  Consider a population of heterogenous agents whose choice behaviors are
partially comparable according to a given primitive ordering. An analyst seeks
to select a choice model, a set of choice functions, to explain the observed
random choice behavior. As a criterion to guide the model selection process, we
propose self-progressiveness ensuring that each aggregate choice behavior
explained by the model has a unique orderly representation within the model. 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. Following this recipe, we identify the set of choice functions
that are essential for the unique orderly representation of random utility
functions. We provide the necessary and sufficient conditions for identifying
the underlying primitive ordering.
