Voting, Self-Consistency, and Debate Topology

The cheapest aggregation: sample N independent agents, majority-vote. Wang et al. 2022 self-consistency did this with one model sampled N times. Multi-agent extends it with **heterogeneous** agents to escape monoculture — different models, different prompts, different temperatures, different contexts. Beyond majority vote, debate topology matters: MultiAgentBench (arXiv:2503.01935, ACL 2025) evaluated star / chain / tree / graph coordination and found **graph best for research**, with a "coordination tax" past ~4 agents. AgentVerse (ICLR 2024) documents two emergent patterns — volunteer behaviors and conformity behaviors — and conformity is both a feature (finding consensus) and a risk (groupthink, Lesson 24). This lesson maps the topology space, builds each variant, and measures the coordination tax.

Learn + Build 1.3 hr Python (stdlib)

Prerequisites: Phase 16 · 07 (Society of Mind and Debate), Phase 16 · 14 (Consensus and BFT)

#Problem

Debate can improve accuracy (Du et al., arXiv:2305.14325). It can also degrade it. Whether debate helps depends on four structural choices:

Who talks to whom (topology).
How many rounds (Du 2023: both rounds and agents matter independently).
Whether agents are heterogeneous (different base models break monoculture).
Whether an adversarial voice is present (steel-manning vs. straw-manning).

Teams that bolt "run 5 agents and vote" onto a task often regress vs. a single agent. The failures are not random. They track topology and heterogeneity. This lesson is the topology map.

#Problem

Keep going. The rest of this lesson is one step away.