Quantifying Divergence in Inter-LLM Communication Through API Retrieval and Ranking

Large language models (LLMs) increasingly operate as autonomous agents that reason over external APIs to perform complex tasks. However, their reliability and agreement remain poorly characterized. We present a unified benchmarking framework to quantify inter-LLM divergence, defined as the extent to which models differ in API discovery and ranking under identical tasks. Across 15 canonical API domains and 5 major model families, we measure pairwise and group-level agreement using set-, rank-, and consensus-based metrics including Average Overlap, Jaccard similarity, Rank-Biased Overlap, Kendall's tau, Kendall's W, and Cronbach's alpha. Results show moderate overall alignment (AO about 0.50, tau about 0.45) but strong domain dependence: structured tasks (Weather, Speech-to-Text) are stable, while open-ended tasks (Sentiment Analysis) exhibit substantially higher divergence. Volatility and consensus analyses reveal that coherence clusters around data-bound domains and degrades for abstract reasoning tasks. These insights enable reliability-aware orchestration in multi-agent systems, where consensus weighting can improve coordination among heterogeneous LLMs. Beyond performance benchmarking, our results reveal systematic failure modes in multi-agent LLM coordination, where apparent agreement can mask instability in action-relevant rankings. This hidden divergence poses a pre-deployment safety risk and motivates diagnostic benchmarks for early detection.