Characterizations of voting rules based on majority margins

TL;DR

This paper investigates margin-based voting rules in ranked elections, establishing their characterization through axioms like Preferential Equality, and discusses their normative justification.

Contribution

It provides a characterization of margin-based voting rules via axioms, clarifying their normative foundations across various voting outputs.

Findings

Margin-based rules are characterized by specific axioms.

Preferential Equality is a key axiom for these rules.

The paper links mathematical properties to normative principles.

Abstract

In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins of victory or loss between candidates, the voting rule yields the same outcome in both elections. Although this is a mathematically natural invariance property to consider, whether it should be regarded as a normative axiom on voting rules is less clear. In this paper, we address this question for voting rules with any kind of output, whether a set of candidates, a ranking, a probability distribution, etc. We prove that a voting rule is margin-based if and only if it satisfies some axioms with clearer normative content. A key axiom is what we call Preferential Equality, stating that if two voters both rank a candidate $x$ immediately above a candidate $y$, then either voter switching to rank $y$ immediately above $x$ will have the same effect on the election outcome as if the other voter made the switch, so each voter's preference for $y$ over $x$ is treated equally.