Modeling and Solving Stable Matching under Probabilistic Preferences with Large Language Models

Large language models (LLMs) have recently demonstrated strong capabilities in understanding and simulating human decisions, suggesting a new way to use LLMs as tools to study social systems. We study two-sided-matching markets, such as dating and job matching. Classical matching models assume deterministic, strict preferences, which violate the real-world setting. We focus on stable matching under stochastic decision behavior and use LLMs to simulate human-like preferences and probabilistic choice patterns. Based on this, we introduce Expected Blocking Pairs (EBP), a continuous measure to quantify stability that generalizes the classic blocking pair notion. We further propose a Hybrid GS-LLM matching method that integrates the celebrated Gale-Shapley (GS) algorithm with probabilistic acceptance decisions. Experiments show that the proposed hybrid method outperforms classical baselines in terms of stability, suggesting that LLMs provide a principled tool for modeling human decisions and for improving robustness of matching under uncertainty.