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：考虑一个由异质主体组成的群体，其选择行为根据给定的原始排序具有部分可比性。群体中可容许的选择函数集合定义了一个选择模型。若与模型一致的所有总体选择行为均可唯一表示为可容许且可比较的选择函数上的概率分布，则称该选择模型为自推进的。我们建立了自推进选择模型与称为格的经典代数结构之间的等价关系。这一等价性为任何选择模型的唯一有序表示提供了精确的约束或扩展方法。为验证该理论，我们刻画了理性选择函数的最小自推进扩展，从而解释了主体为何可能出现选择过载现象。我们给出了识别（唯一）原始排序的充分必要条件，该排序使得选择过载表示适用于某一选择模型。