-I.

$n$	2	3	4	5	6	7	8	9	10	11	Cost
Best-Extension	50.83 $\pm$ 2.32	53.17 $\pm$ 1.60	55.00 $\pm$ 2.10	57.33 $\pm$ 2.66	58.17 $\pm$ 2.71	59.17 $\pm$ 2.64	61.33 $\pm$ 1.51	62.00 $\pm$ 2.10	62.50 $\pm$ 1.52	62.83 $\pm$ 2.14	103.48%

Appendix

Table 15: Consistency Accuracy (%) of Best-Extension across different sample sizes

n

on MATH-Hard-I.

$n$	2	3	4	5	6	7	8	9	10	11	12
Mistral	48.50 $\pm$ 4.85	51.83 $\pm$ 3.37	54.33 $\pm$ 3.14	56.33 $\pm$ 2.80	55.50 $\pm$ 1.97	56.50 $\pm$ 2.07	56.67 $\pm$ 2.42	57.00 $\pm$ 2.00	57.00 $\pm$ 2.45	56.83 $\pm$ 1.17	58.00 $\pm$ 1.79

Appendix

Table 16: Consistency Accuracy (%) of Mistral across different sample sizes

n

on MATH-Hard-II.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	14	Cost
Fuse-Extension	48.00 $\pm$ 3.35	51.17 $\pm$ 2.14	53.33 $\pm$ 2.73	53.33 $\pm$ 2.58	56.50 $\pm$ 2.26	58.33 $\pm$ 2.34	59.17 $\pm$ 0.98	60.00 $\pm$ 1.10	61.83 $\pm$ 1.47	62.17 $\pm$ 1.17	62.00 $\pm$ 1.67	62.00 $\pm$ 1.67	62.50 $\pm$ 0.84	94.94%

Appendix

Table 17: Consistency Accuracy (%) of Fuse-Extension across different sample sizes

n

on MATH-Hard-II.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	Cost
Best-Extension	48.00 $\pm$ 3.90	51.00 $\pm$ 2.37	53.33 $\pm$ 3.98	53.17 $\pm$ 2.99	55.83 $\pm$ 2.14	56.50 $\pm$ 2.66	58.17 $\pm$ 2.79	57.33 $\pm$ 3.44	58.50 $\pm$ 1.97	60.00 $\pm$ 1.10	60.50 $\pm$ 1.64	60.33 $\pm$ 1.37	60.83 $\pm$ 1.60	61.50 $\pm$ 1.52	62.17 $\pm$ 1.72	94.81%

Appendix

Table 18: Consistency Accuracy (%) of Best-Extension across different sample sizes

n

on MATH-Hard-II.

$n$	2	3	4	5	6	7	8	9	10	11	12
Mistral	11.67 $\pm$ 4.03	10.50 $\pm$ 1.52	13.50 $\pm$ 2.74	15.17 $\pm$ 1.60	15.67 $\pm$ 3.14	15.50 $\pm$ 1.87	17.00 $\pm$ 2.28	16.67 $\pm$ 2.73	17.83 $\pm$ 1.83	18.00 $\pm$ 2.76	19.17 $\pm$ 1.17

Appendix

Table 19: Adversarial Consistency Accuracy (%) of Mistral across different sample sizes

n

on MATH-Hard-II.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	14	Cost
Fuse-Extension	12.67 $\pm$ 2.42	12.50 $\pm$ 2.59	12.17 $\pm$ 2.79	13.83 $\pm$ 2.64	14.00 $\pm$ 2.68	14.83 $\pm$ 2.64	14.33 $\pm$ 2.34	14.17 $\pm$ 2.48	14.00 $\pm$ 1.41	14.67 $\pm$ 2.50	16.17 $\pm$ 1.72	16.33 $\pm$ 2.80	18.00 $\pm$ 1.26	54.67%

Appendix

Table 20: Adversarial Consistency Accuracy (%) of Fuse-Extension across different sample sizes

n

on MATH-Hard-II.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	Cost
Best-Extension	12.83 $\pm$ 2.56	12.83 $\pm$ 1.47	13.17 $\pm$ 1.94	15.50 $\pm$ 3.62	14.17 $\pm$ 3.54	15.00 $\pm$ 2.45	15.83 $\pm$ 2.32	16.17 $\pm$ 2.14	16.50 $\pm$ 1.87	16.50 $\pm$ 1.22	16.83 $\pm$ 0.98	17.33 $\pm$ 1.75	16.83 $\pm$ 0.75	18.17 $\pm$ 1.60	17.83 $\pm$ 1.94	47.54%

Appendix

Table 21: Adversarial Consistency Accuracy (%) of Best-Extension across different sample sizes

n

on MATH-Hard-II.

$n$	2	3	4	5	6	7	8	9	Cost
Grok	58.00 $\pm$ 2.28	59.83 $\pm$ 2.86	60.33 $\pm$ 2.25	60.83 $\pm$ 2.32	62.50 $\pm$ 2.59	63.33 $\pm$ 1.63	63.17 $\pm$ 1.94	63.00 $\pm$ 1.67	117.55%

Appendix

Table 22: Consistency Accuracy (%) of Grok across different sample sizes

n

on GPQA-Diamond.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	14	15	Cost
GPT	39.33 $\pm$ 3.14	42.83 $\pm$ 1.72	44.00 $\pm$ 1.41	45.83 $\pm$ 3.19	47.33 $\pm$ 1.75	46.33 $\pm$ 2.73	46.83 $\pm$ 3.60	46.33 $\pm$ 2.73	47.83 $\pm$ 1.60	47.00 $\pm$ 2.10	46.00 $\pm$ 2.37	46.67 $\pm$ 2.42	46.83 $\pm$ 2.64	46.33 $\pm$ 2.42	102.71%

Appendix

Table 23: Consistency Accuracy (%) of GPT across different sample sizes

n

on GPQA-Diamond.

$n$	2	3	4	5	6	7	8	9	10	11	12
Mistral	42.67 $\pm$ 2.94	42.33 $\pm$ 2.58	43.67 $\pm$ 1.97	43.33 $\pm$ 2.34	43.50 $\pm$ 0.84	44.17 $\pm$ 1.33	44.33 $\pm$ 1.03	43.83 $\pm$ 0.75	43.83 $\pm$ 0.41	43.50 $\pm$ 0.55	44.33 $\pm$ 1.03

Appendix

Table 24: Consistency Accuracy (%) of Mistral across different sample sizes

n

on GPQA-Diamond.

$n$	2	3	4	5	6	7	8	9	10	11	12	Cost
Fuse-Extension	58.50 $\pm$ 2.26	61.33 $\pm$ 3.56	61.17 $\pm$ 3.19	62.67 $\pm$ 2.16	60.67 $\pm$ 2.58	58.00 $\pm$ 2.90	57.83 $\pm$ 3.25	57.33 $\pm$ 4.84	57.33 $\pm$ 3.27	58.83 $\pm$ 1.94	59.83 $\pm$ 3.06	96.24%

Appendix

Table 25: Consistency Accuracy (%) of Fuse-Extension across different sample sizes

n

on GPQA-Diamond.

$n$	2	3	4	5	6	7	8	9	10	11	Cost
Best-Extension	59.17 $\pm$ 4.40	61.33 $\pm$ 4.50	60.67 $\pm$ 3.39	61.83 $\pm$ 2.64	62.83 $\pm$ 2.04	63.17 $\pm$ 2.48	61.50 $\pm$ 2.81	62.17 $\pm$ 1.94	62.17 $\pm$ 2.32	62.83 $\pm$ 1.72	99.14%

Appendix

Table 26: Consistency Accuracy (%) of Best-Extension across different sample sizes

n

on GPQA-Diamond.

$n$	2	3	4	5	6	7	8	9	Cost
Grok	57.83 $\pm$ 1.47	59.00 $\pm$ 1.41	60.00 $\pm$ 0.63	60.17 $\pm$ 1.47	61.00 $\pm$ 1.55	61.00 $\pm$ 1.41	60.50 $\pm$ 1.52	60.33 $\pm$ 1.37	115.57%

Appendix

Table 27: Consistency Accuracy (%) of Grok across different sample sizes

n

on MMLU-Pro.

$n$	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	Cost
GPT	45.50 $\pm$ 3.02	45.83 $\pm$ 2.71	47.33 $\pm$ 1.21	47.00 $\pm$ 0.00	47.50 $\pm$ 1.76	47.50 $\pm$ 0.84	47.33 $\pm$ 0.52	47.83 $\pm$ 1.60	47.83 $\pm$ 1.33	48.50 $\pm$ 1.05	47.67 $\pm$ 0.82	47.33 $\pm$ 1.03	47.17 $\pm$ 1.33	47.67 $\pm$ 1.63	47.33 $\pm$ 1.63	103.85%

Appendix

Table 28: Consistency Accuracy (%) of GPT across different sample sizes

n

on MMLU-Pro.

$n$	2	3	4	5	6	7	8	9	10
Mistral	57.50 $\pm$ 2.17	58.83 $\pm$ 1.72	58.00 $\pm$ 1.79	58.33 $\pm$ 2.25	58.67 $\pm$ 3.39	58.33 $\pm$ 2.25	58.33 $\pm$ 2.50	58.17 $\pm$ 2.64	58.67 $\pm$ 2.34

Appendix

Table 29: Consistency Accuracy (%) of Mistral across different sample sizes

n

on MMLU-Pro.

$n$	2	3	4	5	6	7	8	9	10	11	12	Cost
Fuse-Extension	57.67 $\pm$ 2.58	59.00 $\pm$ 1.55	59.83 $\pm$ 1.33	60.83 $\pm$ 1.17	62.33 $\pm$ 2.25	64.33 $\pm$ 2.07	64.33 $\pm$ 2.25	66.17 $\pm$ 2.32	65.83 $\pm$ 2.23	64.50 $\pm$ 1.76	64.50 $\pm$ 2.07	99.23%

Appendix

Table 30: Consistency Accuracy (%) of Fuse-Extension across different sample sizes

n

on MMLU-Pro.

$n$	2	3	4	5	6	7	8	9	10	11	Cost
Best-Extension	57.67 $\pm$ 2.07	59.17 $\pm$ 1.83	57.83 $\pm$ 2.04	59.00 $\pm$ 2.45	60.50 $\pm$ 2.35	62.50 $\pm$ 3.08	63.33 $\pm$ 3.20	64.17 $\pm$ 3.06	63.67 $\pm$ 2.50	63.17 $\pm$ 3.31	99.88%

Appendix

Table 31: Consistency Accuracy (%) of Best-Extension across different sample sizes

n

on MMLU-Pro.

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SVR-MAD: A Bayesian-Inspired Framework for Posterior-Guided Multi-Agent Debate

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Open paper AskPDF arXiv

Multi-Agent Debate (MAD) improves LLM-agent accuracy but suffers from rapid context growth, limiting scalability in larger multi-agent settings. Existing methods prune low-utility communications using prior signals, such as token-level log-likelihoods or LLM self-reported confidence. However, these signals become unreliable under hallucination, degrading the accuracy of MAD methods that rely on them. We propose SVR-MAD, a Bayesian-inspired MAD framework that treats pre-debate signals as priors and debate outcomes as posterior-style evidence for estimating agent correctness. SVR-MAD uses this evidence to incrementally construct the communication graph, prioritizing agents whose answers survive peer challenges. Experiments across multiple LLMs and benchmarks show that SVR-MAD reduces token cost by up to 61% while matching or improving accuracy relative to the most accurate competing MAD baseline.

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