Some studies (e.g., Lepelley et al. 2018; Miller 2017) recently examined the effect of closeness on the probability of observing the monotonicity paradox in three-candidate elections under Scoring Elimination Rules. It was shown that the frequency of such a paradox significantly increases as elections become more closely contested. In this chapter we consider the effect of closeness on one of the most studied notions in social choice theory: The election of the Condorcet winner, i.e., the candidate who defeats any other opponent in pairwise majority comparisons, when she exists. To be more concrete, we use the well-known concept of the Condorcet efficiency, that is, the conditional probability that a voting rule will elect the Condorcet winner, given that such a candidate exists. Our results, based on the Impartial Anonymous Culture (IAC) assumption, show that closeness has also a significant effect on the Condorcet efficiency of some voting rules in the class of Scoring Rules and Scoring Elimination Rules.
