Consider a population of heterogenous 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 each 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 well-known algebraic structures called lattices. This equivalence provides for a precise recipe to restrict or extend any choice model for unique orderly representation. To prove out, we characterize the minimal self-progressive extension of rational choice functions, explaining why agents might exhibit choice overload. We provide necessary and sufficient conditions for the identification of a (unique) primitive ordering that renders our choice overload representation to a choice model.

翻译：考虑一个异质性主体群体，其选择行为根据给定的原始排序具有部分可比性。该群体中可容许的选择函数集合定义了一个选择模型。若与该模型一致的每个总体选择行为都能唯一地表示为可比选择函数上的概率分布，则该选择模型是自我递进的。我们建立了自我递进选择模型与称为格（lattice）的著名代数结构之间的等价关系。这种等价关系为限制或扩展任何选择模型以实现唯一有序表示提供了精确方法。为了验证这一点，我们刻画了理性选择函数的最小自我递进扩展，从而解释了主体为何可能表现出选择过载现象。我们给出了识别（唯一）原始排序的充要条件，该排序使我们的选择过载表示回归到选择模型。