An axiomatic approach to finite means

Campión, María Jesús; Candeal, Juan Carlos; Catalán, Raquel García; Giarlotta, Alfio; Greco, Salvatore; Induráin, Esteban; Montero, Javier

doi:10.1016/j.ins.2018.04.091

Cited by 7 publications

(8 citation statements)

References 42 publications

(56 reference statements)

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“…The system of axioms introduced here is new. It constitutes a slight modification of a more restrictive axiomatic system that was recently introduced in [7] in an interdisciplinary setting that includes Information Sciences. 3.-In section V the formal definition of a ranking fusion function is introduced along with some examples and properties.…”

Section: Manuscriptmentioning

confidence: 99%

“…The task of finding a new axiomatic system to define abstract means was done in [7], looking for practical applications into multidisciplinary contexts that include Information Sciences. As a matter of fact, Definition IV.1 included below is a slight variation (indeed a bit less restrictive) that the one introduced in [7].…”

Section: Theorem Iii5 (Arrow's Impossibility Theorem)mentioning

confidence: 99%

“…Thus, if we adopt now the concept of a general mean as a new setting to aggregate different in-dividual rankings, avoiding the Arrovian approach that leads to impossibility results, the output ranking resulting of the computation of corresponding mean will indeed act as a social ranking. The good news is that general means do actually exist in most contexts, as analyzed in [7].…”

Section: Theorem Iii5 (Arrow's Impossibility Theorem)mentioning

confidence: 99%

“…To do so, we will work with a variation of a new axiomatic theoretical setting, recently introduced (see [7]) -in contexts of Information Sciences, Social Choice and Decision Making-to understand what a mean on an abstract set should be. Then we will introduce ranking fusion functions and score functions that do indeed satisfy the conditions involved in the axioms of that new frame.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously, different aggregation rules, even when they fit well in the new set of suitable axioms that, as mentioned above, we will introduce in the spirit of [7], could generate different rankings. So, it is reasonable to ask ourselves: Is there a ranking that could be considered optimal in some sense?…”

Section: Introductionmentioning

confidence: 99%

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Aggregation of Individual Rankings Through Fusion Functions: Criticism and Optimality Analysis

Bustince

Bedregal

Arrastia

et al. 2022

IEEE Trans. Fuzzy Syst.

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Throughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the Social Choice -where well-known impossibility results as the Arrovian ones are encountered-and the Decision-Making approaches -where the necessity of fusing rankings is unavoidable-. Moreover it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice one should look for the maximal elements with respect to such orders defined on rankings.

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Section: Manuscriptmentioning

confidence: 99%

Section: Theorem Iii5 (Arrow's Impossibility Theorem)mentioning

confidence: 99%

Section: Theorem Iii5 (Arrow's Impossibility Theorem)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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