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

Summer Eunhyung Ann; Haokun Liu; Chenhao Tan

cs.MAAug 24, 2026

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

Authors: Summer Eunhyung Ann, Haokun Liu, Chenhao Tan

Organizations: Department of Computer Science, University of Chicago, Chicago, IL, USA.

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: The interaction tax on optimization tasks. Different model families (Claude, GPT-4o, Gemini) find structurally different solutions. When agents exchange full candidate solutions, their proposals converge and diversity is lost. When agents generate independently and the best is selected, diversity is preserved.

Figure 2: (a) Aggregate MEG for all ten configurations (95% CI, 9 tasks). MoA is the only configuration whose confidence interval includes zero. (b) MIG quadrant scatter (

x

-axis = same-model MIG,

y

-axis = diverse-model MIG). MAgICoRe, Chain, and Debate occupy the interaction tax zone (bottom-right quadrant), where full-solution interaction helps same-model agents but hurts once models are diverse. MoA escapes to the top-right because its proposers never see each other’s outputs.

Task	Claude	GPT-4o	Gemini	Winner
Circle Packing	$\mathbf{1.000}$	$0.519$	$0.745$	Claude
TSP-50	$\mathbf{0.141}$	—	$0.115$	Claude
Erdős	$0.131$	$\mathbf{0.710}$	$0.142$	GPT-4o
TSP-100	$0.013$	$\mathbf{0.021}$	$0.010$	GPT-4o
DiffBases	$0.209$	$0.264$	$\mathbf{0.610}$	Gemini
Flat Poly	$0.000$	$0.007$	$\mathbf{0.143}$	Gemini

Table 1: Best-of-

N

Q-scores per model on six tasks where scores diverge. Bold = best model. Each model family wins on different tasks.

Configuration	Same MIG	Div MIG	$P$
Chain	$+0.051$	$-0.024$	97%
MAgICoRe	$+0.044$	$-0.035$	99%
Debate	$+0.012$	$-0.078$	88%
HPE	$-0.163$	$-0.145$	38%
MoA	$+0.012$	$+0.016$	42%

Table 2: Mean MIG per configuration family (8 tasks).

P(\text{same}{>}\text{div})

: bootstrap probability that same-model MIG exceeds diverse MIG.

Task	Config	Same	Diverse	Direction
Knapsack-50	MAgICoRe	1/10	2/10	$\approx$
Knapsack-50	Debate	2/10	10/10	Div. helps
3AP-Free-100	MAgICoRe	6/10	3/10	Div. hurts
3AP-Free-100	Debate	6/10	0/10	Div. hurts

Table 3: Explicit feasibility rates on Knapsack and 3AP-Free (

n{=}10

per cell). On Knapsack (fault easy to locate), diverse models help. On 3AP-Free (fault hard to locate), diverse models hurt.

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

Task	MoA	SR	BoN	XCh	HCh	MAgI	VGS	Deb	SS	HPE
Circle Pack	$-0.24$	$-0.03$	$0.00$	$-0.03$	$0.00$	$0.00$	$0.00$	$-0.52$	$0.00$	$-1.00$
DiffBases	$+0.09$	$-0.11$	$0.00$	$-0.11$	$-0.20$	$-0.15$	$-0.13$	$+0.11$	$-0.20$	$-0.20$
Flat Poly	$+0.01$	$-0.06$	$-0.08$	$-0.08$	$-0.08$	$-0.08$	$0.00$	$-0.04$	$-0.08$	$-0.08$
TSP-100	$-0.02$	$-0.02$	$-0.01$	$-0.01$	$-0.02$	$-0.01$	$0.00$	$-0.02$	$-0.01$	$-0.02$
Erdős	$+0.02$	$0.00$	$-0.37$	$-0.13$	$-0.05$	$-0.15$	$-0.48$	$-0.33$	$-0.48$	$-0.48$
MolQED	$-0.01$	$-0.05$	$0.00$	$-0.10$	$-0.12$	$-0.14$	$-0.04$	$+0.02$	$-0.11$	$-0.24$

Appendix

Table 4: Per-task MEG for all ten configurations. MaxCut and LJ-

n{=}41

omitted (all configurations score zero on both tasks).

Task	Claude	GPT-4o	Gemini	Winner
Circle Packing	$\mathbf{1.000}$	$0.519$	$0.745$	Claude
TSP-50	$\mathbf{0.141}$	—	$0.115$	Claude
Erdős	$0.131$	$\mathbf{0.710}$	$0.142$	GPT-4o
TSP-100	$0.013$	$\mathbf{0.021}$	$0.010$	GPT-4o
DiffBases	$0.209$	$0.264$	$\mathbf{0.610}$	Gemini
Flat Poly	$0.000$	$0.007$	$\mathbf{0.143}$	Gemini

Appendix

Table 5: Per-backbone Best-of-

N

Q-scores on six tasks where backbone scores clearly diverge. Bold = best backbone. On Erdős, GPT-4o’s

Q{=}0.710

reflects a trivial constant (Section Y ); Gemini averages

Q{=}0.142

(4/5 seeds score

Q{=}0

, one seed matches GPT-4o).

Configuration	Aggregate $Q$	Min task $Q$
Diverse (Claude $+$ GPT-4o $+$ Gemini)	$0.349$	$>0$
GPT-4o $\times$ 3	$0.215$	$0.000$
Gemini $\times$ 3	$0.250$	$0.000$

Appendix

Table 6: MoA-no-synthesis aggregate

Q

-scores across nine optimization tasks (

n{=}10

per condition). The diverse team and GPT-4o

\times

3 have similar point estimates, but each same-model team catastrophically fails on at least one task (

Q{=}0.000

), while the diverse team never does.

Task type	Regress $0{\to}1$	Any regress	$n$
Constraint (2 tasks)	$\mathbf{0/30}$ (0%)	5/30 (17%)	30
Optimization (2 tasks)	17/30 (57%)	25/30 (83%)	30

Appendix

Table 7: First-round critique regression rate (MAgICoRe, Gemini backbone,

n{=}15

per task). Constraint = Knapsack-50, 3AP-Free-100. Optimization = Erdős, Flat Polynomials.

Task	BoN	Self-Ref	MAgICoRe	$p$
Knapsack-50	0%	13%	47%	$0.003$
3AP-Free-100	0%	7%	73%	${<}0.001$

Appendix

Table 8: Feasibility success rates on two constraint tasks (Gemini backbone,

n{=}15

each). Fisher exact

p

compares MAgICoRe to Best-of-

N

Configuration	Same MIG	Div MIG	$P$
Chain	$+0.051$	$-0.024$	97%
MAgICoRe	$+0.044$	$-0.035$	99%
Debate	$+0.012$	$-0.078$	88%
HPE	$-0.163$	$-0.145$	38%
MoA	$+0.012$	$+0.016$	42%

Appendix

Table 9: Mean MIG per configuration family (8 tasks).

P(\text{same}{>}\text{div})

: bootstrap probability that same-model MIG exceeds diverse MIG.

Term	Estimate	95% CI
Intercept (same $+$ selection)	$+0.182$	$[+0.123,\;+0.246]$
Diversity	$+0.188$	$[+0.073,\;+0.299]$
Synthesis	$-0.010$	$[-0.111,\;+0.094]$
Diversity $\times$ Synthesis	$+0.046$	$[-0.132,\;+0.226]$

Appendix

Table 10:

2{\times}2

factorial estimates (

N{=}120

, 10,000 task-stratified bootstrap). Diversity is the only factor whose CI excludes zero.

Task withheld	$\hat{\beta}_{\text{div}}$	95% CI	$p$
None ( $N{=}120$ )	$+0.188$	$[+0.073,\;+0.299]$	${<}0.001$
Erdős ( $n{=}80$ )	$+0.014$	$[-0.109,\;+0.139]$	$0.84$
DiffBases ( $n{=}80$ )	$+0.265$	$[+0.142,\;+0.381]$	${<}0.001$
MolQED ( $n{=}80$ )	$+0.286$	$[+0.125,\;+0.442]$	${<}0.001$

Appendix

Table 11: Leave-one-out sensitivity of the diversity main effect. Only removing Erdős drops the coefficient to near zero.

Figure 3: Per-round visible-score trajectories on two optimization tasks. (a) DiffBases: sequential interaction often improves at step 2 but loses that advantage by the final step. (b) Erdős: diverse interaction improves at round 2 then regresses at round 3 after agents exchange full outputs. (c) Erdős: diverse MoA-nosynth achieves broader coverage than same-backbone Best-of-

N

Configuration	Avg pairwise distance
MoA (no synthesis)	$0.315$
Best-of- $N$ (same model)	$0.312$
Debate	$0.309$
MoA (diverse $+$ synthesis)	$0.229$

Appendix

Table 12: Mean pairwise solution distance. After synthesis, diverse MoA distance (

0.315

) falls to

0.229

Task	$\rho$	Top-3 overlap	Top-1 inv?
MaxCut	$0.891$	2/3	Yes
Circle Packing	$1.000$	3/3	No
DiffBases	$0.806$	2/3	No
Flat Poly	$1.000$	3/3	No
TSP-100	$1.000$	3/3	No
LJ- $n{=}41$	$1.000$	3/3	No

Appendix

Table 13: Spearman rank correlation between visible and hidden configuration rankings per task (

n{=}10

configurations). Three tasks show

\rho<1

Family	Cfg	MCut	CPack	DBases	FPoly	TSP1	LJ41	Erdős	MolQ
MAgICoRe	homo	$0.00$	$0.00$	$+0.05$	$0.00$	$0.00$	$0.00$	$\mathbf{+0.33}$	$-0.03$
MAgICoRe	mixed	$0.00$	$0.00$	$-0.07$	$0.00$	$-0.01$	$0.00$	$\mathbf{-0.28}$	$+0.09$
Debate	homo	$0.00$	$-0.52$	$+0.31$	$+0.04$	$-0.01$	$0.00$	$+0.14$	$+0.13$
Debate	mixed	$0.00$	$-0.60$	$-0.14$	$+0.02$	$0.00$	$0.00$	$+0.14$	$-0.04$
Chain	homo	$0.00$	$0.00$	$0.00$	$0.00$	$-0.01$	$0.00$	$\mathbf{+0.43}$	$-0.01$
XChain	mixed	$0.00$	$-0.03$	$-0.06$	$-0.03$	$+0.01$	$0.00$	$\mathbf{-0.08}$	$+0.01$

Appendix

Table 14: MIG per task for five configuration families (eight optimization tasks). Bold marks Erdős sign flips. On tasks with no Q-score variance (MaxCut, LJ-n41), MIG is zero for all configurations.

Configuration	Role	Mechanism	Ref.
Single-Shot	Control	One model, one attempt, no iteration.	—
Best-of- $N$ ( $N{=}8$ )	Control	8 independent samples, return visible-best.	—
Self-Refine	Control	Same model generates, critiques, revises for 3 rounds.	Madaan et al., 2023
VGS	Control	Evolutionary loop (pop. 4, gen. 5, elite 2) with visible scores as fitness.	Romera-Paredes et al., 2024
Homo-Chain	Multi	4 same-model agents in sequence, each revises prior output. Visible-best returned.	This work
Cross-Chain	Multi	3-agent chain (Claude $\to$ GPT-4o $\to$ Gemini). Visible-best returned.	This work

Appendix

Table 15: Agent configurations. All operate under the same budget vector

(T{=}200\text{K},\,W{=}600\text{s},\,C{=}30\text{s},\,K{=}25)

. HPE = Hierarchical Planner-Executor. Two MoA ablations (same-model proposers, no synthesis) are used in the

2{\times}2

analysis.

Task	Improved	Copied	Degraded
Circle Packing	60%	40%	0%
Molecule QED	20%	80%	0%
Erdős	10%	80%	10%
Flat Polynomials	0%	100%	0%
TSP-100	0%	100%	0%
TSP-50	0%	90%	10%

Appendix

Table 16: Synthesis output classified relative to the best-scoring proposer. On five of seven tasks synthesis copies the best proposal

\geq

80% of the time. On Difference Bases it degrades 50% of the time.

Task	Config	Iter	BoN	$d$	$p$
Flat Poly	MAgI-G	2.087	1.899	$+1.25$	$0.002$
Flat Poly	SR-G	2.020	1.899	$+1.02$	$0.009$
TSP-100	MAgI-G	53,351	50,786	$+1.42$	$0.001$
TSP-100	SR-G	53,239	50,786	$+1.46$	$0.001$
TSP-50	MAgI-G	24,167	23,103	$+1.23$	$0.002$
MolQED	MAgI-G	0.863	0.859	$+0.05$	$0.93$

Appendix

Table 17: Within-backbone comparisons (Gemini,

n{=}15

per condition). Positive

d

= iterative configuration is worse.

Task	Domain	Type	Objective
Circle Packing	Geometry	Optimization	Maximize radius of $n$ non-overlapping circles in a unit square
Difference Bases	Combinatorics	Optimization	Find a set whose pairwise differences cover all residues mod $n$
Erdős Overlap	Analysis	Optimization	Minimize $\max_{t}\int\|f(x)f(x{+}t)\|\,dx$ over translates
Flat Polynomials	Algebra	Optimization	Minimize $\\|p\\|_{\infty}$ for a polynomial with $\pm 1$ coefficients
TSP-50 / TSP-100	Routing	Optimization	Minimize tour length for 50 or 100 cities
MaxCut	Graph theory	Optimization	Maximize cut value in a fixed graph

Appendix

Table 18: Benchmark tasks. Four optimization tasks are adapted from AlphaEvolve (Georgiev et al., 2025) with smaller parameterizations. Two constraint tasks test interaction under checkable violations.

Task	Same $+$ Sel	Same $+$ Syn	Div $+$ Sel	Div $+$ Syn	Div contr.	Syn contr.
DiffBases	$0.202$	$0.071$	$0.237$	$0.287$	$+0.126$	$-0.041$
Erdős	$0.031$	$0.071$	$0.568$	$0.497$	$+0.482$	$-0.016$
MolQED	$0.314$	$0.377$	$0.307$	$0.437$	$+0.026$	$+0.097$

Appendix

Table 19: Mean

Q

-scores for each arm of the

2{\times}2

diversity

\times

synthesis factorial, broken down by task (

n{=}10

per cell). The diversity contrast shows that Erdős drives the aggregate diversity coefficient, DiffBases contributes moderately, and MolQED contributes near zero. The synthesis contrast is near zero on all three tasks.

Synthesizer	$\hat{\beta}_{\text{div}}$	95% CI
Claude Sonnet 4	$+0.234$	$[+0.106,\;+0.355]$
GPT-4o	$+0.176$	$[+0.049,\;+0.303]$
Gemini 2.5 Flash	$+0.170$	$[+0.044,\;+0.298]$

Appendix

Table 20: Diversity coefficient under three synthesizer backbones. The coefficient remains positive and significant for all three synthesizers. The synthesis coefficient remains near zero regardless of which model synthesizes.

Task	Strategy type	Claude	GPT-4o	Gemini
Erdős	Trivial constant	0/10	5/5	5/5
	Binary/block pattern	4/10	0/5	0/5
	Smooth/cosine-based	2/10	0/5	0/5
	Mathematical reasoning	6/10	0/5	0/5
DiffBases	Sidon sets ( $B_{2}$ sets)	4/10	0/5	1/5
	Triangular numbers	1/10	5/5	1/5

Appendix

Table 21: Strategy frequency per backbone on Erdős and DiffBases, classified from rawOutput keywords across all single-shot seeds. Categories are non-exclusive keyword tags. GPT-4o outputs a trivial constant (

{\approx}0.005

) on 100% of Erdős runs. Gemini also produces near-trivial constants (all zeros, raw score

{\approx}0.503

). Only Claude generates structurally varied, non-trivial solutions. On DiffBases, GPT-4o uses triangular numbers on every run.

Task	$\sigma^{2}_{W}$	$\sigma^{2}_{B}$	$B/W$	Diversity useful?
Circle Packing	$0.017$	$0.253$	$15.2$	Yes
MolQED	$0.015$	$0.030$	$2.0$	Yes
Flat Poly	$0.054$	$0.070$	$1.3$	Marginal
Erdős	$0.050$	$0.061$	$1.2$	Marginal
TSP-100	$0.020$	$0.010$	$0.5$	No
MaxCut	$0.0001$	$0.00002$	$0.3$	No

Appendix

Table 22: Variance decomposition of single-shot

Q

-scores across three backbones (

n{=}5

seeds each). Between-model variance (

\sigma^{2}_{B}

) measures how different the model means are. Within-model variance (

\sigma^{2}_{W}

) measures per-seed noise. A

B/W

ratio above

1

indicates that models are more different from each other than from themselves, the prerequisite for backbone diversity to help. Two tasks clearly meet this criterion (

B/W\geq 2

) and two are marginal (

B/W\approx 1.2

–

1.3

). LJ-

n{=}41

and TSP-50 are omitted (LJ because all models score

Q{=}0

, TSP-50 for incomplete backbone coverage).

Task	Cl–GPT $\rho$	Cl–Gem $\rho$	GPT–Gem $\rho$	Error indep.
Erdős	$+0.18$	— (const)	— (const)	Yes
DiffBases	$+0.05$	$+0.12$	$+0.17$	Yes
MolQED	$-0.45$	$-0.20$	$-0.33$	Yes (anti-corr)
TSP-100	$+0.38$	$+0.50$	$+0.41$	No (correlated)

Appendix

Table 23: Spearman rank correlations of per-seed hidden scores between model pairs on four tasks with nonzero cross-model Q-score variance. Low or negative

\rho

indicates uncorrelated errors (diversity helps). Positive

\rho

indicates correlated errors (diversity adds less). Gemini is constant on Erdős (all seeds produce

Q{=}0.000

), precluding correlation.

Task	Backbone	MAgICoRe	Best-of- $N$	$d$	$p$
Flat Poly	Gemini	2.087	1.899	$+1.25$	$0.002$
Flat Poly	GPT-4o	2.951	2.251	$+1.30$	$0.001$
TSP-100	Gemini	53,351	50,786	$+1.42$	$0.001$
TSP-100	GPT-4o	53,529	50,128	$+2.64$	${<}0.001$

Appendix

Table 24: MAgICoRe vs. Best-of-

N

on two optimization tasks, two backbones (

n{=}15

each). The loss replicates on both tested backbones, with large effect sizes.

Task	S-Shot	BoN	VGS	MAgICoRe
Knapsack-50	7%	0%	27%	47%
3AP-Free-100	0%	0%	13%	73%

Appendix

Table 25: Constraint feasibility rates by configuration type (Gemini backbone,

n{=}15

). Critique outperforms evolution on both tasks.

Task	Configuration	Same	Diverse	Direction
Knapsack-50	MAgICoRe	1/10	2/10	$\approx$
Knapsack-50	Debate	2/10	10/10	Div. helps
3AP-Free-100	MAgICoRe	6/10	3/10	Div. hurts
3AP-Free-100	Debate	6/10	0/10	Div. hurts

Appendix

Table 26: Constraint feasibility rates by backbone condition (

n{=}10

per cell). On Knapsack (trivially checkable), diverse backbones help. On 3AP-Free (reasoning-required), diverse backbones hurt.

Task	Configuration	Step $1{\to}2$	Step $2{\to}3$	Pattern
DiffBases	Debate (same)	$0.950$	$0.891$	Slight conv.
	Debate (diverse)	$0.956$	$\mathbf{0.479}$	Collapse r3
	MAgICoRe (div.)	$0.953$	$0.815$	Convergence
Erdős	Debate (same)	$0.500$	—	Single change
	Cross-Chain	$0.128$	$0.199$	Low throughout
	MAgICoRe (div.)	$0.448$	$0.293$	Shrinking

Appendix

Table 27: Pairwise solution distance between consecutive steps within each run, averaged over seeds. On Debate diverse, distance drops sharply after agents exchange outputs (round 2

\to

3), confirming diversity collapse in real time. Metrics: Jaccard distance for DiffBases (discrete sets), cosine distance for Erdős (continuous arrays), Levenshtein distance for MolQED (SMILES strings).

Configuration	Task	Round 1	Round 2	Round 3
Debate (same)	DiffBases	436	132	66
Debate (diverse)	DiffBases	889	72	274
Debate (same)	Erdős	4.61	1.24	0.62
Debate (diverse)	Erdős	1.28	0.30	0.38

Appendix

Table 28: Per-round visible scores for same-model and diverse Debate on two tasks (lower is better for both, bold = best round). Same-model Debate improves monotonically. Diverse Debate reverses direction at round 3 after agents have exchanged their full outputs.

Task	Dir	Step 0	Step 1	Step 2	Trend	Note
TSP-100	$\downarrow$	$54{,}054$	$53{,}686$	$53{,}638$	Slight impr.	Still below BoN
Flat Poly	$\downarrow$	$2.290$	$2.297$	$2.345$	Degrading	Values, not struct.
Mol. QED	$\uparrow$	$0.731$	$\mathbf{0.830}$	$0.785$	Peak revert	Step 1 lost
Erdős	$\downarrow$	$0.699$	$0.504$	— ∗	Conv. trivial	12/15 $\to$ $0.250$

Appendix

Table 29: Mean devScore at each MAgICoRe step (step 0 = initial attempt, step 1 = after first critique, step 2 = after second critique), averaged over

n{=}15

seeds. Direction arrows indicate whether lower (

\downarrow

) or higher (

\uparrow

) is better. ∗ Only 2/15 Erdős seeds reach step 2.

Task	Diverse spread	Same spread	Ratio
Erdős	$0.448$	$0.207$	$2.2{\times}$
MolQED	$0.222$	$0.152$	$1.5{\times}$
DiffBases	$1500$	$3045$	$0.5{\times}$

Appendix

Table 30: Mean pairwise score spread among MoA proposers within each run, measuring how different the proposals are before synthesis. Diverse proposers produce

2.2{\times}

more score spread than same-model proposers on Erdős. On DiffBases, within-model variance dominates, so backbone diversity adds less spread.

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As multi-agent architectures and agent-to-agent protocols proliferate, a fundamental question arises: what actually happens when autonomous LLM agents interact at scale? We study this question empirically using data from Moltbook, an AI-agent-only social platform, with 800K posts, 3.5M comments, and 78K agent profiles. We combine lexical metrics (Jaccard specificity), embedding-based semantic similarity, and LLM-as-judge validation to characterize agent interaction quality. Our findings reveal agents produce diverse, well-formed text that creates the surface appearance of active discussion, but the substance is largely absent. Specifically, while most agents (

67.5\%

) vary their output across contexts,

65\%

of comments share no distinguishing content vocabulary with the post they appear under, and information gain from additional comments decays rapidly. LLM judge based metrics classify the dominant comment types as spam (

28\%

) and off-topic content (

22\%

). Embedding-based semantic analysis confirms that lexically generic comments are also semantically generic. Agents rarely engage in threaded conversation (

5\%

of comments), defaulting instead to independent top-level responses. We discuss implications for multi-agent interaction design, arguing that coordination mechanisms must be explicitly designed; without them, even large populations of capable agents produce parallel output rather than productive exchange.

Abstract

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