The Effect of Closeness on the Election of a Pairwise Majority Rule Winner

Patrizia Pérez-Asurmendi (), Abdelmonaim Tlidi and Mostapha Diss
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Abdelmonaim Tlidi: UCA - Université Cadi Ayyad [Marrakech]

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Abstract: 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.

Date: 2021-01
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Published in Mostapha Diss; Vincent Merlin. Evaluating Voting Systems with Probability Models. Essays by and in Honor of William Gehrlein and Dominique Lepelley, Springer, 2021

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