Characterizations of voting rules based on majority margins

Code

• github.com/epacuit/majority_margins
  OfficialIn papernone★ 0

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, then 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.

Reproductions