Self-progressive choice models

TL;DR

This paper introduces self-progressive choice models, establishing their equivalence with lattices, and provides methods to uniquely represent and extend choice behaviors, explaining phenomena like choice overload.

Contribution

It proposes the concept of self-progressiveness in choice models, linking it to lattice structures, and offers a framework for unique representation and extension of choice behaviors.

Findings

Equivalence between self-progressive models and lattices.

Characterization of choice functions for unique representation.

Explanation of choice overload phenomena.

Abstract

Consider a population of heterogenous agents whose choice behaviors are partially \textit{comparable} according to a given \textit{primitive ordering}.The set of choice functions admissible in the population specifies a \textit{choice model}. As a criterion to guide the model selection process, we propose \textit{self-progressiveness}, ensuring that each aggregate choice behavior explained by the model has a unique orderly representation within the model itself. We establish an equivalence between self-progressive choice models and well-known algebraic structures called \textit{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. This extended model offers an intuitive explanation for the \textit{choice overload} phenomena. We provide the necessary and sufficient conditions for identifying the underlying primitive ordering.