Foundations of self-progressive choice models

Consider a population of agents whose choice behaviors are partially comparable according to given primitive orderings. The set of choice functions admissible in the population specifies a choice model. A choice model is self-progressive if any aggregate choice behavior consistent with the model is uniquely representable as a probability distribution over admissible choice functions that are comparable. We establish an equivalence between self-progressive choice models and (i) well-known algebraic structures called lattices; (ii) the maximizers of supermodular functions over a specific domain of choice functions. We extend our analysis to universally self-progressive choice models which render unique orderly representations independent of primitive orderings.