The Interaction Tax: When Communication Erases Diversity in Multi-Agent Teams
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
| Task | Claude | GPT-4o | Gemini | Winner |
|---|---|---|---|---|
| Circle Packing | Claude | |||
| TSP-50 | — | Claude | ||
| Erdős | GPT-4o | |||
| TSP-100 | GPT-4o | |||
| DiffBases | Gemini | |||
| Flat Poly | Gemini |
| Configuration | Same MIG | Div MIG | |
|---|---|---|---|
| Chain | 97% | ||
| MAgICoRe | 99% | ||
| Debate | 88% | ||
| HPE | 38% | ||
| MoA | 42% |
| Task | Config | Same | Diverse | Direction |
|---|---|---|---|---|
| Knapsack-50 | MAgICoRe | 1/10 | 2/10 | |
| Debate | 2/10 | 10/10 | Div. helps | |
| 3AP-Free-100 | MAgICoRe | 6/10 | 3/10 | Div. hurts |
| Debate | 6/10 | 0/10 | Div. hurts |
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 | ||||||||||
| DiffBases | ||||||||||
| Flat Poly | ||||||||||
| TSP-100 | ||||||||||
| Erdős | ||||||||||
| MolQED |
| Task | Claude | GPT-4o | Gemini | Winner |
|---|---|---|---|---|
| Circle Packing | Claude | |||
| TSP-50 | — | Claude | ||
| Erdős | GPT-4o | |||
| TSP-100 | GPT-4o | |||
| DiffBases | Gemini | |||
| Flat Poly | Gemini |
| Configuration | Aggregate | Min task |
|---|---|---|
| Diverse (Claude GPT-4o Gemini) | ||
| GPT-4o 3 | ||
| Gemini 3 |
| Task type | Regress | Any regress | |
|---|---|---|---|
| Constraint (2 tasks) | (0%) | 5/30 (17%) | 30 |
| Optimization (2 tasks) | 17/30 (57%) | 25/30 (83%) | 30 |
| Task | BoN | Self-Ref | MAgICoRe | |
|---|---|---|---|---|
| Knapsack-50 | 0% | 13% | 47% | |
| 3AP-Free-100 | 0% | 7% | 73% |
| Configuration | Same MIG | Div MIG | |
|---|---|---|---|
| Chain | 97% | ||
| MAgICoRe | 99% | ||
| Debate | 88% | ||
| HPE | 38% | ||
| MoA | 42% |
| Term | Estimate | 95% CI |
|---|---|---|
| Intercept (same selection) | ||
| Diversity | ||
| Synthesis | ||
| Diversity Synthesis |
| Task withheld | 95% CI | ||
|---|---|---|---|
| None ( ) | |||
| Erdős ( ) | |||
| DiffBases ( ) | |||
| MolQED ( ) |
| Configuration | Avg pairwise distance |
|---|---|
| MoA (no synthesis) | |
| Best-of- (same model) | |
| Debate | |
| MoA (diverse synthesis) |
| Task | Top-3 overlap | Top-1 inv? | |
|---|---|---|---|
| MaxCut | 2/3 | Yes | |
| Circle Packing | 3/3 | No | |
| DiffBases | 2/3 | No | |
| Flat Poly | 3/3 | No | |
| TSP-100 | 3/3 | No | |
| LJ- | 3/3 | No |
| Family | Cfg | MCut | CPack | DBases | FPoly | TSP1 | LJ41 | Erdős | MolQ |
|---|---|---|---|---|---|---|---|---|---|
| MAgICoRe | homo | ||||||||
| MAgICoRe | mixed | ||||||||
| Debate | homo | ||||||||
| Debate | mixed | ||||||||
| Chain | homo | ||||||||
| XChain | mixed |
| Configuration | Role | Mechanism | Ref. |
| Single-Shot | Control | One model, one attempt, no iteration. | — |
| Best-of- ( ) | 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 GPT-4o Gemini). Visible-best returned. | This work |
| 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% |
| Task | Config | Iter | BoN | ||
|---|---|---|---|---|---|
| Flat Poly | MAgI-G | 2.087 | 1.899 | ||
| Flat Poly | SR-G | 2.020 | 1.899 | ||
| TSP-100 | MAgI-G | 53,351 | 50,786 | ||
| TSP-100 | SR-G | 53,239 | 50,786 | ||
| TSP-50 | MAgI-G | 24,167 | 23,103 | ||
| MolQED | MAgI-G | 0.863 | 0.859 |
| Task | Domain | Type | Objective |
|---|---|---|---|
| Circle Packing | Geometry | Optimization | Maximize radius of non-overlapping circles in a unit square |
| Difference Bases | Combinatorics | Optimization | Find a set whose pairwise differences cover all residues mod |
| Erdős Overlap | Analysis | Optimization | Minimize over translates |
| Flat Polynomials | Algebra | Optimization | Minimize for a polynomial with 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 |
| Task | Same Sel | Same Syn | Div Sel | Div Syn | Div contr. | Syn contr. |
|---|---|---|---|---|---|---|
| DiffBases | ||||||
| Erdős | ||||||
| MolQED |
| Synthesizer | 95% CI | |
|---|---|---|
| Claude Sonnet 4 | ||
| GPT-4o | ||
| Gemini 2.5 Flash |
| 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 ( sets) | 4/10 | 0/5 | 1/5 |
| Triangular numbers | 1/10 | 5/5 | 1/5 |
| Task | Diversity useful? | |||
|---|---|---|---|---|
| Circle Packing | Yes | |||
| MolQED | Yes | |||
| Flat Poly | Marginal | |||
| Erdős | Marginal | |||
| TSP-100 | No | |||
| MaxCut | No |
| Task | Cl–GPT | Cl–Gem | GPT–Gem | Error indep. |
|---|---|---|---|---|
| Erdős | — (const) | — (const) | Yes | |
| DiffBases | Yes | |||
| MolQED | Yes (anti-corr) | |||
| TSP-100 | No (correlated) |
| Task | Backbone | MAgICoRe | Best-of- | ||
|---|---|---|---|---|---|
| Flat Poly | Gemini | 2.087 | 1.899 | ||
| Flat Poly | GPT-4o | 2.951 | 2.251 | ||
| TSP-100 | Gemini | 53,351 | 50,786 | ||
| TSP-100 | GPT-4o | 53,529 | 50,128 |
| Task | S-Shot | BoN | VGS | MAgICoRe |
|---|---|---|---|---|
| Knapsack-50 | 7% | 0% | 27% | 47% |
| 3AP-Free-100 | 0% | 0% | 13% | 73% |
| Task | Configuration | Same | Diverse | Direction |
|---|---|---|---|---|
| Knapsack-50 | MAgICoRe | 1/10 | 2/10 | |
| Debate | 2/10 | 10/10 | Div. helps | |
| 3AP-Free-100 | MAgICoRe | 6/10 | 3/10 | Div. hurts |
| Debate | 6/10 | 0/10 | Div. hurts |
| Task | Configuration | Step | Step | Pattern |
|---|---|---|---|---|
| DiffBases | Debate (same) | Slight conv. | ||
| Debate (diverse) | Collapse r3 | |||
| MAgICoRe (div.) | Convergence | |||
| Erdős | Debate (same) | — | Single change | |
| Cross-Chain | Low throughout | |||
| MAgICoRe (div.) | Shrinking |
| 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 |
| Task | Dir | Step 0 | Step 1 | Step 2 | Trend | Note |
|---|---|---|---|---|---|---|
| TSP-100 | Slight impr. | Still below BoN | ||||
| Flat Poly | Degrading | Values, not struct. | ||||
| Mol. QED | Peak revert | Step 1 lost | ||||
| Erdős | — ∗ | Conv. trivial | 12/15 |
| Task | Diverse spread | Same spread | Ratio |
|---|---|---|---|
| Erdős | |||
| MolQED | |||
| DiffBases |