Self-ordered choice models

Consider an analyst who, for each menu of alternatives, observes a probability distribution over choices, reflecting heterogeneity in the population's choices. The analyst uses a choice model\textendash consisting of deterministic \textit{choice types} \textendash to explain the data, in the sense that mixtures over the admissible types reproduce the observed choice probabilities. A central difficulty is that such representations are typically non-unique. We introduce self-orderedness, a criterion ensuring that every probabilistic choice pattern the analyst can explain admits a unique and ordered representation. We show that self-ordered models are exactly those whose choice types form a \textit{lattice}. This equivalence provides a precise recipe to restrict or extend any choice model for unique ordered representation. Following this recipe, we identify the choice types that are essential for the unique ordered representation of random utility functions. This extension adds economically meaningful non-rational behaviors linked to choice overload and enables identification of the underlying order.