Borda’s Paradox with weighted scoring rules

Diss, Mostapha; Gehrlein, William V.

doi:10.1007/s00355-010-0522-1

Cited by 23 publications

(10 citation statements)

References 15 publications

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“…The same remark is valid for the example with n = 10 where AB = 4 and AC = BC = 2. This result is also consistent with the literature on the probability of Borda's paradox (e.g., Diss and Gehrlein, 2012;Gehrlein and Lepelley, 2010b). …”

Section: If the Strongly Non-cyclic Condition Is Not Satisfied: A)supporting

confidence: 92%

“…In other words, the region for which the strong Borda paradox does not occur is much more important when s → 1 2 . This result is not new and is consistent with the existing literature dealing with the probability of the strong Borda paradox under various scenarios (e.g., Diss and Gehrlein, 2012;Gehrlein and Lepelley, 2010b). However, one of the particularity of our paper is that this result is general and it does not depend on the restrictions on the individuals' preferences.…”

Section: If the Strongly Non-cyclic Condition Is Not Satisfied: A)supporting

confidence: 90%

“…Gehrlein and Lepelley (2010b) examined the probability that the two paradoxes will be observed with Plurality rule and Negative Plurality rule (another specific weighted scoring rule, which is defined later) under a well-known assumption about the voters' preferences. Diss and Gehrlein (2012) extend that analysis by considering all the class of weighted scoring rules and taking into account different assumptions about the individuals' preferences. Notice that Gehrlein and Lepelley (2010b) also analyzed the impact that degrees of mutual coherence among voters' preferences will have on the likelihood of observing the two forms of Borda's paradox under Plurality rule and Negative Plurality rule.…”

Section: Related Literaturementioning

confidence: 99%

“…Finally, it is worthwhile to mention that some empirical studies have been conducted in order to discuss if the two forms of Borda's paradox have occurred in real-life elections. The reader is refereed to Diss and Gehrlein (2012) and Gehrlein and Lepelley (2010a).…”

Section: Related Literaturementioning

confidence: 99%

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Another perspective on Borda’s paradox

Diss

Tlidi

2017

Theory Decis

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Abstract:This paper presents the conditions required for a profile in order to never exhibit either the strong or the strict Borda paradoxes under all weighted scoring rules in three-candidate elections. The main particularity of our paper is that all the conclusions are extracted from the differences of votes between candidates in pairwise majority elections. This way allows us to answer new questions and provide an organized knowledge of the conditions under which a given profile never shows one of the two paradoxes. Keywords:Voting, Geometry, Borda's Paradox, Condorcet Pairwise Procedure, Borda, Plurality, Negative Plurality, Weighted Scoring Rules. JEL codes: D71, D72Another perspective on Borda's paradox * Mostapha Diss † Abdelmonaim Tlidi ‡ This version: November 23, 2016Abstract This paper presents the conditions required for a profile in order to never exhibit either the strong or the strict Borda paradoxes under all weighted scoring rules in three-candidate elections. The main particularity of our paper is that all the conclusions are extracted from the differences of votes between candidates in pairwise majority elections. This way allows us to answer new questions and provide an organized knowledge of the conditions under which a given profile never shows one of the two paradoxes.

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Section: If the Strongly Non-cyclic Condition Is Not Satisfied: A)supporting

confidence: 92%

Section: If the Strongly Non-cyclic Condition Is Not Satisfied: A)supporting

confidence: 90%

Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

See 2 more Smart Citations

Another perspective on Borda’s paradox

Diss

Tlidi

2017

Theory Decis

Self Cite

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“…However, every WSR other than BR can exhibit both of these this phenomena, and representations have been obtained for the associated limiting probabilities for each in Diss and Gehrlein (2009 IAC / both decrease as increases for the interval 0 Ä Ä :5, so that the likelihood of the outcome is maximized by both PR and NPR. However, every WSR other than BR can exhibit both of these this phenomena, and representations have been obtained for the associated limiting probabilities for each in Diss and Gehrlein (2009 IAC / both decrease as increases for the interval 0 Ä Ä :5, so that the likelihood of the outcome is maximized by both PR and NPR.…”

Section: Borda's Paradoxmentioning

confidence: 95%