Probability Contracts: Accuracy, Coherence, and Decisions Across LLM Interfaces

Han Chen, Yingrui Li

Equivalent probability requests can lead to different decisions even when both reports are valid. We introduce probability contracts, a benchmark that connects exact finite-world posteriors, validated event alignment, interface coherence, and failure-aware decision evaluation. Across four model-interface configurations on 1,000 worlds, Kev has lower aggregate canonical posterior error than Jev but larger complement and coarsening residuals; accuracy ordering varies by stratum. Jev's Event and Choice interfaces change the binary action on 32.8% of valid pairs at defer cost 0.10. Post-hoc analyses show that disagreement certifies only 11-52% of mean binary pair error and does not consistently outperform confidence for selection. An action-region characterization and a standard scoring-rule identity explain averaging's expected Brier guarantee relative to random interface selection, but not a decision-loss guarantee at each cost. The loss contrast takes both signs on a 99-cost grid for every configuration; small penalties where both policies beat deferral have pointwise intervals containing zero. Secondary checks specified before collection include a separate 400-root cohort, where…