Condorcet efficiency of general weighted scoring rules under IAC: indifference and abstention

Abstract : In an election, individuals may sometimes abstain or report preferences that include ties among candidates. How abstention or ties within individual preferences impact the performances of voting rules is a natural question addressed in the literature. We reconsider this question with respect to one of the main characteristics of a voting rule: its Condorcet efficiency; that is the conditional probability that the rule selects a Condorcet winner assuming that one exists. We explore the impact of both ties and abstention on the Condorcet efficiency of the whole class of weighted scoring rules in three-candidate elections under the Impartial Anonymous Culture assumption. It appears in general that the possibility of indifference or abstention increases or decreases the Condorcet efficiency of weighted scoring rules depending of the rule in consideration or the probability distribution on the set of observable voting situations.