Random Preference Model

We introduce the Random Preference Model (RPM), a non-parametric and flexible discrete choice model. RPM is a rank-based stochastic choice model where choice options have multi-attribute representations. It takes preference orderings as the main primitive and models choices directly based on a distribution over partial or complete preference orderings over a ï¬nite set of alternatives. This enables it to capture context-dependent behaviors while maintaining adherence to the regularity axiom. In its output, it provides a full distribution over the entire preference parameter space, accounting for inferential uncertainty due to limited data. Each ranking is associated with a subspace of utility functions and assigned a probability mass based on the expected log-likelihood of those functions in explaining the observed choices. We propose a two-stage estimation method that separates the estimation of ranking-level probabilities from the inference of preference parameters variation for a given ranking, employing Monte Carlo integration with subspace-based sampling. To address the factorial complexity of the ranking space, we introduce scalable approximation strategies: restricting the support of RPM to a randomly sampled or orthogonal basis subset of rankings and using partial permutations (top-k lists). We demonstrate that RPM can effectively recover underlying preferences, even in the presence of data inconsistencies. The experimental evaluation based on real data conï¬rms RPM variants consistently outperform multinomial logit (MNL) in both in-sample ï¬t and holdout predictions across different training sizes, with support-restricted and basis-based variants achieving the best results under data scarcity. Overall, our ï¬ndings demonstrate RPM's flexibility, robustness, and practical relevance for both predictive and explanatory modeling.