Reformulating the Value Restriction and the Not-Strict Value Restriction in Terms of Possibility Preference Map

TL;DR

This paper introduces the possibility preference map (PPM), a new mathematical tool, to reformulate Sen's value restriction and Pattanaik's not-strict value restriction, simplifying their expressions in social choice theory.

Contribution

The paper presents a novel PPM framework that reformulates key social preference restrictions, offering a more elegant minmax representation.

Findings

Reformulations are mathematically elegant and simplified.

PPM provides a new perspective on social preference restrictions.

Potential for improved analysis of social choice conditions.

Abstract

In social choice theory, Sen's value restriction and Pattanaik's not-strict value restriction are both attractive conditions for testing social preference transitivity and/or non-empty social choice set existence. This article introduces a novel mathematical representation tool, called possibility preference map (PPM), for weak orderings, and then reformulates the value restriction and the not-strict value restriction in terms of PPM. The reformulations all appear elegant since they take the form of minmax.