Self-progressive choice models
Abstract
Consider a population of heterogenous agents whose choice behaviors are partially comparable according to a given primitive ordering.The set of choice functions admissible in the population specifies a choice model. As a criterion to guide the model selection process, we propose 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 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 choice overload phenomena. We provide the necessary and sufficient conditions for identifying the underlying primitive ordering.
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