Title: "Characterizations of voting rules based on majority margins"
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.
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