Condorcet-loser dominance among scoring rules

TL;DR

This paper analyzes how different scoring voting rules compare in avoiding the Condorcet loser, highlighting Borda's unique dominance properties among scoring rules.

Contribution

It introduces a dominance relation among scoring rules based on their ability to avoid selecting the Condorcet loser, with Borda identified as uniquely dominant.

Findings

Borda rule CL-dominates all other scoring rules.

Borda is the only scoring rule that CL-dominates some other rule.

The study formalizes a dominance relation among scoring rules.

Abstract

This paper studies a dominance relation among scoring rules with respect to avoiding the selection of the Condorcet loser. In a voting model with three or more alternatives, we say that a scoring rule $f$ Condorcet-loser-dominates (CL-dominates) another scoring rule $g$ if the set of profiles where $f$ selects a Condorcet loser is a proper subset of the set where $g$ does. We show that the Borda rule not only CL-dominates all other scoring rules, but also is the only scoring rule that CL-dominates some scoring rule.