EVINCE: Optimizing Multi-LLM Dialogues Using Conditional Statistics and Information Theory

Abstract

EVINCE (Entropy and Variation IN Conditional Exchanges) is a novel framework for optimizing multi-LLM dialogues using conditional statistics and information theory. It addresses limitations in multi-agent debate (MAS) frameworks, where multiple LLMs chat without behavior modulation or mutual information quality assessment. Using dual entropy optimization to balance perspective diversity and prior knowledge, EVINCE provides quantitative tools to dynamically regulate LLM linguistic behaviors. When mutual information is low and both cross-entropy and Wasserstein distance are high, EVINCE promotes contentious dialogues to expose diverse perspectives and uncover inconsistencies. Conversely, as cross-entropy decreases and mutual information stabilizes, it transitions discussions into a conciliatory phase, encouraging compromise and acknowledgment of valid points. Using information-theoretic metrics and optimizing mutual information, EVINCE emerges as a structured and highly effective framework for multi-LLM collaboration.

Version 5, September 2026. Versions 1-4 presented the entropy-duality principle as a theorem of optimal pairing; Section 2.4 and Appendix C state what the underlying inequalities establish and what they do not, and the empirical claims are rescoped accordingly. The two case studies are unchanged