Deepest Voting: a new way of electing

TL;DR

This paper introduces a unified framework for grading-based voting using the concept of the deepest point in a scatter plot, satisfying key voting properties and connecting to traditional methods.

Contribution

It proposes a novel depth-based approach to voting, unifying various grading methods and analyzing their properties and paradoxes.

Findings

The framework satisfies universality, unanimity, and neutrality.

Traditional voting methods are special cases of the depth-based approach.

Basic voting paradoxes are examined within this new framework.

Abstract

This article aims to present a unified framework for grading-based voting processes. The idea is to represent the grades of each voter on d candidates as a point in R^d and to define the winner of the vote using the deepest point of the scatter plot. The deepest point is obtained by the maximization of a depth function. Universality, unanimity, and neutrality properties are proved to be satisfied. Monotonicity and Independence to Irrelevant Alternatives are also studied. It is shown that usual voting processes correspond to specific choices of depth functions. Finally, some basic paradoxes are explored for these voting processes.