The Sensitivity of Weight Selection on the Condorcet Efficiency of Weighted Scoring Rules

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