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:考虑一个代理人群体,他们的选择行为根据给定的原始排序进行部分比较。可采用的选择功能集合规定了一个选择模型。如果与模型一致的任何聚集选择行为都可以唯一地表示为可比较的可采用选择功能上的概率分布,则选择模型为自适应进阶选择模型。我们建立了自适应进阶选择模型和(i)称为格的众所周知的代数结构;(ii)特定选择函数域上超模型函数的极大值限制之间的等价性。我们将分析扩展到普遍自适应进阶选择模型,独立于原始排序,因此呈现出独特的有序表现。