Recursive Monotonicity of the Scorix: Borda Meets Condorcet

Pérez‐Fernández, Raúl; Baets, Bernard De

doi:10.1007/s10726-017-9525-y

Cited by 4 publications

(7 citation statements)

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“…In this section, we recall several monotonicity‐based consensus states that can be considered as cornerstones of social choice theory where families of ranking rules lead to the same social outcome. For more details concerning Sections 2.1, 2.2, and 2.3 we refer to Pérez‐Fernández and co‐workers . In the considered problem setting, each of

r

voters expresses a strict total order relation or ranking

≻_{j}

on a set

scriptC = {a_{1}, \dots, a_{k}}

k

candidates, that is, the asymmetric part of a total order relation

≽_{j}

scriptC

.…”

Section: Preliminariesmentioning

confidence: 99%

“…For more details concerning Sections 2.1, 2.2, and 2.3 we refer to Pérez-Fernández and co-workers. [15][16][17][18] In the considered problem setting, each of r voters expresses a strict total order relation or ranking j ≻ on a set C a a = { ,…, } k 1 of k candidates, that is, the asymmetric part of a total order relation j ≽ on C . The set of all rankings on C is denoted by C ( ) and the position at which candidate a i is ranked in a ranking j ≻ is denoted by P a ( ) j i (we consider position 1 to be the best).…”

Section: Preliminariesmentioning

confidence: 99%

“…This means that, given a scorix, it is not possible to identify whether or not it is recursively monotone without knowing the profile of rankings. For more details, we refer to Pérez‐Fernández and De Baets (Remark 3).…”

mentioning

confidence: 99%

“…Definition 4 (Pérez-Fernández and De Baets 15 ). Let C be a set of k candidates, R be the profile of r rankings on C given by the voters and S be the scorix induced by R .…”

mentioning

confidence: 99%

“…Definition 5 (Pérez-Fernández and De Baets 15 ). Let C be a set of k candidates and r be the number of voters.…”

mentioning

confidence: 99%

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The acclamation consensus state and an associated ranking rule

Pérez‐Fernández

Baets

2019

Int J Intell Syst

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The study of conditions, under which the existence of an “absolute” best winner can be assured, is a hot topic in the field of social choice. Unanimity is an evident example of a condition under which the winner is obvious. However, many more properties weaker than unanimity have been analysed in literature: the presence of a Condorcet winner, strong stochastic transitivity, the presence of a candidate that Borda dominates all other candidates, etc. Unfortunately, one could easily find a prominent ranking rule, for which the outcome does not agree with these relaxed conditions. In this study, we aim to identify a condition weaker than unanimity, but under which the social outcome is still obvious. This condition, defined as the conjunction of three properties already studied by the present authors and hereinafter referred to as acclamation, will be proven to be a meeting point for the most prominent ranking rules in social choice theory, and will be used for introducing an intuitively appealing ranking rule.

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r

voters expresses a strict total order relation or ranking

≻_{j}

on a set

scriptC = {a_{1}, \dots, a_{k}}

k

candidates, that is, the asymmetric part of a total order relation

≽_{j}

scriptC

.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

“…Definition 4 (Pérez-Fernández and De Baets 15 ). Let C be a set of k candidates, R be the profile of r rankings on C given by the voters and S be the scorix induced by R .…”

mentioning

confidence: 99%

“…Definition 5 (Pérez-Fernández and De Baets 15 ). Let C be a set of k candidates and r be the number of voters.…”

mentioning

confidence: 99%

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