The $$q$$ q -majority efficiency of positional rules

Courtin, Sébastien; Mathieu, Martin; Moyouwou, Issofa

doi:10.1007/s11238-014-9451-2

Cited by 10 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.…”

Section: Methodsmentioning

confidence: 99%

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

Diss

Kamwa

Tlidi³

2018

SSRN Journal

View full text Add to dashboard Cite

Section: Methodsmentioning

confidence: 99%

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

Diss

Kamwa

Tlidi³

2018

SSRN Journal

View full text Add to dashboard Cite

“…The concepts of q-Condorcet winner and q-majority equilibrium have been studied in Greenberg [5], Sari [10], Baharad and Nitzan [1], and Courtin et al [3]. The following result shows that for large enough q, any q-Condorcet winner is socially acceptable.…”

Section: Definitionsmentioning

confidence: 98%

Condorcet winners and social acceptability

Mahajne

Volij

2019

Soc Choice Welf

View full text Add to dashboard Cite

We say that an alternative is socially acceptable if the number of individuals who rank it among their most preferred half of the alternatives is at least as large as the number of individuals who rank it among the least preferred half. A Condorcet winner may not be socially acceptable. However, if preferences are single-peaked or satisfy the single-crossing property, any Condorcet winner is socially acceptable.

show abstract

“…, 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.…”

Section: Evaluating the Probability Of Voting Situationsmentioning

confidence: 99%

Extensions of the Simpson voting rule to the committee selection setting

2019

View full text Add to dashboard Cite

Committee selection rules are procedures selecting sets of candidates of a given size on the basis of the preferences of the voters. There are in the literature two natural extensions of the well-known singlewinner Simpson voting rule to the multiwinner setting. The first method gives a ranking of candidates according to their minimum number of wins against the other candidates. Then, if a fixed number k of candidates are to be elected, the k best ranked candidates are chosen as the overall winners. The second method gives a ranking of committees according to the minimum number of wins of committee members against committee nonmembers. Accordingly, the committee of size k with the highest score is chosen as the winner. We propose an in-depth analysis of those committee selection rules, assessing and comparing them with respect to several desirable properties among which unanimity, fixed majority, nonimposition, stability, local stability, Condorcet consistency, some kinds of monotonicity, resolvability and consensus committee. We also investigate the probability that the two methods are resolute and suffer the reversal bias, the Condorcet loser paradox and the leaving member paradox. We compare the results obtained with the ones related to further well-known committee selection rules. The probability assumption on which our results are based is the widely used Impartial Anonymous Culture. AbstractCommittee selection rules are procedures selecting sets of candidates of a given size on the basis of the preferences of the voters. There are in the literature two natural extensions of the wellknown single-winner Simpson voting rule to the multiwinner setting. The first method gives a ranking of candidates according to their minimum number of wins against the other candidates. Then, if a fixed number k of candidates are to be elected, the k best ranked candidates are chosen as the overall winners. The second method gives a ranking of committees according to the minimum number of wins of committee members against committee nonmembers. Accordingly, the committee of size k with the highest score is chosen as the winner. We propose an in-depth analysis of those committee selection rules, assessing and comparing them with respect to several desirable properties among which unanimity, fixed majority, non-imposition, stability, local stability, Condorcet consistency, some kinds of monotonicity, resolvability and consensus committee. We also investigate the probability that the two methods are resolute and suffer the reversal bias, the Condorcet loser paradox and the leaving member paradox. We compare the results obtained with the ones related to further well-known committee selection rules. The probability assumption on which our results are based is the widely used Impartial Anonymous Culture.

show abstract

The $$q$$ q -majority efficiency of positional rules

Cited by 10 publications

References 9 publications

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

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

Condorcet winners and social acceptability

Extensions of the Simpson voting rule to the committee selection setting

Contact Info

Product

Resources

About