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The Interaction Tax: When Communication Erases Diversity in Multi-Agent Teams

Summer Eunhyung Ann, Haokun Liu, Chenhao Tan

arXiv:2608.23541v1cs.MAcs.AI

TL;DR

Multi-agent systems rely on interaction to combine diverse solutions, but it remains unclear how exchanging complete candidate outputs affects that diversity. Across 11 verifier-scored optimization tasks under matched budgets, the paper finds that full-solution interaction is a weak default because solutions converge, while independent proposals preserve diverse gains.

  • Problem

    Multi-agent systems use interaction to combine diverse solutions, but diversity helps only if differences survive subsequent communication.

  • Method

    The study compares single-agent and multi-agent workflows from three model families across 11 verifier-scored optimization tasks under identical resource budgets.

  • Results

    Full-solution interaction causes solutions to converge within one round, while MoA is the only configuration whose diverse-model MIG remains positive.

  • Takeaways & Limitations

    Multi-agent performance depends more on what information agents exchange and when it is exposed than on the number of agents.

  • Takeaways & Limitations

    The findings may not transfer unchanged beyond verifier-scored optimization problems, and the study does not test which lower-bandwidth information channel is best.

Abstract

from arXiv · show

Does multi-agent LLM interaction help or hurt? Some work reports gains from debate (Du et al., 2024), critique loops (Chen et al., 2025), and mixture-of-agents synthesis (Wang et al., 2025), while other work finds that interaction adds cost without improving quality under equal budgets (Tran & Kiela, 2026; Xu et al., 2026; Jarrett et al., 2025), or that independent sampling already captures multi-agent gains (Li et al., 2024). We argue this contradiction partly reflects a missing distinction, because not all multi-agent communication is equal. Different model families find structurally different solutions, but when agents read each other's complete outputs, their proposals converge within one round, erasing the diversity that motivates using multiple models. We call this the interaction tax. We test 11 verifier-scored optimization tasks under matched budgets and find that full-solution interaction is a weak default. Independent proposal generation avoids this collapse. Full-solution interaction mainly makes agents stay close to the first solution they see instead of trying different approaches, and critique helps only if the violated rule is easy for the LLM to find and fix. These results suggest that multi-agent performance depends less on the number of agents than on the information they exchange, and interaction helps only when agents share the right information at the right time.

1. Introduction

The introduction argues that multi-agent interaction can erase the model diversity that motivates using multiple agents. Across 11 verifier-scored optimization tasks, full-solution interaction is a weak default, while independent generation and targeted critique can preserve or recover useful differences.

  • Motivation: Different models can find structurally different optimization solutions, so diversity helps teams cover more of the solution space.Claude, GPT-4o, and Gemini each achieve the best score on at least one task, while each same-model team scores zero on at least one task.
  • Study design: The study evaluates multi-agent interaction on 11 verifier-scored optimization tasks using deterministic scalar scores for candidate solutions.Each agent outputs a candidate solution, and a deterministic verifier returns a scalar score.
  • Alternatives to full-solution exchange: Independent candidate generation before synthesis avoids the collapse by preserving diversity until selection or synthesis.MoA is identified as an example, and selecting the best independently generated candidate preserves diversity.
  • Alternatives to full-solution exchange: Critique helps when agents can locate and repair the exposed fault, but it is less reliable when the fault is difficult to find.The introduction contrasts Knapsack, where critique can help, with 3AP-Free, where the fault is harder to locate.
  • Interaction tax: Full-solution exchange makes agents’ later proposals more similar after one round, erasing useful differences especially in diverse-model teams.The authors call this loss the interaction tax; it can help same-model teams that begin with similar solutions.

2. Related Work

Prior work reports both benefits and losses from multi-agent interaction, while evolutionary methods preserve diversity without agent communication. Ensemble theory explains why convergence can reduce diversity and frames the interaction tax as a structural instance of this effect.

  • Single vs. multi-agent comparisons: Prior studies report gains from debate, solver-reviewer-refiner loops, and mixture-of-agents synthesis, alongside multi-agent losses under various conditions.The cited gains concern factuality, math accuracy, and language benchmarks; the cited losses arise under conditions examined by Tran and Kiela, Xu et al., Li et al., and Jarrett et al.
  • Evolutionary approaches: Evolutionary LLM approaches preserve population diversity through selection pressure rather than agent interaction, sidestepping the convergence mechanism studied here.Examples include FunSearch, Evolution through Large Models, and AlphaEvolve for mathematical discovery.
  • Ensemble diversity theory: Ensemble theory decomposes ensemble error into mean member error minus a diversity term, implying that communication-driven convergence shrinks diversity toward zero.The paper characterizes the interaction tax as a structural instance of this effect.

3. Methods

The study compares ten multi-agent and single-agent configurations under identical resource budgets, using visible evaluators for search and hidden evaluators for final assessment. It distinguishes graded-feedback from hard-validity tasks and evaluates gains relative to independent generation and single-agent baselines.

  • Setup: Each workflow runs under identical resource budgets, uses a visible dev evaluator during search, and undergoes one final evaluation by a hidden evaluator.The hidden evaluator is stricter, more complete, or robustness-shifted than the visible evaluator.
  • Configurations: The benchmark tests ten configurations built from Claude Sonnet 4, GPT-4o, and Gemini 2.5 Flash, including four single-agent baselines and multi-agent workflows.The single-agent baselines are Single-Shot, Best-of-N sampling, Self-Refine, and Verifier-Guided Search; multi-agent workflows include Chain, MAgICoRe, and Debate.
  • Interaction analysis: MAgICoRe, Chain, and Debate fall in the interaction-tax zone, where full-solution interaction helps same-model agents but hurts when models are diverse.MoA avoids this zone because its proposers never see one another’s outputs.
  • Task and scoring structure: Graded-feedback tasks provide meaningful scores for most well-formed answers, whereas hard-validity tasks require structural-rule satisfaction before scores become meaningful.Raw scores are normalized to Q ∈[0, 1]; the main benchmark uses five seeds per cell, while the 2×2 factorial uses ten seeds on three tasks.
  • Metrics: Positive MEG indicates outperforming every single-agent baseline, while positive MIG indicates improvement over independent generation.Because the diverse parallel baseline benefits from coverage, negative diverse MIG is considered a conservative finding.

4. Results

Diverse teams improve task coverage and performance under controlled selection, but full-solution interaction erases that diversity within one round and can reduce gains. Critique reverses this tax only when shared information identifies a concrete, repairable fault.

  • Diversity creates coverage: Diverse proposers never score zero across tasks, while every same-model team has at least one task with Q=0.The Claude + GPT-4o + Gemini team has aggregate Q comparable to the best same-model team.
  • Controlled diversity advantage: +0.188 diversity coefficient (CI [+0.073, +0.299], p<0.001) in a 2×2 factorial experiment, while the synthesis coefficient is near zero.The experiment crossed same versus diverse proposers with MoA synthesis versus best-score selection on three tasks, using N=120 and task-stratified bootstrap.
  • The interaction tax: −0.024, −0.035, and −0.078 diverse-model MIG for Chain, MAgICoRe, and Debate respectively, versus positive same-model MIG.Bootstrap P(same>div) is at least 88%; MoA’s MIG instead rises from +0.012 to +0.016, implicating full-solution interaction.
  • How convergence happens: Mean pairwise solution-representation distance falls from 0.315 before interaction to 0.229 after one round of full-output exchange.On Erd˝os, diverse Debate reaches a strong intermediate score at round 2 but regresses at round 3 after agents read full solutions.
  • Critique helps only when the fault is easy to locate: Critique reverses the interaction tax when faults are concrete and repairable, but the first critique round degrades graded-feedback solutions 57% of the time (17/30 runs).In Knapsack-50, critics can repair capacity violations by removing or swapping overweight items; graded-feedback critique more often provides general guidance.

5. Discussion and Conclusion … C. Quickstart Reproduction

The paper concludes that full-solution interaction often erases proposal diversity, motivating independent generation, selective low-bandwidth coordination, and critique only for locally verifiable violations. It presents a reproducible optimization workflow while noting task-dependent limitations and implementation requirements.

  • 5. Discussion and Conclusion: Full-solution interaction destroys diversity because agents’ solutions converge within one round, whereas MoA preserves positive diverse MIG by hiding proposers’ outputs.The conclusion identifies independent proposal generation as the configuration that avoids interaction-driven collapse.
  • 5. Discussion and Conclusion: Multi-agent performance depends more on exchanged information and exposure timing than agent count; scores, method descriptions, and failure causes may preserve exploration while enabling coordination.Full candidate solutions create strong convergence, while lower-bandwidth signals are proposed as a way to coordinate without exposing complete solutions.
  • 5. Discussion and Conclusion: The findings are limited by task dependence, small seed counts, feasibility analysis on two hard-validity tasks, and uncertain transfer beyond verifier-scored optimization.Removing Erdős reduces the diversity coefficient to +0.014 with a confidence interval crossing zero; the main benchmark uses five seeds per condition, while the diversity factorial uses ten seeds on three tasks.
  • A. Workflow Recipe: The practical contribution is a reusable workflow for AI-assisted math, CS, and ML optimization.The workflow is framed around performance and correctness gains rather than universal time savings.
  • A. Workflow Recipe: The workflow uses 2–3 diverse model families, independent candidate generation, deterministic ranking, conditional critique-and-revision, and stricter held-out verification.Interaction is skipped when violations are not local and checkable; otherwise critique passes are permitted after independent generation.
  • A. Workflow Recipe: +0.188 backbone diversity appears in the 2×2 factorial, while critique raises feasibility from 0% to 47–73% only on verifiable constraint tasks.The backbone-diversity result is driven by the Erdős task, so the reported gain is not presented as task-independent.
  • B. Reproducibility and Verification: The artifact supports inspectable and rerunnable verification through exact prompts, pinned models, deterministic evaluators, saved traces, and scripts reproducing tables and figures.Cached results allow inspection without rerunning API calls, while ordinary API access supports rerunning the workflow within a few hours.

D. Minimal End-to-End Example · E. Artifact Contents

A minimal Molecule QED example shows the synthesizer selecting the strongest independent proposal from interpretable structures and score gaps, while fixed high-scoring outputs can erase diversity. The repository includes the task data, configurations, run traces, analysis scripts, and offline reproduction tools.

  • D. Minimal End-to-End Example: Three proposers independently generate Molecule QED candidates, after which the synthesizer receives all three outputs and their development scores.The example uses seed 1, with higher QED considered better.
  • D. Minimal End-to-End Example: The synthesizer’s reasoning compares molecular structures and attributes lower QED to suboptimal LogP or molecular weight and insufficient structural complexity.It identifies Agent 1’s methoxybenzene–pyrimidine molecule as synthetically accessible and structurally suitable.
  • D. Minimal End-to-End Example: 0.8279 is Agent 1’s cited QED score, which the synthesizer treats as excellent when selecting the final molecule.The passage describes the selected molecule as synthetically accessible.
  • D. Minimal End-to-End Example: The final output repeats Agent 1’s SMILES and records devScore = 0.828 and hiddenScore = 0.738.The synthesizer correctly identifies the best proposal using its interpretable structure and large score gap.
  • D. Minimal End-to-End Example: 0.83 ≫0.55 illustrates the score gap that supports synthesis selecting one proposal over the others.On tasks where a backbone produces a fixed high-scoring constant, synthesis always converges to that constant and erases other proposals’ diversity.
  • E. Artifact Contents: The repository contains all 11 task instances with embedded development and hidden evaluators, plus verbatim prompt templates for all 10 configurations.It also provides pinned model identifiers for the experiments.
  • E. Artifact Contents: The artifact includes 1,556 saved JSON run traces containing raw model outputs, development scores, and hidden scores.These traces support reproducing the recorded experimental runs.
  • E. Artifact Contents: Python analysis scripts reproduce every table and figure, while an offline runner re-executes any cell from scratch.Together, these tools provide the repository’s stated reproduction workflow.

F. Full Per-Task MEG … M. Convergence Mechanism

The paper reports per-task and per-backbone comparisons, checks capability and critique confounds, analyzes diversity effects and sensitivity, and identifies full-output exchange as the point where diversity collapses. Across these analyses, the results emphasize that interaction outcomes depend on task, backbone, configuration family, and exchanged information.

  • F. Full Per-Task MEG: Table 4 reports per-task MEG for all ten configurations, omitting MaxCut and LJ-n=41 because every configuration scores zero.
  • G. Per-Backbone Coverage: Backbone coverage is evaluated using Best-of-N Q-scores on six tasks where backbone scores clearly diverge.On Erd˝os, GPT-4o’s Q=0.710 reflects a trivial constant, while Gemini averages Q=0.142 across seeds.
  • H. Capability Confound Check: MoA-no-synthesis comparisons show similar point estimates for diverse teams and GPT-4o×3, but every same-model team catastrophically fails on at least one task.Each same-model team has Q=0.000 on at least one task, whereas the diverse team never does.
  • I. Critique Regression Rates: First-round critique regression rates are measured on four tasks using the Gemini backbone, separating constraint from optimization tasks.The constraint tasks are Knapsack-50 and 3AP-Free-100; the optimization tasks are Erd˝os and Flat Polynomials.
  • I. Critique Regression Rates: Feasibility success rates compare MAgICoRe with Best-of-N on two constraint tasks, with significance assessed using Fisher exact p-values.
  • J. MIG per Configuration Family: Mean MIG is compared across configuration families on eight tasks, while a 2×2 factorial analysis tests diversity and other factors.The factorial analysis uses N=120 and 10,000 task-stratified bootstrap samples; diversity is the only factor whose CI excludes zero.
  • L. Leave-One-Out Sensitivity: Leave-one-out sensitivity shows that removing Erd˝os is the only exclusion that reduces the diversity main-effect coefficient to near zero.
  • M. Convergence Mechanism: On Erd˝os, diverse Debate improves at round 2 through critique exchange but collapses at round 3 when agents read full solutions.The damage occurs at full-output exchange rather than gradually; on DiffBases, sequential interaction often improves at step 2 but loses its advantage by the final step.

N. Diversity Collapse … S. Within-Backbone Comparisons (n=15)

Across the reported analyses, diverse multi-agent synthesis reduces solution diversity, while configuration comparisons examine rank agreement, MIG, shared budgets, synthesis behavior, and within-backbone effects. The evidence centers on how information exchange and synthesis shape multi-agent optimization outcomes.

  • N. Diversity Collapse: 0.315 falls to 0.229 after synthesis, indicating that diverse-proposer MoA loses mean pairwise solution distance.The reported comparison is MoA distance without synthesis versus MoA with diverse proposers and synthesis.
  • O. Visible–Hidden Rank Agreement: Visible and hidden configuration rankings were compared using Spearman rank correlation across 10 configurations per task, with three tasks showing ρ < 1.The table caption reports the rank-agreement analysis and its scope.
  • P. Per-Task MIG Breakdown: MIG was reported per task for five configuration families across eight optimization tasks, and was zero for all configurations on MaxCut and LJ-n41 because Q-score variance was absent.Bold marks Erdős sign flips in the reported breakdown.
  • Q. Agent Configurations: All configurations used the same budget vector: T=200K, W=600s, C=30s, and K=25.The configurations included HPE and two MoA ablations: same-model proposers and no synthesis.
  • Q. Agent Configurations: Proposer calls used temperature 0.7, while critique and synthesis calls used 0.3–0.5 consistently across backbones.The temperature settings were held constant by call type and backbone.
  • Q. Agent Configurations: Synthesis copied the best-scoring proposer ≥80% of the time on five of seven tasks but degraded performance 50% of the time on Difference Bases.The table classifies synthesis output relative to the best-scoring proposer.
  • S. Within-Backbone Comparisons (n=15): Within-backbone comparisons evaluated Gemini with n=15 per condition, where positive d indicates that the iterative configuration was worse.The table defines the direction of the reported effect size.

T. Task Descriptions · U. Representative Prompt Templates

The paper evaluates multi-agent interaction on benchmark optimization and constraint tasks, while representative prompts standardize proposer and reviewer roles across configurations. The main experimental distinction is orchestration: whether agents see prior outputs and whether critique is used.

  • T. Task Descriptions: The benchmark includes four smaller-parameterized AlphaEvolve optimization tasks and two constraint tasks designed to test interaction under checkable violations.The benchmark task suite is described as containing these adapted optimization and constraint categories.
  • T. Task Descriptions: MaxCut and LJ-n=41 are omitted from most analyses because every configuration scores Q=0 under the available budget.Their uniform scores provide no signal for comparing configurations.
  • U. Representative Prompt Templates: The proposer prompt directs a mathematical optimization agent to return only executable Python code printing the solution as a JSON object.This prompt structure is used in MoA, Best-of-N, and Single-Shot configurations.
  • U. Representative Prompt Templates: The proposer’s user message supplies the objective, parameters, constraints, input data, and evaluation-function specification, followed by a single-code-block output requirement.These elements define the task input and expected response format.
  • U. Representative Prompt Templates: The reviewer prompt asks a mathematical reviewer to assess correctness and identify specific errors, constraint violations, or improvements.This prompt is used in MAgICoRe and Debate configurations.
  • U. Representative Prompt Templates: Reviewers receive the objective and proposed solution alongside its visible score, then provide numbered issues and concrete improvement suggestions.The visible score and solution code are included in the reviewer’s user message.
  • U. Representative Prompt Templates: The proposer prompt remains identical across configurations; only orchestration differs, while critique, synthesis, planning, and execution prompts are configuration-specific.All prompts are included verbatim in the release artifact, whose representative templates illustrate two prompt structures.

V. Example Multi-Agent Exchange

The Cross-Chain example shows sequential interaction converging on GPT-4o’s degenerate constant, which is genuinely best-scoring on Erdős but erases strategy diversity. Independent generation preserves the other models’ distinct proposals while still selecting the same best score.

  • Sequential interaction: Claude first proposes a structured sparse function using binary patterns, with a dev score of 0.500.Claude reasons about minimizing overlap with translates.
  • Sequential interaction: GPT-4o then outputs the trivial constant f = 0.5, achieving a dev score of 0.250 after seeing Claude’s solution.GPT-4o defaults to near-constant functions regardless of input context, with Q=0.710, the best single backbone on Erdős.
  • Sequential interaction: Gemini produces another structured binary pattern with a dev score of 0.694, but visible-best selection chooses GPT-4o’s 0.250 output.On Erdős, lower raw scores are better; after Q-normalization, higher Q is always better.
  • Diversity collapse: GPT-4o’s constant has Q=0.710 but contributes zero strategy diversity because every GPT-4o seed produces the identical output.When GPT-4o appears in the chain, Claude’s and Gemini’s non-trivial solutions are discarded in favor of the degenerate constant.
  • Independent generation: Under independent generation, the three models produce raw scores of 2.47 (Q=0), 0.34 (Q=0.710), and 0.50 (Q=0), selecting 0.34 (Q=0.710) as best.Independent generation preserves multiple candidate outputs instead of forcing later agents toward the first visible solution.

W. Per-Task 2×2 Cell Means … AM. Extended Prompt Templates

Across per-task, backbone, and trajectory analyses, diversity helps only when models explore genuinely different solution regions, while full-solution interaction or synthesis can erase that diversity and sometimes degrade performance. The implementation uses matched budgets and prompts that explicitly aggregate, debate, critique, or divide work into complementary subtasks.

  • W. Per-Task 2×2 Cell Means: Erdős contributes +0.482 to the diversity contrast, versus +0.126 for DiffBases and +0.026 for MolQED, while synthesis is near zero or slightly negative across tasks.Removing Erdős reduces the aggregate diversity coefficient from +0.188 to +0.014.
  • X. Cross-Synthesizer Replication: All three synthesizer backbones yield a positive, significant diversity coefficient, while the synthesis coefficient remains near zero regardless of synthesizer.This indicates the null synthesis effect is not attributable to one unusually weak or strong synthesizer.
  • Y. Model Strategy Classification: On Erdős, GPT-4o and Gemini repeat stereotyped outputs across seeds, so a nominal three-backbone ensemble has effectively one non-trivial contributor; on DiffBases, GPT-4o uses triangular numbers on every run.Interaction can therefore discard structurally different Claude or Gemini solutions in favor of GPT-4o’s fixed Erdős constant, which scores Q=0.710.
  • Z. Within-Model vs. Between-Model Variance; AA. Inter-Model Error Correlation: Diversity is most informative when between-model variance dominates within-model noise, with two tasks meeting B/W ≥2 and two marginal at B/W ≈1.2–1.3.When B/W < 1, another backbone contributes no more than resampling the same model; low or negative inter-model error correlation is likewise associated with diversity helping.
  • AB. Cross-Backbone Replication; AC. Constraint Feasibility Gradient: The optimization loss pattern replicates on Gemini and GPT-4o, while critique-based configurations outperform evolutionary search on both tested tasks.Within Gemini, Single-Shot beats Best-of-N on Knapsack, 7% vs. 0%; diverse backbones help Knapsack but hurt 3AP-Free-100.
  • AF. Step-Level Solution Distance; AG. Per-Round Debate Scores: Diverse Debate peaks at round 2 after critique exchange, then regresses at round 3 after full-output exchange, whereas same-model Debate improves monotonically.Consecutive-step solution distance also drops sharply after diverse agents exchange outputs, confirming real-time diversity collapse.
  • AH. MAgICoRe Step-by-Step Trajectories; AI. Proposer Score Spread; AK. Additional Transcript Examples: MAgICoRe critique frequently degrades optimization solutions: Molecule QED peaks at step 1 (+13.5%), while 12 of 15 Erdős seeds converge to the trivial constant with raw score 0.250 (Q=0.710).Independent MoA proposals on Erdős remain diverse, with 2.2× greater score spread than same-model proposals; synthesis can erase that diversity.
  • AE. Formal Metric Definitions; AJ. Relation to Open-Ended Agent Systems; AL. Protocol Implementation Details; AM. Extended Prompt Templates: The protocol uses matched budgets and pinned backbones, with independent MoA proposers, neutral Debate synthesis, critique-and-refinement MAgICoRe roles, and HPE prompts requiring genuinely complementary executor foci.The extended templates instruct aggregators and synthesizers to return only valid JSON, while HPE explicitly forbids every executor from attempting the whole problem.
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