The sensitivity of weight selection on the Condorcet efficiency of weighted scoring rules

Abstract

A weighted scoring rule, Rule λ, on three alternative elections selects the winner by awarding 1 point to each voter's first ranked candidate, λ points to the second ranked candidate, and zero to the third ranked candidate. The Condorcet winner is the candidate that would defeat each other candidate in a series of pairwise elections by majority rule. The Condorcet efficiency of Rule λ is the conditional probability that Rule λ selects the Condorcet winner, given that a Condorcet winner exists. Borda rule (λ=1/2) is the weighted scoring rule that maximizes Condorcet efficiency. The current study considers the conditional probability that Borda rule selects the Rule λ winner, given that Rule λ elects the Condorcet winner with a large electorate.