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

arXiv:2604.22760v1 Announce Type: cross Abstract: 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.