Condorcet-loser dominance among scoring rules
TLDR
This paper introduces Condorcet-loser dominance for scoring rules, showing the Borda rule uniquely excels at avoiding Condorcet losers.
Key contributions
- Defines "Condorcet-loser dominance" (CL-dominance) for comparing voting scoring rules.
- CL-dominance means one rule selects a Condorcet loser in fewer profiles than another.
- Proves the Borda rule CL-dominates all other scoring rules in voting models.
- Establishes Borda as the *only* scoring rule capable of CL-dominating any other rule.
Why it matters
This paper highlights the Borda rule's exceptional robustness in avoiding undesirable Condorcet losers. It provides strong theoretical justification for its use in multi-alternative voting systems, enhancing fairness.
Original 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.
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