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

Mostapha Diss, Patrizia Pérez-Asurmendi () and Abdelmonaim Tlidi ()
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Abdelmonaim Tlidi: University Cadi Ayyad of Marrakesh, LMPEQ

A chapter in Evaluating Voting Systems with Probability Models, 2021, pp 75-95 from Springer

Abstract: 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
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DOI: 10.1007/978-3-030-48598-6_4

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