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.

翻译：考虑一个群体，其中个体的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。如果一个选择模型是自我递进的，那么与该模型一致的所有聚合选择行为均可唯一地表示为可比的可容许选择函数上的概率分布。我们建立了自我递进选择模型与以下两者之间的等价关系：（i）称为格结构的著名代数结构；（ii）在特定选择函数域上超模函数的最大化者。我们将分析扩展到普遍自我递进选择模型，该类模型能够在不依赖原始排序的情况下实现唯一的序表示。