A generalization to networks of Young’s characterization of the Borda rule

IF 4.5 3区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Daniela Bubboloni, Michele Gori
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引用次数: 0

Abstract

We prove that, for any given set of networks satisfying suitable conditions, the net-oudegree network solution, the net-indegree network solution, and the total network solution are the unique network solutions on that set satisfying neutrality, consistency and cancellation. The generality of the result obtained allows to get an analogous result for social choice correspondences: for any given set of preference profiles satisfying suitable conditions, the net-oudegree social choice correspondence, the net-indegree social choice correspondence and the total social choice correspondence are the unique social choice correspondences on that set satisfying neutrality, consistency and cancellation. Using the notable fact that several well-known voting rules coincide with the restriction of the net-outdegree social choice correspondence to appropriate sets of preference profiles, we are able to deduce a variety of new and known characterization theorems for the Borda rule, the Partial Borda rule, the Averaged Borda rule, the Approval Voting, the Plurality rule and the anti-Plurality rule, among which Young’s characterization of the Borda rule and Fishburn’s characterization of the Approval Voting.

将杨的波达规则的特征推广到网络
证明了对于任何给定的满足适当条件的网络集合,网络外度解、网络内度解和网络总解是该集合上满足中立性、一致性和消去性的唯一网络解。所得结果的通用性使得我们可以得到社会选择对应的类似结果:对于任何给定的满足适当条件的偏好概况集,净度社会选择对应、净度社会选择对应和总社会选择对应是该集合上满足中立性、一致性和消去性的唯一社会选择对应。利用一些众所周知的投票规则与网络外度社会选择对应于适当偏好配置文件集的限制相一致的值得注意的事实,我们能够为Borda规则、部分Borda规则、平均Borda规则、批准投票、多数规则和反多数规则推导出各种新的和已知的特征定理。其中Young对Borda规则的描述和Fishburn对赞成投票的描述。
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来源期刊
Annals of Operations Research
Annals of Operations Research 管理科学-运筹学与管理科学
CiteScore
7.90
自引率
16.70%
发文量
596
审稿时长
8.4 months
期刊介绍: The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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