Beyond Matching Stability: Solution Selection in Large Language Models

Matching problems can have several stable matchings that favor different sides of a market. We measure which stable matching LLMs choose, comparing generic requests for a stable matching with explicit requests for a stable matching that is optimal for neither side of the market. On the same 50 markets with five participants per side and one response per market and request, Opus 5.5, Fable 5.1, and GPT-6 Astra return one side's optimum on 100% of generic requests, yet produce the requested alternative on 98 to 100% of explicit requests, with or without an assurance that one exists. Their one-sided default therefore does not come from an inability to find other stable matchings. GPT-6 Sol, GPT-6 Luna, and GPT-5.6 Terra follow the explicit request less reliably. Across six framings of these markets, the favored side is the one that meets at least two of three conditions: the prompt calls it "Group 1", lists its preferences first, and uses its members as the keys of the requested JSON answer. Evaluations should therefore measure the default choice and compliance with a stated selection rule alongside stability. We also discuss the implications of these results for using LLMs as neutral referees in allocation problems.