Another Perspective on Borda's Paradox

Diss, Mostapha; Tlidi, Abdelmonaim

doi:10.2139/ssrn.2875342

Cited by 2 publications

(3 citation statements)

References 14 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is important to notice that this paradox is also known in the literature as the strong Borda paradox. This type of problem for k = 1 is studied by Diss and Gehrlein (2012); Diss and Tlidi (2018); Fishburn and Gehrlein (1976); Gehrlein and Lepelley (2010b), among others. It is important to notice that, since a k-Condorcet loser set for (C, V, p) is a k-Condorcet winner for (C, V, p r ), if a csr is Condorcet consistent and immune to the reversal bias then it is immune to the Condorcet loser paradox.…”

Section: The Probability Of Suffering the Condorcet Loser Paradoxmentioning

confidence: 99%

“…7 Recall that a csr R is resolute if, for every (C, V, p) ∈ E and k ∈ [|C|−1], |R(C, V, p, k)| = 1; R suffers the reversal bias if there exist (C, V, p) ∈ E and k ∈ [|C| − 1] such that |R(C, V, p, k)| = 1 and R(C, V, p, k) = R(C, V, p r , k); R suffers the Condorcet loser paradox if there exist (C, V, p) ∈ E, k ∈ [|C| − 1] and W * ∈ 2 C k such that W * is a k-Condorcet loser set for (C, V, p), that is, for every x ∈ W * and y ∈ C \ W * , c p (x, y) < |V | 2 , and R(C, V, p, k) = {W * }; R suffers the leaving member paradox if there exist (C, V, p) ∈ E, k ∈ [|C| − 1] with k = 1, and 7 Those properties are largely studied in the literature. See for instance, Bubboloni and Gori (2016), Diss and Doghmi (2016), Diss and Gehrlein (2012), Diss and Tlidi (2018), Duggan and Schwartz (2000), Fishburn and Gehrlein (1976), Gehrlein and Lepelley (2010b), Jeong and Ju (2017), Kamwa and Merlin (2015), Saari and Barney (2003), and Staring (1986).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Extensions of the Simpson voting rule to the committee selection setting

2019

Self Cite

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

Section: The Probability Of Suffering the Condorcet Loser Paradoxmentioning

confidence: 99%

mentioning

confidence: 99%

Extensions of the Simpson voting rule to the committee selection setting

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…The study of the likelihood of each of these three paradoxes is well addressed in the social choice literature. Without been exhaustive, the reader may refer to the theoretical works of Diss and Gehrlein (2012), Diss and Tlidi (2018), Fishburn (1976, 1978a), Gehrlein and Lepelley (2017, 2011, 2010b, 1998, Lepelley (1996Lepelley ( , 1993, Lepelley et al (2000a,b), Saari (1994), Saari and Valognes (1999), Tataru and Merlin (1997). We can also mention that there are some empirical works that looked after these paradoxes in real-world data; we refer to the works of Bezembinder (1996), Colman and Poutney (1978), Riker (1982), Taylor (1997), Van Newenhizen (1992, Weber (1978).…”

Section: Introductionmentioning

confidence: 99%

On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules

Kamwa¹

2018

Group Decis Negot

View full text Add to dashboard Cite

The Borda Effect, first introduced by Colman and Poutney (1978), occurs in a preference aggregation process using the Plurality rule if given the (unique) winner there is at least one loser that is preferred to the winner by a majority of the electorate. Colman and Poutney (1978) distinguished two forms of the Borda Effect: -the Weak Borda Effect describing a situation under which the unique winner of the Plurality rule is majority dominated by only one loser; and -the Strong Borda Effect under which the Plurality winner is majority dominated by each of the losers. The Strong Borda Effect is well documented in the literature as the Strong Borda Paradox. Colman and Poutney (1978) showed that the probability of the Weak Borda Effect is not negligible; they only focused on the Plurality rule. In this note, we extend the work of Colman and Poutney (1978) by providing in three-candidate elections, the representations for the limiting probabilities of the (Weak) Borda Effect for the whole family of the scoring rules and scoring runoff rules. We highlight that there is a relation between the (Weak) Borda Effect and the Condorcet efficiency. We perform our analysis under the Impartial Culture and the Impartial Anonymous Culture which are two well-known assumptions often used for such a study.

show abstract

Another Perspective on Borda's Paradox

Cited by 2 publications

References 14 publications

Extensions of the Simpson voting rule to the committee selection setting

Extensions of the Simpson voting rule to the committee selection setting

On the Likelihood of the Borda Effect: The Overall Probabilities for General Weighted Scoring Rules and Scoring Runoff Rules

Contact Info

Product

Resources

About