Multi-Agent Debate and Collaboration

> Du et al. (ICML 2024, "Society of Minds") run N model instances that independently propose answers, then iteratively critique each other over R rounds to converge. Improves factuality, rule-following, reasoning. Sparse topology beats full mesh on token cost.

Type: Learn + Build

Languages: Python (stdlib)

Prerequisites: Phase 14 · 12 (Workflow Patterns), Phase 14 · 05 (Self-Refine and CRITIC)

Time: ~60 minutes

Learning Objectives

• Explain the debate protocol: N proposers, R rounds, converge on a shared answer.
• Describe why debate improves factuality, rule-following, and reasoning.
• Explain sparse topology: not every debater needs to see every other.
• Implement a stdlib debate over a scripted LLM with full-mesh and sparse variants; measure token cost vs accuracy.

The Problem

Self-Refine (Lesson 05) is one model critiquing itself — risks groupthink. CRITIC (Lesson 05) grounds critique in external tools — not always available. Debate introduces a third mode: multiple instances, cross-critique, convergence by disagreement.

The Concept

Society of Minds (Du et al., ICML 2024)

• N model instances independently propose answers to the same question.
• Over R rounds, each model reads the others' proposals and critiques them.
• Models update their answers based on the critiques.
• After R rounds, return the convergent answer.

Original experiments used N=3, R=2 due to cost. Accuracy improves with more agents and more rounds on hard problems (MMLU, GSM8K, Chess Move Validity, biography generation).

Cross-model combinations beat single-model debates: ChatGPT + Bard together > either alone.

Sparse topology

"Improving Multi-Agent Debate with Sparse Communication Topology" (arXiv:2406.11776, 2024-2025) showed full-mesh debate is not always optimal. Sparse topologies (star, ring, hub-and-spoke) can match accuracy at lower token cost. Each debater sees only a subset of peers.

Implications:

• Full mesh N=5, R=3 = 5 × 3 = 15 proposals, each reading 4 peers = 60 critique ops.
• Star N=5, R=3 (one hub + 4 spokes) = 15 proposals, spokes read only the hub = 12 critique ops.

When debate helps

• Factuality. N independent proposals, cross-check reduces hallucination.
• Rule-following. Chess move validity — one model misses a rule, others catch it.
• Open-ended reasoning. Multiple framings narrow in on the right answer.

When debate hurts

• Latency-sensitive UX. N × R serial rounds is latency you may not have.
• Cost-sensitive scale. N × R tokens per question.
• Simple factual lookups. One lookup is cheaper than five debates.

2026 practical instantiations

• Anthropic orchestrator-workers (Lesson 12) — one variant of debate with a synthesis step.
• LangGraph supervisor (Lesson 13) — central router + specialist agents can implement debate as a node.
• OpenAI Agents SDK (Lesson 16) — agents handoff back and forth for iterative critique.
• Multi-agent evals — pair debate + evaluator-optimizer for eval signal.

Where this pattern goes wrong

• Convergence collapse. All agents converge on the first wrong answer. Mitigate with required disagreement rounds.
• Hub failure. In a star topology, a bad hub corrupts everyone. Rotate or use multiple hubs.
• Prompt homogenization. All agents use the same prompt; they produce the same answers. Use diverse prompts and/or models.

Build It

code/main.py implements stdlib debate:

• Debater class (scripted LLM with per-debater opinion drift).
• FullMeshDebate and SparseDebate runners.
• Three questions: one factual, one rule-based, one reasoning.
• Metrics: convergent answer, rounds to convergence, total critique ops.

Run it:

python3 code/main.py

Output: per-protocol accuracy and cost; sparse matches full mesh on 2/3 questions at lower cost.

Use It

• Anthropic orchestrator-workers for simple 2-3-worker debates.
• LangGraph for stateful multi-round debate with checkpointing.
• Custom for research or specialized correctness guarantees.

Ship It

outputs/skill-debate.md scaffolds a multi-agent debate with configurable topology, N, R, and a convergence rule.

Exercises

1. Implement a "forced disagreement" rule: in round 1, every debater must produce a distinct proposal. Measure effect on convergence speed.
2. Add a confidence-weighted aggregation: debaters return (answer, confidence); aggregator weights by confidence. Does it help?
3. Swap one "agent" for a different scripted LLM with different opinions. Does heterogeneity improve accuracy?
4. Measure token cost for full mesh vs sparse on your 3 questions. Plot cost vs accuracy.
5. Read the Society of Minds paper. Port your toy to N=5, R=3. What breaks? What gets better?

Key Terms

Further Reading

• Du et al., Society of Minds (arXiv:2305.14325) — canonical multi-agent debate
• Sparse Communication Topology (arXiv:2406.11776) — sparse topology results
• Anthropic, Building Effective Agents — orchestrator-workers as a debate variant
• Madaan et al., Self-Refine (arXiv:2303.17651) — single-model self-critique counterpart