Volumetric Aggregation Methods for Scoring Rules with Unknown Weights

IF 3.6 4区 管理学 Q2 MANAGEMENT
Paolo Viappiani
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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.

Abstract Image

未知权重评分规则的体积聚合方法
评分规则是一种常用的排名汇总方法;在社会选择、信息检索和体育等许多场合都经常使用。评分规则的参数是权重向量(评分向量),每个位置一个权重向量,将每个投票者位置对应的权重相加得到的分数最大化的候选者即为获胜者。众所周知,正确设置权重是一项至关重要的任务,因为不同的候选人可以通过不同的评分向量获胜。在本文中,我们提供了几种方法来确定考虑到所有可能权重的获胜者。我们首先提出了 VolumetricTop,这是一种根据代表给备选方案带来最高分的权重集的超多面体对备选方案进行排名的规则,并从社会选择理论的角度对该规则进行了详细分析。为了克服它的一些局限性,我们随后提出了另外两种方法:卷积-径流(Volumetric-runoff)是一种迭代淘汰与最小区域相关的备选方案的规则,直到找到赢家为止;卷积-锦标赛(Volumetric-tournament)则是在成对比较中匹配备选方案;我们对这些规则提出了一些见解。最后,我们提供了一些使用所提方法进行等级聚合的测试案例。
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来源期刊
CiteScore
5.70
自引率
6.70%
发文量
32
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.
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