Connected Incomplete Preferences

TL;DR

This paper introduces the concept of connected preferences with topologically connected comparability domains, providing conditions for continuity and characterizing their maximal domains, thus extending classical decision theory results.

Contribution

It defines connected preferences, establishes necessary and sufficient conditions for their continuity, and characterizes their maximal domains of comparability.

Findings

Connected preferences have topologically connected maximal domains.

Necessary and sufficient conditions for continuous connected preferences are provided.

The results extend classical decision theory by linking topology and preference structure.

Abstract

This paper explores a new class of incomplete preferences -- termed ``connected preferences'' -- in which maximal domains of comparability are topologically connected. We provide necessary and sufficient conditions for continuous preferences to be connected. We also characterize their maximal domains of comparability. Our results extend classical findings in decision theory by linking topological properties of the choice space with the structure of preferences, offering a novel perspective on incompleteness in economic models.