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 finite 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 confirms RPM variants consistently outperform multinomial logit (MNL) in both in-sample fit and holdout predictions across different training sizes, with support-restricted and basis-based variants achieving the best results under data scarcity. Overall, our findings demonstrate RPM's flexibility, robustness, and practical relevance for both predictive and explanatory modeling.