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.

翻译：将选择行为根据特定原始顺序可部分比较的代理人视为一个群体。在人口中可接受的一系列选择功能指定了一种选择理论。如果任何与该理论一致的总选择行为都具有独特的代表性,则选择理论具有自我渐进性,作为相对于可受理的选择功能的概率分布,我们确立了自我渐进选择理论和(一)众所周知的代数结构(lattices);(二)超模化功能的最大化。