The Euclidean geometry of cardinal welfare functions

TL;DR

This paper introduces a novel Euclidean geometric framework for analyzing voting methods, leveraging group actions to extend voting criteria to diverse ballot types.

Contribution

It provides a new geometric perspective on voting methods and extends criteria to arbitrary ballot compositions using group actions.

Findings

New Euclidean geometric approach to voting analysis

Extension of voting criteria to arbitrary ballots

Insight into symmetry and group actions in voting theory

Abstract

We exploit the standard inner product of Euclidean space to provide a new direction from which one can understand and analyze certain voting methods. Using this perspective along with the action of the symmetric and special orthogonal groups on the vector space of profiles, we extend some natural voting criteria to ballots of arbitrary composition type.