REVIEW 5 major objections 5 minor 2 cited by
Efficient Leave-one-out Approximation in LLM Multi-agent Debate Based on Introspection
T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read IntrospecLOO claims a single final-round prompt can approximate leave-one-out evaluation in LLM multi-agent debates, reducing token complexity from quadratic to linear.
desk verdict A genuinely cheap and novel prompting idea for approximating leave-one-out in LLM debates, but the evaluation never establishes that it actually approximates LOO at the decision level—and the paper's own case study contradicts it. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The IntrospecLOO prompt is the mechanism: 'Now, please rethink this question by disregarding the response from Agent {Agent Name}. Can you give an updated answer?' appended as a final round. The complexity argument is the supporting identity: comparing Eq. (2), which counts (N-1) agents re-debating for T rounds at O(RT $N^{2}$), with Eq. (3), which counts a single extra (N-1)-agent round at O(RN). The token-complexity gap is what makes the approximation practically interesting.
What would settle it
The case study in Figures 5-7 is a direct counterexample: with Agent 4 removed, the full leave-one-out debate's majority answer is (D), while the IntrospecLOO round's majority answer is (A). A systematic test would count how often IntrospecLOO's final majority diverges from the true LOO majority across the benchmark sets; if the divergence rate is material, the approximation does not hold at the instance level.
Extended reading notes
Core claim
The central claim is that a single post-debate introspection prompt can approximate leave-one-out evaluation. After T rounds of debate among N agents, IntrospecLOO asks each of the N-1 agents who are not being evaluated to 'rethink this question by disregarding the response from Agent X' and provide an updated answer; the updated answers are aggregated by majority vote. The paper argues this yields the same kind of contribution signal as removing Agent X from the beginning of the debate, at far lower cost: true LOO requires O(RT $N^{2}$) tokens per evaluated agent, whereas IntrospecLOO requires only O(RN). The empirical results report closeness to the LOO baseline on three benchmarks, with the approximation holding for both high-performing and under-performing agents.
Load-bearing premise
The method assumes that telling an agent to mentally delete one peer's answers at the end of a debate produces the same final answer as that peer never having spoken, a one-step counterfactual that is never verified per instance.
Editorial extensions
If this is right
- Agent-level contribution analysis becomes affordable for debates with many agents, since the per-agent evaluation cost stops depending on the number of debate rounds.
- The method is a prompting-only change: it can be added to an existing debate pipeline without retraining or altering the aggregation rule.
- The reported trend-alignment between IntrospecLOO and LOO suggests the approximation can be used to identify which agents help or hurt performance, for later team refinement.
Reading between the lines
- Because a single final-round instruction cannot undo influences an agent had on the reasoning of others in earlier rounds, the approximation is likely to capture final-round influence more than trajectory-shaping influence; this is an editorial inference, not a claim in the paper.
- The Figure 7 case study contradicts the approximation at the instance level (IntrospecLOO majority A vs. true LOO majority D), so the paper's claims of effectiveness should be read as average trend-level agreement rather than per-instance fidelity.
- One testable extension would be to use the per-agent IntrospecLOO deltas as a weighting or pruning signal in subsequent debates, turning the evaluation method into an online improvement mechanism.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes IntrospecLOO, a prompting method that appends an extra round to an LLM multi-agent debate in which each remaining agent is asked to disregard the response of a designated agent and update its answer. The authors claim this approximates the leave-one-out (LOO) approach for contribution evaluation while reducing token complexity from O(RT N^2) to O(RN) per evaluated agent. The paper presents a query-complexity analysis and experiments on GSM, MMLU, and Biography datasets, comparing accuracy and trend directions across various group sizes and agent-type ratios.
Significance. If the approximation were faithful, the paper would address a practically important cost bottleneck in LLM multi-agent systems: evaluating each agent's contribution by re-running full debates is expensive. The complexity analysis is a useful formalization, and the idea of using a single post-hoc introspection prompt is simple and appealing. However, the evidence presented does not establish that IntrospecLOO approximates LOO at the decision level. The paper lacks a direct per-instance agreement metric, its own case study shows a majority mismatch, and no statistical tests support the claimed closeness. As it stands, the central approximation claim is not validated, though the underlying complexity arithmetic is sound.
major comments (5)
- [Section III-A and Section IV-B] The paper never directly measures the agreement between IntrospecLOO and LOO at the instance or decision level. All reported comparisons are aggregate accuracy scores or differences of differences, such as the Bland-Altman plots in Figures 3 and 4, which compare Original-LOO against Original-IntrospecLOO. Two methods can have similar average deviations from Original while disagreeing on almost every individual debate. The authors should report a per-instance agreement rate, for example the fraction of questions where the IntrospecLOO majority answer equals the LOO majority answer, as well as agreement for each remaining agent's individual answer.
- [Section IV-B.4, Figures 6 and 7] The paper's own case study provides a direct counterexample to the approximation claim. In the LOO debate shown in Figure 6 (leaving David out), the final answers are D, A, D, yielding majority D. In the IntrospecLOO debate shown in Figure 7 (disregarding David), the final answers are D, A, A, yielding majority A. The authors do not acknowledge this mismatch. This counterexample must be discussed; at a minimum, the paper should quantify how frequently such decision-level flips occur across the evaluation set.
- [Section III-A] The introspective prompt asks agents to disregard the response from a designated agent after all debate rounds have already occurred. Since earlier rounds may have influenced the agents' reasoning and final answers, this prompt has no mechanism to undo the influence of the removed agent on the preceding rounds. The paper provides no theoretical or empirical argument that a single post-hoc adjustment is equivalent to counterfactually removing the agent from the entire debate. This is the central assumption of the method and needs to be justified or substantially qualified.
- [Section IV-B / Tables I-IV] No statistical significance tests are performed for the differences between IntrospecLOO and LOO. The tables report means and standard deviations over five seeds, but there are no paired comparisons across seeds, no confidence intervals on the differences, and no adjustment for multiple comparisons. The "trend match" criterion (blue highlighting) is qualitative and not defined with a threshold or a statistical test. The claim that "results are generally close" is therefore not supported by the reported evidence.
- [Section III-B] The complexity analysis is arithmetically correct for the incremental cost of evaluating one agent, but the paper should state clearly that the total cost of evaluating all N agents with IntrospecLOO is still O(RN^2) additional tokens (N extra rounds, each involving N-1 agents), not O(RN). The introduction claims "reduces the token complexity from O(RT N^2) to O(N)" without the factor R and without the per-agent qualifier. This is an overclaim that should be corrected, and the per-agent vs. all-agent distinction should be explicit throughout.
minor comments (5)
- [Introduction] The statement "reduces the token complexity from O(RT N^2) to O(N)" appears to be missing the factor R and the qualifier "per evaluated agent"; the correct expression derived in Eq. (3) is O(RN).
- [Section IV-B] The Bland-Altman plots in Figures 3-4 compare (Original-LOO) vs (Original-IntrospecLOO) differences rather than directly comparing LOO and IntrospecLOO outcomes. A more direct visualization, such as a scatterplot of per-instance majority answers or a confusion matrix, would be more informative for the approximation claim.
- [Section IV-A] The paper uses 200 randomly selected questions for GSM and MMLU and 100 for Biography, with five random seeds. These are relatively small sample sizes, and the paper should report the exact seeds or construct confidence intervals that account for both instance-level and seed-level variability.
- [Section IV-A.2] The designation of GPT-3.5-turbo agents as "high-performing" and Baichuan2-7B agents as "under-performing" is based on model family rather than verified task performance in the debate setting; a preliminary performance check would strengthen the setup and interpretation of the ratio experiments.
- [Notation] There are several typographical issues in mathematical expressions, including missing spaces and missing multiplication dots (e.g., "O(RT N2)toO(N)"). These should be corrected in a revision.
Circularity Check
No significant circularity: the approximation claim is an empirical hypothesis tested against an external LOO oracle; the complexity analysis is independent, and minor self-citations are not load-bearing.
full rationale
The paper's central claim is that the IntrospecLOO prompting scheme approximates the outcome of a full leave-one-out debate at lower token cost. This claim is not derived from the method's own assumptions in a circular way; it is an empirical hypothesis evaluated by comparing IntrospecLOO against an independently computed LOO baseline on three benchmarks. The complexity reduction in Section III-B is a self-contained counting argument over token usage, independent of experimental outcomes. No parameter is fitted to LOO data and then renamed as a prediction; the IntrospecLOO prompt is a fixed heuristic. The cited prior work from the same authors ([7], [10]) is used only as background for LOO in collaborative learning and does not justify the core approximation step. The paper's own case study (Figures 6-7) shows a discrepancy between LOO and IntrospecLOO outcomes, but this is a correctness/validity concern about the approximation's fidelity, not a circularity: the approximation is not made true by construction. Thus the derivation chain is not circular, and the score reflects only the presence of minor non-load-bearing self-citations.
Assumptions & free parameters
assumptions (3)
- domain assumption Asking an agent to disregard a named peer's responses in one final round is causally equivalent to that peer never having participated in the debate.
- domain assumption Majority voting over agent answers is the correct aggregation for debate outcomes.
- domain assumption GPT-3.5-turbo and Baichuan2-7B are representative of high- and low-performing agents.
Cite this review
Pith. "Pith review of Efficient Leave-one-out Approximation in LLM Multi-agent Debate Based on Introspection." pith.science (2026). https://pith.science/paper/MKC7WHXX
@misc{pith2026250522192,
author = {Pith},
title = {Pith review of: Efficient Leave-one-out Approximation in LLM Multi-agent Debate Based on Introspection},
year = {2026},
howpublished = {\url{https://pith.science/paper/MKC7WHXX}},
note = {Machine review of arXiv:2505.22192}
}
read the original abstract
Multi-agent systems based on large language models (LLMs) advance automatic task completion in various fields, where debate is a common cooperation form for agents to solve complicated problems with reasoning and cross-review to solidify answers. Assessing the individual contributions of agents within these debates is crucial for system refinement and outcome reliability. Traditional leave-one-out (LOO) method offers a clear framework for evaluating each agent's role but face challenges in LLM-based systems due to high computational costs and associated financial implications. This paper presents introspective-leave-one-out (IntrospecLOO), a simple yet effective prompting for approximation of LOO in LLM-powered multi-agent debates. IntrospecLOO introduces an additional querying round after standard debates, prompting agents to update their answers while ignoring responses from a designated agent. This strategy effectively isolates and gauges each participant's influence at a reduced query complexity compared to the original LOO approaches. Validation through experiments on three benchmark datasets confirms the effectiveness of IntrospecLOO.
Figures
Figures from the paper (3 more)
Forward citations
Cited by 2 Pith papers
-
Multi-Agent Debate Strategies: Survey, Taxonomy, and Challenges
A systematic review of 141 papers derives a three-axis taxonomy of multi-agent debate design (participants, interaction, agreement) and shows the field has converged on a narrow default pattern.
-
Branch-and-Browse: Efficient and Controllable Web Exploration with Tree-Structured Reasoning and Action Memory
Branch-and-Browse, a tree-structured web agent with page-level action memory, reports 35.8% success and up to 40.4% less time than the cited Tree Search baseline on WebArena.
Reference graph
Works this paper leans on
-
[1]
Improving factuality and reasoning in language models through multiagent debate,
Y . Du, S. Li, A. Torralba, J. B. Tenenbaum, and I. Mordatch, “Improving factuality and reasoning in language models through multiagent debate,” arXiv preprint arXiv:2305.14325, 2023
arXiv 2023
-
[2]
Autogen: Enabling next-gen llm applications via multi-agent conversation framework,
Q. Wu, G. Bansal, J. Zhang, Y . Wu, S. Zhang, E. Zhu, B. Li, L. Jiang, X. Zhang, and C. Wang, “Autogen: Enabling next-gen llm applications via multi-agent conversation framework,”arXiv preprint arXiv:2308.08155, 2023
arXiv 2023
-
[3]
J. Li, Q. Zhang, Y . Yu, Q. Fu, and D. Ye, “More agents is all you need,” arXiv preprint arXiv:2402.05120, 2024
arXiv 2024
-
[4]
Computational experiments meet large language model based agents: A survey and perspective,
Q. Ma, X. Xue, D. Zhou, X. Yu, D. Liu, X. Zhang, Z. Zhao, Y . Shen, P. Ji, J. Liet al., “Computational experiments meet large language model based agents: A survey and perspective,”arXiv preprint arXiv:2402.00262, 2024
arXiv 2024
-
[5]
The rise and potential of large language model based agents: A survey,
Z. Xi, W. Chen, X. Guo, W. He, Y . Ding, B. Hong, M. Zhang, J. Wang, S. Jin, E. Zhouet al., “The rise and potential of large language model based agents: A survey,”arXiv preprint arXiv:2309.07864, 2023
arXiv 2023
-
[6]
Dynamic llm-agent network: An llm-agent collaboration framework with agent team optimization,
Z. Liu, Y . Zhang, P. Li, Y . Liu, and D. Yang, “Dynamic llm-agent network: An llm-agent collaboration framework with agent team optimization,” arXiv preprint arXiv:2310.02170, 2023
arXiv 2023
-
[7]
A survey on contribution evaluation in vertical federated learning,
Y . Cui, C.-j. Huang, Y . Zhang, L. Wang, L. Fan, X. Zhou, and Q. Yang, “A survey on contribution evaluation in vertical federated learning,”arXiv preprint arXiv:2405.02364, 2024
arXiv 2024
-
[8]
Survey on contribution evaluation for federated learning,
Y . Wang, G. Li, and K. Li, “Survey on contribution evaluation for federated learning,”Journal of Software, vol. 34, no. 3, pp. 1168–1192, 2022
work page 2022
Show all 22 references
-
[9]
Incentive allocation in vertical federated learning based on bankruptcy problem,
A. Khan, M. t. Thij, F. Thuijsman, and A. Wilbik, “Incentive allocation in vertical federated learning based on bankruptcy problem,”arXiv preprint arXiv:2307.03515, 2023
2023 arXiv
-
[10]
A bargaining-based approach for feature trading in vertical federated learning,
Y . Cui, L. Yao, Z. Li, Y . Li, B. Ding, and X. Zhou, “A bargaining-based approach for feature trading in vertical federated learning,”arXiv preprint arXiv:2402.15247, 2024
2024 arXiv
-
[11]
Efficient participant contribution evaluation for horizontal and vertical federated learning,
J. Wang, L. Zhang, A. Li, X. You, and H. Cheng, “Efficient participant contribution evaluation for horizontal and vertical federated learning,” in 2022 IEEE 38th International Conference on Data Engineering (ICDE). IEEE, 2022, pp. 911–923
2022
-
[12]
Hierarchical federated learning incentivization for gas usage estimation,
H. Sun, X. Tang, C. Yang, Z. Yu, X. Wang, Q. Ding, Z. Li, and H. Yu, “Hierarchical federated learning incentivization for gas usage estimation,” arXiv preprint arXiv:2307.00233, 2023
2023 arXiv
-
[13]
Tradinggpt: Multi- agent system with layered memory and distinct characters for enhanced financial trading performance,
Y . Li, Y . Yu, H. Li, Z. Chen, and K. Khashanah, “Tradinggpt: Multi- agent system with layered memory and distinct characters for enhanced financial trading performance,”arXiv preprint arXiv:2309.03736, 2023
2023 arXiv
-
[14]
Medagents: Large language models as collaborators for zero-shot medical reasoning,
X. Tang, A. Zou, Z. Zhang, Y . Zhao, X. Zhang, A. Cohan, and M. Gerstein, “Medagents: Large language models as collaborators for zero-shot medical reasoning,”arXiv preprint arXiv:2311.10537, 2023
2023 arXiv
-
[15]
Chateval: Towards better llm-based evaluators through multi- agent debate,
C.-M. Chan, W. Chen, Y . Su, J. Yu, W. Xue, S. Zhang, J. Fu, and Z. Liu, “Chateval: Towards better llm-based evaluators through multi- agent debate,”arXiv preprint arXiv:2308.07201, 2023
2023 arXiv
-
[16]
Examining inter- consistency of large language models collaboration: An in-depth analysis via debate,
K. Xiong, X. Ding, Y . Cao, T. Liu, and B. Qin, “Examining inter- consistency of large language models collaboration: An in-depth analysis via debate,” inThe 2023 Conference on Empirical Methods in Natural Language Processing, 2023
2023
-
[17]
Camel: Communicative agents for
G. Li, H. A. A. K. Hammoud, H. Itani, D. Khizbullin, and B. Ghanem, “Camel: Communicative agents for” mind” exploration of large scale language model society,”arXiv preprint arXiv:2303.17760, 2023
2023 arXiv
-
[18]
Prompt valuation based on shapley values,
H. Liu, X. Mao, H. Xia, J. Lou, and J. Liu, “Prompt valuation based on shapley values,”arXiv preprint arXiv:2312.15395, 2023
2023 arXiv
-
[19]
Llm-blender: Ensembling large language models with pairwise ranking and generative fusion,
D. Jiang, X. Ren, and B. Y . Lin, “Llm-blender: Ensembling large language models with pairwise ranking and generative fusion,” inProceedings of the 61st Annual Meeting of the Association for Computational Linguistics (V olume 1: Long Papers), 2023, pp. 14 165–14 178
2023
-
[20]
Large language models are effective text rankers with pairwise ranking prompting,
Z. Qin, R. Jagerman, K. Hui, H. Zhuang, J. Wu, J. Shen, T. Liu, J. Liu, D. Metzler, X. Wanget al., “Large language models are effective text rankers with pairwise ranking prompting,”arXiv preprint arXiv:2306.17563, 2023. User: You are expert in everything and always give corre...
2023 arXiv
-
[22]
<copy other agents’ responses>
So, there are 70 ways to draw 4 balls in alternating colors. Since there are a total of 48 draws (4 draws x 12 balls), we can find the probability by dividing the number of ways to draw 4 balls in alternating colors by the total number of draws. Probability = 70 / 48 = 15 / 12...
-
[70]
<copy other agents’ responses>
So, there are 70 ways to draw 4 balls in alternating colors. Since there are a total of 48 draws (4 draws x 12 balls), we can find the probability by dividing the number of ways to draw 4 balls in alternating colors by the total number of draws. Probability = 70 / 48 = 15 / 12...
Reviewed August 7, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.