{"title":"Volumetric Aggregation Methods for Scoring Rules with Unknown Weights","authors":"Paolo Viappiani","doi":"10.1007/s10726-023-09872-8","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":47553,"journal":{"name":"Group Decision and Negotiation","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Group Decision and Negotiation","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1007/s10726-023-09872-8","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MANAGEMENT","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
The idea underlying the journal, Group Decision and Negotiation, emerges from evolving, unifying approaches to group decision and negotiation processes. These processes are complex and self-organizing involving multiplayer, multicriteria, ill-structured, evolving, dynamic problems. Approaches include (1) computer group decision and negotiation support systems (GDNSS), (2) artificial intelligence and management science, (3) applied game theory, experiment and social choice, and (4) cognitive/behavioral sciences in group decision and negotiation. A number of research studies combine two or more of these fields. The journal provides a publication vehicle for theoretical and empirical research, and real-world applications and case studies. In defining the domain of group decision and negotiation, the term `group'' is interpreted to comprise all multiplayer contexts. Thus, organizational decision support systems providing organization-wide support are included. Group decision and negotiation refers to the whole process or flow of activities relevant to group decision and negotiation, not only to the final choice itself, e.g. scanning, communication and information sharing, problem definition (representation) and evolution, alternative generation and social-emotional interaction. Descriptive, normative and design viewpoints are of interest. Thus, Group Decision and Negotiation deals broadly with relation and coordination in group processes. Areas of application include intraorganizational coordination (as in operations management and integrated design, production, finance, marketing and distribution, e.g. as in new products and global coordination), computer supported collaborative work, labor-management negotiations, interorganizational negotiations, (business, government and nonprofits -- e.g. joint ventures), international (intercultural) negotiations, environmental negotiations, etc. The journal also covers developments of software f or group decision and negotiation.