Self-progressive choice models

Consider a population of heterogenous agents whose choice behaviors are partially $\mathit{\text{comparable}}$ according to a given $\mathit{\text{primitive}}\mathit{\text{ordering}}$.The set of choice functions admissible in the population specifies a $\mathit{\text{choice}}\mathit{\text{model}}$. As a criterion to guide the model selection process, we propose $\mathit{\text{self-progressiveness}}$, ensuring that each aggregate choice behavior explained by the model has a unique orderly representation within the model itself. We establish an equivalence between self-progressive choice models and well-known algebraic structures called $\mathit{\text{lattices}}$. This equivalence provides for a precise recipe to restrict or extend any choice model for unique orderly representation. Following this recipe, we identify the set of choice functions that are essential for the unique orderly representation of random utility functions. This extended model offers an intuitive explanation for the $\mathit{\text{choice}}\mathit{\text{overload}}$ phenomena. We provide the necessary and sufficient conditions for identifying the underlying primitive ordering.