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

A weighted scoring rule, Rule , on three alternative elections selects the winner by awarding 1 point to each voter's first ranked candidate, 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 is the conditional probability that Rule selects the Condorcet winner, given that a Condorcet winner exists. Borda rule (=1/2) is the weighted scoring rule that maximizes Condorcet efficiency. The current study considers the conditional probability that Borda rule selects the Rule winner, given that Rule elects the Condorcet winner with a large electorate.