When Does Multi-Agent Collaboration Help? An Entropy Perspective

Multi-agent systems (MAS) have emerged as a prominent paradigm for leveraging large language models (LLMs) to tackle complex tasks. However, the mechanisms governing the effectiveness of MAS built upon publicly available LLMs, specifically the underlying rationales for their success or failure, remain largely unexplored. In this paper, we revisit MAS through the perspective of $\mathit{\text{entropy}}$, considering both intra- and inter-agent dynamics by investigating entropy transitions during problem-solving across various topologies, six reasoning benchmarks, and two agentic tasks. By analyzing 245 features spanning token-, agent-, and round-level entropy, we counterintuitively find that a single agent outperforms MAS in approximately 43.3% of cases, and that entropy dynamics are largely determined during the first round of interaction. Furthermore, we provide three key observations: 1) $\mathit{\text{Certainty}}\mathit{\text{Preference}}$: peak entropy directly harms and stable entropy directly benefits MAS correctness; 2) $\mathit{\text{Base}}\mathit{\text{Entropy}}$: base models with lower entropy during problem-solving causally drive MAS performance; and 3) $\mathit{\text{Task}}\mathit{\text{Awareness}}$: entropy dynamics of MAS play varying roles across different tasks. Building on these insights, we introduce a simple yet effective algorithm, the $\mathit{\text{Entropy}}\mathit{\text{Judger}}$, to select solutions from MAS’s pass@$k$ results, leading to consistent accuracy improvements across all MAS configurations and tasks. Our source code is available at \href{https://github.com/AgenticFinLab/multiagent-entropy}{this https URL}.