Volumetric Aggregation Methods for Scoring Rules with Unknown Weights

Paolo Viappiani ()
Additional contact information
Paolo Viappiani: Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres, LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: Scoring rules are a popular method for aggregating rankings; they are frequently used in many settings, including social choice, information retrieval and sports. Scoring rules are parametrized by a vector of weights (the scoring vectors), one for each position, and declare as winner the candidate that maximizes the score obtained when summing up the weights corresponding to the position of each voter. It is well known that properly setting the weights is a crucial task, as different candidates can win with different scoring vectors. In this paper, we provide several methods to identify the winner considering all possible weights. We first propose VolumetricTop, a rule that ranks alternatives based on the hyper-polytope representing the set of weights that give the alternative the highest score, and provide a detailed analysis of the rule from the point-of-view of social choice theory. In order to overcome some of its limitations, we then propose two other methods: Volumetric-runoff, a rule that iteratively eliminates the alternative associated with the smallest region until a winner is found, and Volumetric-tournament, where alternatives are matched in pairwise comparisons; we provide several insights about these rules. Finally we provide some test cases of rank aggregation using the proposed methods.

Date: 2024-02-25
New Economics Papers: this item is included in nep-spo
Note: View the original document on HAL open archive server: https://hal.science/hal-04440153v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Group Decision and Negotiation, 2024, 33 (3), pp.515-563. ⟨10.1007/s10726-023-09872-8⟩

Downloads: (external link)
https://hal.science/hal-04440153v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04440153

DOI: 10.1007/s10726-023-09872-8

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().