Strategic Manipulability of Self-­Selective Social Choice Rules

Abstract

We provide exact relations giving the probability of individual and coalitional manipulation of three specific social choice functions (Borda rule, Copeland rule, Plurality rule) in three-alternative elections when the notion of self-selectivity is imposed. The results suggest that the Borda rule is more vulnerable to coalitional manipulation than the Copeland rule and the Plurality rule. However, Plurality rule seems to be more vulnerable to individual manipulability when the number of voters is greater than a certain threshold value. In addition, the probability of individual and coalitional manipulation tends to vanish significantly when the notion of selfselectivity is imposed.

The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency

“…Despite the fact that the Chamberlin-Courant rule is appropriate to ensure proportional representation, computing the outcomes can be computationally intractable (see for instance Betzler et al, 2013, Procaccia et al, 2008, Skowron et al, 2013a, 2015. As this drawback may compromise the use of this rule in real elections, the aim of this paper was to determine how often the outcome of the CCR may coincide with that of the following well-known rules: The k-Plurality rule, the k-Borda rule, the k-Negative Plurality rule and the Bloc rule.…”

“…This technique has been widely used in numerous studies in order to evaluate the probability of electoral events in the case of three-candidate elections under the IAC assumption. For further information in this regard, we refer the reader to the recent studies of Courtin et al (2015), Diss (2015), , , 2016, 2015, Kamwa and Valognes (2017), Lepelley et al (2018), and Smaoui et al (2016). There are strong algorithms that enable to specify the Ehrhart polynomials for many problems in the case of three-candidate elections.…”

“…It is clear that the CCE is simply the extension of the single-winner Condorcet eciency of voting rules to multiwinner context as it is the conditional probability that a given voting rule elects the Condorcet winner when one exists. For further details on the Condorcet eciency in the single-winner framework, the reader may refer to the works of Diss andGehrlein (2015, 2012) and the recent books of Gehrlein andLepelley (2017, 2011), among others. The second contribution of this paper is to compute the Condorcet committee eciency of the CCR according to the same values of the pair (k, m) that have been considered in Diss and Doghmi (2016), i.e., m ∈ {4, 5, 6} and 1 ≤ k ≤ m − 1.…”

“…For this, our volumes are found with the use of the algorithm Convex which is a MAPLE package for convex geometry written by Franz (2016). This package works with the same general procedure that was implemented in Cervone et al (2005) and recently used in other studies, e.g., Diss and Doghmi (2016), Diss andGehrlein (2015, 2012), Gehrlein et al (2015) and Moyouwou and Tchantcho (2017).…”

Extensions of the Simpson voting rule to the committee selection setting

“…, n 6 ) subject to the following conditions: n 1 + n 2 − n 5 − n 6 > 0 (the Plurality score of candidate x is greater than the one of z), n 3 + n 4 − n 5 − n 6 > 0 (the Plurality score of y is greater than the one of z), n i ≥ 0 for each i ∈ [6], and 6 i=1 n i = n. As recently pointed out in the literature of social choice theory, Ehrhart polynomials are the appropriate mathematical tool to study such problems (Gehrlein andLepelley, 2011, 2017;Lepelley et al, 2008;Wilson and Pritchard, 2007). In fact, they have been widely used in numerous studies analyzing the probability of electoral events in the case of three-candidate elections under IAC assumption (Courtin et al, 2015;Diss, 2015;Gehrlein andLepelley, 2011, 2017;Gehrlein et al, 2015Gehrlein et al, , 2016Gehrlein et al, , 2018Kamwa and Valognes, 2017;Lepelley et al, 2017;Smaoui et al, 2016). There exist strong algorithms that enable to specify the Ehrhart polynomials for many problems in the case of three-candidate elections.…”