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

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.