Closed paths in graphs vs. voting theory

IF 0.9 4区经济学 Q3 ECONOMICS Theory and Decision Pub Date : 2024-05-01 DOI:10.1007/s11238-024-09981-z

Donald G. Saari

引用次数: 0

Abstract

Features of graphs that hinder finding closed paths with particular properties, as represented by the Traveling Salesperson Problem—TSP, are identified for three classes of graphs. Removing these terms leads to a companion graph with identical closed path properties that is easier to analyze. A surprise is that these troubling graph factors are precisely what is needed to analyze certain voting methods, while the companion graph’s terms are what cause voting theory complexities as manifested by Arrow’s Theorem. This means that the seemingly separate goals of analyzing closed paths in graphs and analyzing voting methods are complementary: components of data terms that assist in one of these areas are the source of troubles in the other. Consequences for standard decision methods are in Sects. 2.5, 3.7 and the companion paper (Saari in Theory Decis 91(3):377–402, 2021). The emphasis here is on paths in graphs; incomplete graphs are similarly handled.

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图中的封闭路径与投票理论

通过旅行推销员问题（Traveling Salesperson Problem-TSP），确定了三类图形中阻碍找到具有特定属性的封闭路径的特征。剔除这些因素后，就能得到具有相同封闭路径特性的伴生图，而且更容易分析。令人惊讶的是，这些令人不安的图因素恰恰是分析某些投票方法所需要的，而伴图的术语则是导致投票理论复杂性的原因，如阿罗定理所示。这意味着，分析图中的封闭路径和分析投票方法这两个看似不同的目标是相辅相成的：在其中一个领域有帮助的数据术语的组成部分，在另一个领域却是问题的根源。对标准决策方法的影响见第 2.5 节、第 3.7 节和第 3.8 节。2.5 节、3.7 节及相关论文（萨里在《理论决策》中的论文 91(3):377-402, 2021 年）。这里的重点是图中的路径；不完整图也有类似的处理方法。

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Theory and Decision Multiple-

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1.60

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0.00%

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期刊介绍： The field of decision has been investigated from many sides. However, research programs relevant to decision making in psychology, management science, economics, the theory of games, statistics, operations research, artificial intelligence, cognitive science and analytical philosophy have remained separate. Theory and Decision is devoted to all aspects of decision making belonging to such programs, but addresses also possible cross-fertilizations between these disciplines which would represent effective advances in knowledge. The purpose of the journal is to let the engineering of choice gradually emerge both for individual and for collective decision making. Formalized treatments will be favoured, to the extent that they provide new insights into the issues raised and an appropriate modeling of the situation considered. Due to its growing importance, expermentation in decision making as well as its links to the cognitive sciences will be granted special attention by Theory and Decision. Of particular interest are: Preference and belief modeling, Experimental decision making under risk or under uncertainty, Decision analysis, multicriteria decision modeling, Game theory, negotiation theory, collective decision making, social choice, Rationality, cognitive processes and interactive decision making, Methodology of the decision sciences. Applications to various problems in management and organization science, economics and finance, computer-supported decision schemes, will be welcome as long as they bear on sufficiently general cases. Analysis of actual decision making processes are also relevant topics for the journal, whether pertaining to individual, collective or negotiatory approaches; to private decisions or public policies; to operations or to strategic choices. Officially cited as: Theory Decis

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