Choice functions based on sets of strict partial orders: an axiomatic characterisation

TL;DR

This paper provides a comprehensive axiomatic framework for choice functions derived from sets of strict partial orders, unifying various existing models such as total orders, weak orders, and probability measures.

Contribution

It introduces a very general axiomatic characterization that encompasses multiple types of order-based choice functions, including those based on probability and previsions.

Findings

Unifies various order-based choice models under a single axiomatic framework

Includes special cases like total orders, weak orders, and probability measures

Provides a broad foundation for analyzing choice functions in decision theory

Abstract

Methods for choosing from a set of options are often based on a strict partial order on these options, or on a set of such partial orders. I here provide a very general axiomatic characterisation for choice functions of this form. It includes as special cases axiomatic characterisations for choice functions based on (sets of) total orders, (sets of) weak orders, (sets of) coherent lower previsions and (sets of) probability measures.