Multi-agent debate improves decision quality through structured argumentation between LLM agents. Mechanism: Multiple agents take positions, present arguments, critique each other, refine positions through rounds, converge on conclusion. Debate formats: Point-counterpoint, panel discussion, adversarial critique, Socratic questioning. Roles: Proposer (suggests solutions), critic (finds flaws), synthesizer (combines insights), judge (evaluates arguments). Why it works: Different agents catch different errors, adversarial pressure improves quality, diverse perspectives emerge, explicit reasoning is more verifiable. Implementation: Multiple model instances with different system prompts, structured conversation protocol, judge selects final answer. Use cases: Complex decisions, fact-checking, brainstorming refinement, ethical analysis, red-teaming. Benchmarks: Improves accuracy on reasoning tasks, especially when models have complementary strengths. Variations: Society of mind architectures, role-playing simulations, competitive game theory scenarios. Trade-offs: Much higher computational cost, complex orchestration, may not converge on some topics. Powerful technique for high-stakes decisions requiring multiple perspectives.