{"title":"图中的封闭路径与投票理论","authors":"Donald G. Saari","doi":"10.1007/s11238-024-09981-z","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":47535,"journal":{"name":"Theory and Decision","volume":"13 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Closed paths in graphs vs. voting theory\",\"authors\":\"Donald G. Saari\",\"doi\":\"10.1007/s11238-024-09981-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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.</p>\",\"PeriodicalId\":47535,\"journal\":{\"name\":\"Theory and Decision\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory and Decision\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.1007/s11238-024-09981-z\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory and Decision","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s11238-024-09981-z","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
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.
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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