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Dynamic Coordination Strategy Selection for Enterprise Multi-Agent Systems
Thanh Luong Tuan
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
Last extracted: 7/8/2026, 11:18:55 PM
Summary
The paper evaluates dynamic coordination strategy selection for enterprise multi-agent systems, comparing single-agent, consensus, debate, and synthesis across 30 tasks, five problem classes, and four model arms. It finds that while pre-registered exact-winner predictions fail, dynamic routing serves as a robust near-best heuristic (within 0.10 quality-score points of the optimal strategy). The study highlights that structured compliance verification (PC4) strongly favors single-agent execution over consensus, and finds no significant performance difference between Vietnamese and English domain tasks. The authors conclude that enterprise coordination should adopt dynamic routing as a calibrated default rather than a deterministic rule.
Entities (16)
Relation Signals (12)
PC4 → empiricalbeststrategy → single_agent
confidence 95% · all four model arms select single_agent as the exact best condition
PC1 → predictedstrategy → consensus
confidence 95% · pre-registered strategy mapping
PC2 → predictedstrategy → debate
confidence 95% · pre-registered strategy mapping
PC3 → predictedstrategy → synthesis
confidence 95% · pre-registered strategy mapping
PC4 → predictedstrategy → consensus
confidence 95% · pre-registered strategy mapping
PC5 → predictedstrategy → synthesis
confidence 95% · pre-registered strategy mapping
dynamic routing → conclusion → near-best heuristic
confidence 90% · dynamic strategy selection is a useful near-best heuristic
Sonnet rubric → judged → sonnet
confidence 90% · All 1,440 generated outputs are judged by a fixed Sonnet rubric
Sonnet rubric → judged → gemma_openrouter
confidence 90% · All 1,440 generated outputs are judged by a fixed Sonnet rubric
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Abstract
Abstract:Enterprise multi-agent systems increasingly expose multiple coordination patterns, but deployments often lack evidence for when to use consensus, debate, synthesis, or a simpler single-agent workflow. This paper evaluates whether coordination strategy should be selected dynamically by problem class rather than fixed globally. We run a frozen matrix of 30 enterprise tasks spanning six industries, five problem classes, four execution conditions, three replications per cell, and four model arms: qwen_local, sonnet, gemma_openrouter, and an auxiliary openai cloud-validation arm. All 1,440 generated outputs are judged by a fixed Sonnet rubric. The main finding is bounded and operationally useful, but it is not the original strict H1. The pre-registered exact-winner/CI criterion is not supported: exact winner identity is unstable across model arms, and several predicted strategies are close to, but not above, the best observed alternative. A weaker near-best routing claim is strongly supported. In every pre-registered model arm and problem class, and again in the auxiliary OpenAI validation arm, the predicted strategy is within 0.10 quality-score points of the best observed condition. Structured compliance verification is the clearest exception to the original mapping: all arms favor single_agent rather than consensus. A pre-registered Kendall's W test finds no reliable difference between Vietnamese-domain and English-domain tasks in how consistently the four coordination conditions are ranked (mean W of 0.20 in both strata; signed-rank p = .85), so H2 is not supported. We conclude that enterprise coordination policy should use dynamic routing as a calibrated default, not as a deterministic winner-selection law.
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- Source: https://arxiv.org/abs/2606.00804v2
- Canonical: https://arxiv.org/abs/2606.00804v2
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Dynamic Coordination Strategy Selection for Enterprise Multi-Agent Systems Thanh Luong Tuan Golden Gate University, San Francisco Foundation AgenticOS (FAOS) Corresponding author. Email: tluongtuan@my.ggu.edu. ORCID: 0009-0000-1199-837X (May 2026) Abstract Enterprise multi-agent systems increasingly expose multiple coordination patterns, but deployments often lack evidence for when to use consensus, debate, synthesis, or a simpler single-agent workflow. This paper evaluates whether coordination strategy should be selected dynamically by problem class rather than fixed globally. We run a frozen matrix of 30 enterprise tasks spanning six industries, five problem classes, four execution conditions, three replications per cell, and four model arms: qwen_local, sonnet, gemma_openrouter, and an auxiliary openai cloud-validation arm. All 1,440 generated outputs are judged by a fixed Sonnet rubric. The main finding is bounded and operationally useful, but it is not the original strict H1. The pre-registered exact-winner/CI criterion is not supported: exact winner identity is unstable across model arms, and several predicted strategies are close to, but not above, the best observed alternative. A weaker near-best routing claim is strongly supported. In every pre-registered model arm and problem class, and again in the auxiliary OpenAI validation arm, the predicted strategy is within 0.10 quality-score points of the best observed condition. Structured compliance verification is the clearest exception to the original mapping: all arms favor single_agent rather than consensus. A pre-registered Kendall’s W test finds no reliable difference between Vietnamese-domain and English-domain tasks in how consistently the four coordination conditions are ranked (mean W of 0.20 in both strata; signed-rank p=.85p=.85), so H2 is not supported. We conclude that enterprise coordination policy should use dynamic routing as a calibrated default, not as a deterministic winner-selection law. 1. Introduction Multi-agent language-model systems now include a wide range of coordination primitives, including role-based collaboration, debate, consensus, voting, and synthesis. Prior work has shown that these patterns can improve reasoning, software development, factuality, and deliberation in some settings, while also raising concerns about cost, evaluation rigor, and over-generalization [Guo et al., 2024, Tran et al., 2025, Du et al., 2024, Smit et al., 2024, Wu et al., 2024]. The enterprise deployment question is narrower than whether multi-agent systems can help in general. Operators need to know which coordination pattern should run for a concrete task class. Using the wrong coordination pattern can add latency, cost, verbosity, or integration error without improving the answer. This is especially relevant in regulated domains, multilingual settings, and workflow automation contexts where the desired output may be a checklist, a risk tradeoff, a creative design, or a clarifying question rather than a single factual answer. RA-1 studies this routing problem directly. The research question is: Does dynamic strategy selection, choosing among consensus, debate, synthesis, and single-agent execution by problem class, produce more reliable enterprise multi-agent decisions than a fixed global coordination strategy? We treat the answer as a policy-calibration problem, not as a blanket referendum on multi-agent systems. The study first tests whether a pre-registered mapping from problem class to coordination strategy predicts exact winners, then asks whether the same mapping remains operationally useful as a near-best routing heuristic. 2. Related Work Survey work on LLM-based multi-agent systems maps the growing design space of agent roles, communication mechanisms, collaboration protocols, and application settings [Guo et al., 2024, Chen et al., 2024a, Tran et al., 2025]. Framework papers such as AutoGen, MetaGPT, ChatDev, AgentVerse, and CAMEL demonstrate that role-structured interaction can be used to compose more complex workflows than a single prompt call [Wu et al., 2024, Hong et al., 2024, Qian et al., 2024, Chen et al., 2024b, Li et al., 2023]. MDAgents is the closest dynamic-strategy comparator because it adapts solo and group collaboration structures to medical task complexity [Kim et al., 2024]. Debate is one of the most studied coordination mechanisms. Multi-agent debate can improve some forms of reasoning and factuality [Du et al., 2024] and can encourage divergent thinking [Liang et al., 2024]. At the same time, recent critiques caution against treating debate as a universal solution and emphasize evaluation design, model heterogeneity, and cost-performance tradeoffs [Smit et al., 2024, Zhang et al., 2025]. This paper follows that caution: it compares debate against consensus, synthesis, and single-agent execution across enterprise task classes rather than assuming that debate should dominate. Other work on collective decision-making, mechanism design, negotiation, and multi-agent risk highlights that coordination mechanisms can change incentives, failure modes, and governance properties [Yang et al., 2024, Dütting et al., 2024, Hua et al., 2024, Hammond et al., 2025]. RA-1 contributes an enterprise-specific empirical matrix for strategy routing: it studies the interaction between task class, industry context, model arm, and coordination strategy. Because RA-1’s contribution is an evaluation design as much as a coordination mechanism, it also sits alongside the agent-benchmarking literature. AgentBench evaluates single LLM-as-agent performance across eight interactive environments [Liu et al., 2024], and MultiAgentBench extends evaluation to collaboration and competition among multiple agents [Zhu et al., 2025]. GPTSwarm reframes agent systems as optimizable graphs and tunes topology and routing automatically [Zhuge et al., 2024]. RA-1 differs from all three in measurement target: rather than ranking models or auto-optimizing topology, it holds the coordination primitives fixed and asks which primitive a deployment should select for a given problem class, under a fixed judge and a pre-registered prediction grid. The judge-validity and measurement questions these benchmarks raise, namely what is scored, by whom, and with what coupling between judge and generator, motivate the threats analysis in Section 7. 3. Methods 3.1 Design The completed RA-1 matrix contains 1,440 valid judged outputs. The confirmatory design uses three pre-registered model arms: Qwen local, Sonnet, and Gemma through OpenRouter. OpenAI was added as an auxiliary cloud-validation arm and is reported as robustness evidence rather than as part of the original confirmatory model set. Model arm Role in study Judged rows Expected rows Coverage qwen_local pre-registered secondary/open-weight arm 360 360 1.0000 sonnet pre-registered primary arm 360 360 1.0000 gemma_openrouter pre-registered tertiary arm 360 360 1.0000 openai auxiliary cloud-validation arm 360 360 1.0000 Total 1,440 1,440 1.0000 The experimental factors are: • Strategy condition: single_agent, consensus, debate, and synthesis. • Industry: six enterprise domains, including English and Vietnamese domain tasks. • Problem class: five pre-registered problem classes. • Replication: three replications per task-condition cell. • Model arm: Qwen local, Sonnet, Gemma through OpenRouter, and OpenAI as an auxiliary arm. The four strategy conditions operationalize common enterprise coordination choices. single_agent uses one agent with no coordination. consensus collects independent proposals and chooses a shared or majority recommendation. debate frames opposing positions and uses an arbiter. synthesis integrates multiple proposals into a combined output. 3.2 Problem Classes and Predictions The pre-registered strategy mapping was: Problem class Definition Predicted strategy PC1 High-uncertainty risk decision consensus PC2 Conflicting-objective tradeoff debate PC3 Novel design synthesis synthesis PC4 Structured compliance verification consensus PC5 Ambiguous-requirement clarification synthesis The original H1 scoring language expected predicted winners by problem class, with a strict winner/CI interpretation in the experimental design. We therefore report two readings separately: the pre-registered strict H1 and a weaker post-hoc operational tolerance-band reading. Under the tolerance-band reading, a predicted strategy is counted as a near-best hit when it is within 0.10 quality-score points of the best observed condition for that model and problem class. 3.3 Judging and Analysis All outputs were judged using a fixed Sonnet rubric. The analysis reports mean quality scores by model, problem class, and condition; strict exact-winner agreement; post-hoc H1 tolerance-band hits; the H2 Vietnamese-versus-English strategy-differentiation test via industry-language-stratified Kendall’s W; H3 cross-model winner agreement; and formal cell-level tests. The formal scaffold uses dependency-light tests over the completed judged matrix: • Friedman permutation tests for within-cell strategy effects. • Paired bootstrap confidence intervals for predicted strategy versus the best non-predicted strategy. • Exact signed-rank sign-flip enumeration for paired post-hoc comparisons, with Bonferroni adjustment where applicable. The paired unit is task by replication within a model/problem-class cell, and the omnibus family is the set of model-by-problem-class cells. Friedman p-values use deterministic within-block permutation with 5,000 repetitions at α=.05α=.05. Bootstrap intervals use paired resampling with 5,000 repetitions and are reported as predicted strategy minus the best non-predicted strategy. Pairwise p-values use exact signed-rank sign-flip enumeration with Bonferroni adjustment over the three non-predicted comparators where applicable. For H2, Kendall’s W (the coefficient of concordance over the four conditions) is computed per model arm within the Vietnamese and English industry strata through the identity W=χF2/(m(k−1))W=χ^2_F/(m(k-1)) applied to the same average-rank Friedman statistic; the Vietnamese-minus-English W difference is then tested across the pre-registered (model, problem-class) pairs with the exact signed-rank statistic. All permutation and bootstrap procedures use a fixed seed (20260527), so the reported intervals are reproducible. These tests calibrate the strength of the language used; they are not treated as proof that the predicted strategy is statistically superior in every cell. 4. Results 4.1 H1: Strict Exact-Winner Support Fails, but Near-Best Routing Holds Under the original strict exact-winner interpretation, H1 is not supported. The predicted strategy is not consistently the exact best condition, and the formal intervals do not support a blanket claim of predicted-strategy superiority. Under the post-hoc 0.10 tolerance-band rule, the mapping remains operationally strong. The predicted strategy is near-best in all pre-registered arms and in the auxiliary OpenAI arm (Δ = gap between best observed and predicted strategy; all Δ<0.10 <0.10): Model arm Role PC1 Δ PC2 Δ PC3 Δ PC4 Δ PC5 Δ Hits Gemma pre-registered 0.034 0.060 0.000 0.096 0.010 5/5 Qwen pre-registered 0.000 0.051 0.000 0.075 0.008 5/5 Sonnet pre-registered 0.011 0.023 0.000 0.063 0.004 5/5 OpenAI auxiliary 0.003 0.021 0.006 0.038 0.015 5/5 This supports the revised headline claim that dynamic strategy selection is a useful near-best heuristic. It does not support the stronger pre-registered claim that the predicted strategy is always the strict winner. 4.2 Formal Cell Results The formal tests preserve the same boundary. Friedman permutation tests detect strategy effects in 9 of 15 pre-registered model/problem-class cells (α=.05α=.05). In all pre-registered cells but one, the 95% bootstrap interval for the predicted strategy minus the best non-predicted strategy includes zero or favours the alternative; the single exception is Qwen PC3, where the predicted synthesis strategy exceeds the best non-predicted strategy by only 0.025 (95% CI [0.003, 0.048]), a margin far below the pre-registered 0.10 winner threshold. In no cell does the predicted strategy fall outside the 0.10 tolerance band. The correct interpretation is therefore that predicted strategies are consistently near-best, not consistently best. The full per-cell Friedman statistics, bootstrap intervals, and comparator deltas for all four arms are in Appendix D. 4.3 H2: The Pre-Registered Kendall’s W Test Does Not Support a Vietnamese–English Difference H2 predicted that Vietnamese-language industries would show larger strategy-effect spreads than English-language industries, with the pre-registered test specified as an industry-stratified Friedman comparison of Kendall’s W. Running that test on the completed matrix does not support H2. Averaged over the five problem classes, mean Kendall’s W is 0.204 in the Vietnamese stratum and 0.201 in the English stratum across the three pre-registered arms. The Vietnamese-minus-English W difference is positive in 8 of 15 pre-registered (model, problem-class) pairs, with a mean difference of 0.003 (signed-rank p=.85p=.85; bootstrap 95% CI [−0.069,0.070][-0.069,0.070]). The interval straddles zero, so the test provides no evidence that strategies differentiate more reliably in Vietnamese domains. Model arm Role Mean W (EN) Mean W (VI) ΔW W (VI −- EN) Gemma pre-registered 0.2779 0.1739 −0.1040-0.1040 Qwen pre-registered 0.2047 0.2294 0.02470.0247 Sonnet pre-registered 0.1207 0.2083 0.08760.0876 OpenAI auxiliary 0.0517 0.1094 0.05780.0578 The per-arm directions conflict. Sonnet and Qwen lean toward larger Vietnamese concordance, but Gemma reverses, with substantially higher concordance in the English stratum. That reversal also explains why an earlier descriptive metric was misleading. A raw spread of condition means (best minus worst) is larger for Vietnamese tasks in three arms, but spread measures the magnitude of mean gaps, not the consistency of the strategy ranking. Gemma carries the largest raw Vietnamese spread yet the lowest Vietnamese concordance, because its large gaps come with rankings that shuffle across tasks and replications. The pre-registered concordance test is the operative one, and it returns a null. The full stratified packet, including per-cell W and block counts, is reported in Appendix B. 4.4 H3: Exact Winner Identity Does Not Generalize Strict cross-model winner agreement is weak: Problem class Gemma Qwen Sonnet OpenAI auxiliary Agreement PC1 single_agent consensus single_agent debate mixed PC2 single_agent consensus consensus consensus mixed PC3 consensus synthesis synthesis consensus mixed PC4 single_agent single_agent single_agent single_agent unanimous PC5 consensus consensus consensus single_agent mixed H3 is not supported under exact winner identity. The model-stable claim is weaker: the pre-registered strategy is usually close to best, but the identity of the exact best condition varies. 5. Discussion 5.1 Dynamic Routing Is Useful, but Only as a Near-Best Heuristic The strongest RA-1 result is not that a hand-authored routing table perfectly predicts winners. The strict pre-registered exact-winner criterion fails. The useful result is that the routing table avoids large misses across the three pre-registered arms, with the auxiliary OpenAI arm showing the same near-best pattern. For enterprise deployment, this is still valuable. A near-best routing policy can reduce the risk of defaulting every task into the same coordination pattern while keeping policy complexity manageable. The practical policy is: use problem-class routing as a default, monitor exceptions, and allow confidence- or ambiguity-based escalation. 5.2 PC4 Is a Coordination-Harm Exception The clearest policy revision is PC4. Structured compliance verification was pre-registered as consensus-favored, but all four model arms select single_agent as the exact best condition: Model arm PC4 best condition single_agent consensus debate synthesis Gemma single_agent 0.9532 0.8571 0.9338 0.8171 OpenAI single_agent 0.8932 0.8551 0.8878 0.8154 Qwen single_agent 0.9196 0.8447 0.8499 0.7803 Sonnet single_agent 0.8624 0.7990 0.8237 0.8188 A systematic coding of every PC4 coordination-harm row confirms the mechanism. Across the 62 material coordination-harm rows (a coordination condition scoring at least 0.05 below the paired single-agent baseline), the judge flags incorrect regulatory or sanctions-list citations in all 62 (100%); it marks one or more required obligations wrong or missing in 32 (52%); and the coordination response runs at least 1.5 times the length of the paired single-agent answer in 23 (37%). The signature is consistent across model arms and across the consensus, debate, and synthesis conditions. Deterministic threshold checks leave little room for multi-agent diversity to add value, while aggregation reliably appends external sanctions machinery, broad anti-financing references, or penalty claims that the rubric scores as incorrect. The Vietnamese banking threshold task banking_vn_T6 carries the largest single drops, but the citation-overreach pattern is not confined to it. Named worst-gap rows with judge rationale are sampled in Appendix A, and the full per-row coding is in Appendix C. The revised policy is: Original class Original predicted default Empirical revision Routing implication PC4: structured compliance verification consensus single_agent exact-best in all four arms Use single-agent for deterministic checks; escalate only when rules conflict or confidence is low. 5.3 PC2 Should Split Into Adversarial Decisions and Balanced Postures PC2 also needs refinement. The original prediction favored debate for conflicting-objective tradeoffs. Debate remains within the H1 tolerance band, but it is not exact-best in any model arm: Model arm Best condition single_agent consensus debate synthesis Gemma single_agent 0.9181 0.9118 0.8579 0.8812 OpenAI consensus 0.9340 0.9458 0.9250 0.9410 Qwen consensus 0.8979 0.9229 0.8722 0.8993 Sonnet consensus 0.8778 0.8799 0.8567 0.8744 A systematic coding of the PC2 coordination-harm rows tells a softer story than PC4. The 33 material coordination-harm rows are small drops rather than collapses. Among the 25 scored on the four-metric rubric, Metric Accuracy is the weakest dimension in 23 (92%), with a mean Metric Accuracy of 0.71 against means of 0.93, 0.81, and 0.91 for terminology fidelity, reasoning coherence, and response stability. The coordination losses on PC2 therefore come from thinner quantitative guardrails, such as missing benchmarks, ratios, or target thresholds, rather than from incoherence or instability, and the magnitude is small enough that debate remains within the H1 tolerance band. This supports treating PC2 as two subtypes rather than declaring a single winner. The full per-row coding is in Appendix C. The revised policy is: Subtype Recommended default Trigger PC2-a: adversarial decision debate The task requires choosing between incompatible options or resolving a contested policy. PC2-b: balanced operating posture consensus or synthesis The task requires preserving multiple objectives with controls. 6. Implications for Practice For enterprise multi-agent orchestration, RA-1 supports a router with five defaults and two immediate edits: Task pattern Routing default after RA-1 High-uncertainty risk decision consensus, with model-specific monitoring Adversarial conflicting-objective decision debate Balanced conflicting-objective operating posture consensus or synthesis Novel design synthesis synthesis Structured compliance verification single_agent, escalate only on ambiguity or conflict Ambiguous-requirement clarification synthesis, with clarification-first guardrails The result also argues against a fixed global coordination policy. Coordination should be used when it changes the evidence, perspectives, or design space; it should be skipped when the task is a deterministic rule check. 7. Threats to Validity Fixed-Judge Bias All outputs were scored by a fixed Sonnet rubric. This improves consistency but may favor outputs that match Sonnet’s style, structure, or implicit preferences. Because Sonnet is also a generator arm, cross-model comparisons should be interpreted as measurements under a Sonnet-judge regime, not as model-independent ground truth. GPT-5.1 second-judge sensitivity study. To test whether the main findings depend on the Sonnet judge, we re-scored all 480 rep-1 outputs with an independent GPT-5.1 judge using the same RA-3 rubric prompts (only the scoring model changed). The Pearson correlation between Sonnet and GPT scores is r=0.40r=0.40 (n=480n=480), indicating moderate agreement. GPT is a more lenient judge overall (mean 0.953 vs. 0.893), but it discriminates well across score values (40 unique scores vs. 27 for Sonnet), so the moderate correlation reflects calibration offset rather than random disagreement. The two headline findings replicate under GPT scoring. First, PC4 single-agent dominance: in all three pre-registered arms, single_agent is the GPT-judge best condition, with the same rank ordering as under the Sonnet judge. Model arm GPT best SA Consensus Debate Synthesis Gemma single_agent 0.943 0.923 0.916 0.725 Qwen single_agent 0.943 0.782 0.815 0.817 Sonnet single_agent 0.929 0.683 0.857 0.834 OpenAI (auxiliary) consensus 0.945 1.000 0.838 0.982 The auxiliary OpenAI arm reverses—GPT judges its own outputs more favorably, a self-preference signal expected and limited to the auxiliary arm. Second, H1 near-best routing holds in 13 of 15 pre-registered (model, problem-class) pairs under GPT scoring, compared with 15 of 15 under the Sonnet judge. Both misses are PC4 cells (Qwen and Sonnet), where the pre-registered consensus default trails single-agent by 0.16 and 0.25 under the GPT judge—precisely the PC4 single-agent exception identified above, reinforced rather than contradicted by the second judge. These findings confirm that neither the PC4 exception nor the H1 near-best pattern is an artifact of Sonnet judge preference. Auxiliary OpenAI Arm OpenAI was added as an auxiliary cloud-validation arm after the original three-arm design. It is useful as a robustness check, but should be labelled auxiliary rather than pre-registered primary evidence. Task-Corpus Generalization The corpus spans six enterprise industries and five problem classes, but it remains a curated benchmark. The results should be interpreted as policy evidence for the selected enterprise task families, not as universal proof for all multi-agent workflows. Strategy Implementation The implemented strategies are concrete operationalizations of consensus, debate, and synthesis. Different prompts, agent counts, arbiters, or aggregation policies could change the exact winner identity. Formal-Test Scope The formal analysis uses a statistics scaffold implemented without external library dependencies, so it reproduces in any standard Python environment. It supports the near-best interpretation but should be expanded before final submission if the target venue expects a richer statistical model. 8. Conclusion Pre-registered exact-winner support for coordination strategy routing is not sustained by the RA-1 matrix. The predicted strategy is not the consistent best condition, and bootstrap intervals do not support blanket superiority claims. What the evidence does support is a bounded near-best routing heuristic: in every pre-registered (model, problem-class) pair, and again under an independent GPT-5.1 judge, the predicted strategy stays within 0.10 quality-score points of the observed best. Two refinements follow directly from the data. Structured compliance verification should default to single-agent execution rather than consensus—coordination adds citation overreach without adding answer quality in all four model arms. Conflicting-objective tasks should split by subtype: tasks requiring an adversarial verdict favour debate, while tasks requiring a balanced operating posture with quantitative guardrails favour consensus or synthesis. The broader claim is calibrated: problem-class routing is justified as a practical default, not as a deterministic winner-selection law. Future work should investigate routing thresholds that adapt the tolerance band to task confidence, and extend the corpus to additional regulatory domains where deterministic rule retrieval may interact with multi-agent aggregation in ways the current study cannot fully characterise. Appendix A. Sampled Response Evidence This appendix samples named worst-gap rows behind the PC4 and PC2 coordination-harm patterns and annotates the mechanism in the judge rationale. Systematic counts over all coordination-harm rows are in Appendix C. PC4: structured compliance verification. Task banking_vn_T6 concerns a VND 450 million cash deposit at a Vietnamese bank branch; the rubric requires the VND 400 million cash-transaction threshold, CTR filing, customer due diligence, source-of-funds documentation, sanctions screening, and a suspicious-transaction report within 48 hours. Representative worst rows, each against the paired single-agent baseline of 1.00: Arm Condition Rep Score Gemma synthesis 3 0.20 OpenAI consensus 3 0.40 Qwen synthesis 1 0.40 Sonnet consensus 1 0.40 The low score is not usually a missed threshold: these responses state that VND 450M exceeds the VND 400M trigger and identify the CTR and due-diligence obligations. The loss appears when coordination appends external sanctions lists, broad counter-financing references, or penalty claims that the rubric scores as incorrect—the citation-overreach mechanism quantified in Appendix C. The single-agent answers stay closer to the narrow compliance checklist. PC2: conflicting-objective tradeoff. In healthcare_RA1_PC2_01 (a CFO 20% agency-nurse spend cut against clinical warnings on falls, readmissions, and HCAHPS), Gemma debate rep 2 scores 0.475 against a 0.9125 single-agent baseline—the largest PC2 drop—and the judge flags missing required terms: staffing ratio, falls, readmission, HCAHPS, and acuity. In insurance_vn_RA1_PC2_01 (simpler bancassurance scripts against needs-analysis and cooling-off compliance), Qwen debate rep 2 scores 0.675, below both the single-agent (0.875) and synthesis (0.9125) conditions: it covers the vocabulary but lacks the metric framework and time-bounded monitoring the judge rewards. Unlike PC4, these losses come from thin metric coverage and over-compressed recommendations rather than citation overreach, supporting the PC2-a (adversarial decision) versus PC2-b (balanced operating posture) split. Appendix B. H2 Stratified Concordance Per-cell Kendall’s W (coefficient of concordance over the four coordination conditions) within the Vietnamese (VI: banking_vn, insurance_vn; n=6n=6 task–replication blocks per cell) and English (EN: fintech, insurance, healthcare, software; n=12n=12 blocks per cell) industry strata. ΔW W is VI minus EN. The OpenAI arm is auxiliary and is excluded from the pre-registered paired test. Model arm PC W (VI) W (EN) ΔW W Gemma PC1 0.1861 0.4021 -0.2160 Gemma PC2 0.4639 0.2271 0.2368 Gemma PC3 0.1222 0.3465 -0.2243 Gemma PC4 0.0361 0.1889 -0.1528 Gemma PC5 0.0611 0.2250 -0.1639 OpenAI (aux.) PC1 0.0194 0.0528 -0.0333 OpenAI (aux.) PC2 0.3028 0.0312 0.2715 OpenAI (aux.) PC3 0.1750 0.0472 0.1278 OpenAI (aux.) PC4 0.0139 0.0854 -0.0715 OpenAI (aux.) PC5 0.0361 0.0417 -0.0056 Qwen PC1 0.1750 0.1389 0.0361 Qwen PC2 0.2694 0.1340 0.1354 Qwen PC3 0.4750 0.4882 -0.0132 Qwen PC4 0.0750 0.0590 0.0160 Qwen PC5 0.1528 0.2035 -0.0507 Sonnet PC1 0.3667 0.1799 0.1868 Sonnet PC2 0.1306 0.1382 -0.0076 Sonnet PC3 0.2750 0.1715 0.1035 Sonnet PC4 0.1028 0.0340 0.0687 Sonnet PC5 0.1667 0.0799 0.0868 Pre-registered paired test (3 pre-registered arms × 5 problem classes, n=15n=15 pairs): ΔW W positive in 8 of 15 pairs; mean ΔW=0.003 W=0.003, median 0.0160.016; Wilcoxon signed-rank p=0.85p=0.85; bootstrap 95% CI [−0.069,0.070][-0.069,0.070]. Appendix C. Systematic Failure Coding Codebook (abbreviations used in the per-row tables below). • CO (citation_overreach): the response adds regulatory, sanctions-list, or statutory citations that the judge marks incorrect or unsupported. • RM (requirement_miss): one or more required obligations are stated wrongly or omitted. • VB (verbosity_bloat): the coordination response runs at least 1.5 times the length of the paired single-agent answer. • ML (metric_accuracy_loss): on the PC2 four-metric rubric, the Metric Accuracy submetric collapses relative to the single-agent baseline. A coordination-harm row is material when the coordination condition scores at least 0.05 below the paired single-agent baseline. PC4 (structured compliance verification): 62 material rows. citation_overreach 62 (100%); requirement_miss 32 (52%); verbosity_bloat (length ≥1.5×≥ 1.5×) 23 (37%). Per-arm material rows: Gemma 14, OpenAI 15, Qwen 17, Sonnet 16. Arm Task Cond. Rep Score Δ Labels Gemma fintech_T6 consensus 1 0.67 -0.33 CO, RM Gemma fintech_T6 consensus 2 0.67 -0.33 CO, VB Gemma fintech_T6 synthesis 2 0.56 -0.44 CO, VB Gemma insurance_T6 consensus 1 0.80 -0.20 CO Gemma insurance_T6 synthesis 1 0.75 -0.25 CO, RM, VB Gemma insurance_T6 synthesis 2 0.50 -0.17 CO, RM, VB Gemma healthcare_T6 debate 2 0.67 -0.33 CO Gemma healthcare_T6 synthesis 1 0.67 -0.33 CO, VB Gemma healthcare_T6 synthesis 2 0.67 -0.33 CO, VB Gemma banking_vn_T6 consensus 1 0.50 -0.50 CO Gemma banking_vn_T6 consensus 2 0.50 -0.50 CO Gemma banking_vn_T6 debate 1 0.40 -0.60 CO, RM Gemma fintech_T6 synthesis 3 0.67 -0.33 CO, VB Gemma banking_vn_T6 synthesis 3 0.20 -0.80 CO, RM, VB OpenAI insurance_T6 consensus 2 0.67 -0.08 CO, RM OpenAI insurance_T6 consensus 3 0.71 -0.29 CO, RM OpenAI banking_vn_T6 consensus 3 0.40 -0.60 CO OpenAI insurance_vn_T6 consensus 2 0.33 -0.42 CO OpenAI fintech_T6 debate 3 0.86 -0.14 CO OpenAI insurance_T6 debate 3 0.57 -0.43 CO, RM OpenAI healthcare_T6 debate 3 0.67 -0.33 CO, RM OpenAI insurance_vn_T6 debate 3 0.50 -0.25 CO OpenAI fintech_T6 synthesis 1 0.80 -0.20 CO, RM, VB OpenAI insurance_T6 synthesis 1 0.40 -0.27 CO, RM, VB OpenAI insurance_T6 synthesis 2 0.50 -0.25 CO, RM OpenAI insurance_T6 synthesis 3 0.57 -0.43 CO, RM OpenAI healthcare_T6 synthesis 2 0.67 -0.33 CO, VB OpenAI insurance_vn_T6 synthesis 2 0.50 -0.25 CO OpenAI insurance_vn_T6 synthesis 3 0.50 -0.25 CO, VB Qwen fintech_T6 consensus 1 0.57 -0.10 CO, RM, VB Qwen insurance_vn_T6 consensus 1 0.67 -0.33 CO Qwen fintech_T6 consensus 3 0.67 -0.33 CO, VB Qwen insurance_T6 consensus 2 0.60 -0.40 CO, RM Qwen insurance_T6 consensus 3 0.50 -0.30 CO, RM Qwen insurance_T6 debate 1 0.67 -0.13 CO, RM Qwen fintech_T6 debate 3 0.71 -0.29 CO Qwen insurance_T6 debate 3 0.50 -0.30 CO, RM Qwen insurance_vn_T6 debate 2 0.67 -0.33 CO Qwen insurance_vn_T6 debate 3 0.67 -0.33 CO Qwen insurance_T6 synthesis 1 0.75 -0.05 CO, RM, VB Qwen banking_vn_T6 synthesis 1 0.40 -0.60 CO, RM, VB Qwen insurance_vn_T6 synthesis 1 0.50 -0.50 CO, VB Qwen fintech_T6 synthesis 2 0.50 -0.07 CO, RM, VB Qwen fintech_T6 synthesis 3 0.40 -0.60 CO, RM, VB Qwen insurance_T6 synthesis 2 0.60 -0.40 CO, RM, VB Qwen insurance_T6 synthesis 3 0.50 -0.30 CO, RM Sonnet fintech_T6 consensus 3 0.33 -0.34 CO, RM Sonnet fintech_T6 debate 1 0.57 -0.06 CO Sonnet fintech_T6 debate 3 0.40 -0.27 CO, RM Sonnet insurance_T6 consensus 1 0.80 -0.20 CO Sonnet insurance_T6 debate 2 0.75 -0.25 CO, RM Sonnet insurance_T6 synthesis 1 0.80 -0.20 CO Sonnet healthcare_T6 debate 2 0.67 -0.33 CO Sonnet banking_vn_T6 consensus 1 0.40 -0.60 CO, RM Sonnet banking_vn_T6 consensus 2 0.50 -0.50 CO, RM Sonnet banking_vn_T6 consensus 3 0.50 -0.50 CO Sonnet banking_vn_T6 debate 3 0.40 -0.60 CO, RM Sonnet banking_vn_T6 synthesis 1 0.50 -0.50 CO, RM Sonnet banking_vn_T6 synthesis 2 0.50 -0.50 CO, VB Sonnet banking_vn_T6 synthesis 3 0.40 -0.60 CO, RM, VB Sonnet insurance_vn_T6 debate 1 0.50 -0.50 CO Sonnet insurance_vn_T6 synthesis 2 0.33 -0.34 CO, VB PC2 (conflicting-objective tradeoff): 33 material rows (25 scored on the four-metric rubric). Metric Accuracy is the weakest dimension in 23 of 25 (92%); mean submetric scores are TF 0.93, MA 0.71, RC 0.81, RS 0.91. Per-arm material rows: Gemma 17, OpenAI 3, Qwen 8, Sonnet 5. Arm Task Cond. Rep Score Δ Labels Gemma fintech_T9 debate 1 0.90 -0.10 — Gemma fintech_T9 debate 2 0.93 -0.07 — Gemma fintech_T9 debate 3 0.95 -0.05 — Gemma healthcare_RA1_PC2_01 debate 1 0.82 -0.05 — Gemma healthcare_RA1_PC2_01 debate 2 0.47 -0.44 ML Gemma healthcare_RA1_PC2_01 synthesis 1 0.82 -0.05 — Gemma healthcare_RA1_PC2_01 synthesis 2 0.82 -0.09 — Gemma banking_vn_RA1_PC2_01 consensus 1 0.82 -0.06 — Gemma banking_vn_RA1_PC2_01 debate 3 0.82 -0.09 — Gemma banking_vn_RA1_PC2_01 synthesis 1 0.82 -0.06 — Gemma banking_vn_RA1_PC2_01 synthesis 3 0.82 -0.09 — Gemma insurance_vn_RA1_PC2_01 debate 1 0.82 -0.09 — Gemma insurance_vn_RA1_PC2_01 synthesis 1 0.82 -0.09 — Gemma software_T3 synthesis 1 0.93 -0.07 VB Gemma software_T3 synthesis 2 0.91 -0.06 VB Gemma healthcare_RA1_PC2_01 debate 3 0.82 -0.09 — Gemma software_T3 synthesis 3 0.91 -0.06 VB OpenAI insurance_RA1_PC2_01 debate 1 0.82 -0.10 — OpenAI insurance_vn_RA1_PC2_01 debate 3 0.91 -0.06 — OpenAI insurance_RA1_PC2_01 synthesis 1 0.88 -0.05 — Qwen software_T3 consensus 1 0.93 -0.07 VB Qwen insurance_vn_RA1_PC2_01 debate 1 0.82 -0.05 — Qwen software_T3 debate 1 0.93 -0.07 — Qwen insurance_vn_RA1_PC2_01 debate 2 0.68 -0.20 ML, VB Qwen insurance_vn_RA1_PC2_01 debate 3 0.80 -0.07 — Qwen software_T3 debate 3 0.93 -0.07 VB Qwen software_T3 synthesis 1 0.93 -0.07 VB Qwen software_T3 synthesis 3 0.93 -0.07 VB Sonnet fintech_T9 consensus 3 0.90 -0.10 VB Sonnet fintech_T9 debate 1 0.90 -0.10 — Sonnet fintech_T9 debate 2 0.77 -0.13 — Sonnet fintech_T9 debate 3 0.90 -0.10 — Sonnet fintech_T9 synthesis 1 0.90 -0.10 VB Appendix D. Formal Cell Table Full per-cell formal results for all four model arms and five problem classes. Δ is the best observed mean minus the predicted-strategy mean. “CI” is the paired bootstrap 95% interval for the predicted strategy minus the best non-predicted strategy: a negative interval favours the alternative, and an interval excluding zero on the positive side favours the predicted strategy (the case at Qwen PC3). Friedman p uses within-block permutation (5,000 reps, seed 20260527). OpenAI is auxiliary. Model PC Predicted Best Δ Friedman p CI vs. best non-pred. Gemma PC1 consensus single_agent 0.0342 0.0002 -0.0342 [-0.0647, -0.0074] Gemma PC2 debate single_agent 0.0601 0.0004 -0.0601 [-0.1132, -0.0247] Gemma PC3 synthesis consensus 0.0000 0.0010 -0.0000 [-0.0201, 0.0194] Gemma PC4 consensus single_agent 0.0961 0.0348 -0.0961 [-0.1883, -0.0178] Gemma PC5 synthesis consensus 0.0104 0.0856 -0.0104 [-0.0306, 0.0090] OpenAI* PC1 consensus debate 0.0035 0.4577 -0.0035 [-0.0174, 0.0097] OpenAI* PC2 debate consensus 0.0208 0.0882 -0.0208 [-0.0375, -0.0056] OpenAI* PC3 synthesis consensus 0.0056 0.3355 -0.0056 [-0.0207, 0.0081] OpenAI* PC4 consensus single_agent 0.0381 0.2905 -0.0381 [-0.1360, 0.0478] OpenAI* PC5 synthesis single_agent 0.0153 0.2783 -0.0153 [-0.0312, -0.0007] Qwen PC1 consensus consensus 0.0000 0.0392 +0.0021 [-0.0247, 0.0253] Qwen PC2 debate consensus 0.0507 0.0018 -0.0507 [-0.0757, -0.0278] Qwen PC3 synthesis synthesis 0.0000 0.0004 +0.0247 [0.0029, 0.0485] Qwen PC4 consensus single_agent 0.0749 0.1826 -0.0749 [-0.1442, -0.0114] Qwen PC5 synthesis consensus 0.0076 0.3537 -0.0076 [-0.0174, 0.0021] Sonnet PC1 consensus single_agent 0.0110 0.0112 -0.0110 [-0.0382, 0.0143] Sonnet PC2 debate consensus 0.0232 0.3847 -0.0232 [-0.0450, -0.0035] Sonnet PC3 synthesis synthesis 0.0000 0.0054 +0.0110 [-0.0018, 0.0238] Sonnet PC4 consensus single_agent 0.0633 0.7834 -0.0633 [-0.1947, 0.0753] Sonnet PC5 synthesis consensus 0.0042 0.0632 -0.0042 [-0.0236, 0.0160] * auxiliary arm. References S. Chen, Y. Liu, W. Han, W. Zhang, and T. Liu (2024a) A survey on llm-based multi-agent system: recent advances and new frontiers in application. External Links: 2412.17481 Cited by: 2. Related Work. W. Chen, Y. Su, J. Zuo, C. Yang, C. Yuan, C. Chan, H. Yu, Y. Lu, Y. Hung, C. Qian, Y. Qin, X. Cong, R. Xie, Z. Liu, M. Sun, and J. Zhou (2024b) AgentVerse: facilitating multi-agent collaboration and exploring emergent behaviors. In International Conference on Learning Representations (ICLR), Note: arXiv:2308.10848 Cited by: 2. Related Work. Y. Du, S. Li, A. Torralba, J. B. Tenenbaum, and I. Mordatch (2024) Improving factuality and reasoning in language models through multiagent debate. In Proceedings of the 41st International Conference on Machine Learning (ICML), Note: arXiv:2305.14325 Cited by: 1. Introduction, 2. Related Work. P. Dütting, V. Mirrokni, R. Paes Leme, H. Xu, and S. Zuo (2024) Mechanism design for large language models. In Proceedings of the ACM Web Conference (W), Note: arXiv:2310.10826; W 2024 Best Paper Award Cited by: 2. Related Work. T. Guo, X. Chen, Y. Wang, R. Chang, S. Pei, N. V. Chawla, O. Wiest, and X. Zhang (2024) Large language model based multi-agents: a survey of progress and challenges. In Proceedings of the 33rd International Joint Conference on Artificial Intelligence (IJCAI), Note: arXiv:2402.01680 External Links: Document Cited by: 1. Introduction, 2. Related Work. L. Hammond, A. Chan, J. Clifton, J. Hoelscher-Obermaier, A. Khan, E. McLean, C. Smith, W. Barfuss, J. Foerster, T. Gavenčiak, T. A. Han, E. Hughes, V. Kovařík, J. Kulveit, J. Z. Leibo, et al. (2025) Multi-agent risks from advanced ai. Technical report Technical Report Technical Report #1, Cooperative AI Foundation. Note: arXiv:2502.14143 Cited by: 2. Related Work. S. Hong, M. Zhuge, J. Chen, X. Zheng, Y. Cheng, C. Zhang, J. Wang, Z. Wang, S. K. S. Yau, Z. Lin, L. Zhou, C. Ran, L. Xiao, C. Wu, and J. Schmidhuber (2024) MetaGPT: meta programming for a multi-agent collaborative framework. In International Conference on Learning Representations (ICLR), Note: arXiv:2308.00352; ICLR 2024 Oral Cited by: 2. Related Work. W. Hua, O. Liu, L. Li, A. Amayuelas, J. Chen, L. Jiang, M. Jin, L. Fan, F. Sun, W. Wang, X. Wang, and Y. Zhang (2024) Game-theoretic llm: agent workflow for negotiation games. External Links: 2411.05990 Cited by: 2. Related Work. Y. Kim, C. Park, H. Jeong, Y. S. Chan, X. Xu, D. McDuff, H. Lee, M. Ghassemi, C. Breazeal, and H. W. Park (2024) MDAgents: an adaptive collaboration of llms for medical decision-making. In Advances in Neural Information Processing Systems, Vol. 37. Note: arXiv:2404.15155 Cited by: 2. Related Work. G. Li, H. A. A. K. Hammoud, H. Itani, D. Khizbullin, and B. Ghanem (2023) CAMEL: communicative agents for "mind" exploration of large language model society. In Advances in Neural Information Processing Systems, Vol. 36. Note: arXiv:2303.17760 Cited by: 2. Related Work. T. Liang, Z. He, W. Jiao, X. Wang, Y. Wang, R. Wang, Y. Yang, S. Shi, and Z. Tu (2024) Encouraging divergent thinking in large language models through multi-agent debate. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing (EMNLP), p. 17889–17904. Note: arXiv:2305.19118 External Links: Document Cited by: 2. Related Work. X. Liu, H. Yu, H. Zhang, Y. Xu, X. Lei, H. Lai, Y. Gu, H. Ding, K. Men, K. Yang, S. Zhang, X. Deng, A. Zeng, Z. Du, C. Zhang, S. Shen, T. Zhang, Y. Su, H. Sun, M. Huang, Y. Dong, and J. Tang (2024) AgentBench: evaluating llms as agents. In International Conference on Learning Representations (ICLR), Note: arXiv:2308.03688 Cited by: 2. Related Work. C. Qian, W. Liu, H. Liu, N. Chen, Y. Dang, J. Li, C. Yang, W. Chen, Y. Su, X. Cong, J. Xu, D. Li, Z. Liu, and M. Sun (2024) ChatDev: communicative agents for software development. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (ACL), p. 15174–15186. Note: arXiv:2307.07924 External Links: Document Cited by: 2. Related Work. A. P. Smit, N. Grinsztajn, P. Duckworth, T. D. Barrett, and A. Pretorius (2024) Should we be going mad? a look at multi-agent debate strategies for llms. In Proceedings of the 41st International Conference on Machine Learning (ICML), Proceedings of Machine Learning Research, Vol. 235, p. 45883–45905. Note: arXiv:2311.17371 Cited by: 1. Introduction, 2. Related Work. K. Tran, D. Dao, M. Nguyen, Q. Pham, B. O’Sullivan, and H. D. Nguyen (2025) Multi-agent collaboration mechanisms: a survey of llms. External Links: 2501.06322 Cited by: 1. Introduction, 2. Related Work. Q. Wu, G. Bansal, J. Zhang, Y. Wu, B. Li, E. Zhu, L. Jiang, X. Zhang, S. Zhang, J. Liu, A. H. Awadallah, R. W. White, D. Burger, and C. Wang (2024) AutoGen: enabling next-gen llm applications via multi-agent conversation framework. In Proceedings of the Conference on Language Modeling (COLM), Note: arXiv:2308.08155; Best Paper, ICLR 2024 LLM Agents Workshop Cited by: 1. Introduction, 2. Related Work. J. C. Yang, D. Dailisan, M. Korecki, C. I. Hausladen, and D. Helbing (2024) LLM voting: human choices and ai collective decision-making. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society (AIES), Note: arXiv:2402.01766 External Links: Document Cited by: 2. Related Work. H. Zhang, Z. Cui, J. Chen, X. Wang, Q. Zhang, Z. Wang, D. Wu, and S. Hu (2025) Stop overvaluing multi-agent debate – we must rethink evaluation and embrace model heterogeneity. External Links: 2502.08788 Cited by: 2. Related Work. K. Zhu, H. Du, Z. Hong, X. Yang, S. Guo, Z. Wang, Z. Pang, Z. Li, M. Zhuge, et al. (2025) MultiAgentBench: evaluating the collaboration and competition of llm agents. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (ACL), Note: arXiv:2503.01935 Cited by: 2. Related Work. M. Zhuge, W. Wang, L. Kirsch, F. Faccio, D. Khizbullin, and J. Schmidhuber (2024) GPTSwarm: language agents as optimizable graphs. In Proceedings of the 41st International Conference on Machine Learning (ICML), Note: arXiv:2402.16823 Cited by: 2. Related Work.