Lexicographic Composition of Choice Functions

TL;DR

This paper studies how lexicographic composition of choice functions affects properties like path independence, providing characterizations of constraints that preserve these properties across different input domains.

Contribution

It offers a formal analysis of lexicographic composition, identifying conditions under which key properties are maintained in aggregate choice functions.

Findings

Characterizes constraints preserving path independence.

Analyzes property preservation across input domains.

Provides theoretical foundations for lexicographic choice composition.

Abstract

Lexicographic composition is a natural way to build an aggregate choice function from component choice functions. As the name suggests, the components are ordered and choose sequentially. The sets that subsequent components select from are constrained by the choices made by earlier choice functions. The specific constraints affect whether properties like path independence are preserved. For several domains of inputs, we characterize the constraints that ensure such preservation.