The Makeup of an Influencer: How Confidence Shapes Multi-Agent Debate

As LLM-based multi-agent systems are increasingly used for collective decision-making, who gains influence during deliberation is a central question to predict the outcome and ensure the emergence of a trustworthy consensus. Despite complex, non-linear interactions between agents, we find that the final vote is well captured by a mixture-of-experts model that linearly aggregates agents' initial beliefs. Remarkably, its router can be approximated by a graph neural network operating solely on initial beliefs. This representation enables us to characterize how influence is allocated during deliberation. We find that influence is shaped by agents' self-assessed confidence, confidence as perceived by others, and initial alignment with other agents' views. Our findings reveal a surprisingly simple structure underlying multi-agent deliberation, with implications for both the efficient design of multi-agent systems and their vulnerability to overconfident opinions.