A Partial Order on Preference Profiles

TL;DR

This paper introduces a new theoretical framework for comparing preference profiles using a partial order based on Pareto frontiers and ranking vectors, enabling meaningful analysis of preference structures.

Contribution

It defines a partial order on preference profiles, characterizes extremal elements, and illustrates the role of individualistic preferences within this framework.

Findings

Characterization of maximal and minimal elements under the partial order

A method to compare preference profiles via ranking vectors and Pareto frontiers

Illustration of how individualistic preferences can be maximal

Abstract

We propose a theoretical framework under which preference profiles can be meaningfully compared. Specifically, given a finite set of feasible allocations and a preference profile, we first define a ranking vector of an allocation as the vector of all individuals' rankings of this allocation. We then define a partial order on preference profiles and write "$P \geq P^{'}$", if there exists an onto mapping $\psi$ from the Pareto frontier of $P^{'}$ onto the Pareto frontier of $P$, such that the ranking vector of any Pareto efficient allocation $x$ under $P^{'}$ is weakly dominated by the ranking vector of the image allocation $\psi(x)$ under $P$. We provide a characterization of the maximal and minimal elements under the partial order. In particular, we illustrate how an individualistic form of social preferences can be maximal in a specific setting. We also discuss how the framework can be further generalized to incorporate additional economic ingredients.