A generalization to networks of Young's characterization of the Borda rule

TL;DR

This paper generalizes Young's characterization of the Borda rule to networks, establishing unique solutions satisfying neutrality, consistency, and cancellation, and derives new and known characterizations for various voting rules.

Contribution

It extends Young's characterization to network solutions and social choice correspondences, unifying and generalizing existing characterizations of multiple voting rules.

Findings

Unique network solutions satisfying key axioms are identified.

Several voting rules are characterized as restrictions of these solutions.

New and known theorems for Borda, Approval Voting, and others are derived.

Abstract

We prove that, for any given set of networks satisfying suitable conditions, the net-oudegree network solution, the net-indegree network solution, and the total network solution are the unique network solutions on that set satisfying neutrality, consistency and cancellation. The generality of the result obtained allows to get an analogous result for social choice correspondences: for any given set of preference profiles satisfying suitable conditions, the net-oudegree social choice correspondence, the net-indegree social choice correspondence and the total social choice correspondence are the unique social choice correspondences on that set satisfying neutrality, consistency and cancellation. Using the notable fact that several well-known voting rules coincide with the restriction of net-oudegree social choice correspondence to appropriate sets of preference profiles, we are able to deduce a variety of new and known characterization theorems for the Borda rule, the Partial Borda rule, the Averaged Borda rule, the Approval Voting, the Plurality rule and the anti-Plurality rule, among which Young's characterization of the Borda rule and Fishburn's characterization of the Approval Voting.