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 theory. A choice theory is self-progressive if any aggregate choice behavior consistent with the theory is uniquely representable as a probability distribution over admissible choice functions that are comparable. We establish an equivalence between self-progressive choice theories 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 theories which render unique orderly representations independent of primitive orderings.

翻译：考虑一个行为选择部分可依据给定原始序进行比较的智能体群体。该群体中容许的选择函数集合构成一种选择理论。若与该理论相容的任何聚合选择行为均可唯一表示为可比较的容许选择函数上的概率分布，则称这种选择理论为"自进"的。我们建立了自进选择理论与以下两类对象之间的等价关系：（i）被称为格结构的著名代数结构；（ii）特定选择函数域上超模函数的最大化算子。我们将分析扩展至普适自进选择理论，该类理论能独立于原始序而生成唯一的序化表示。