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Dynamics of ideal efforts and consensus in a multi-layer network game 多层网络博弈中理想努力与共识的动态
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-05-01 DOI: 10.1016/j.mathsocsci.2025.102421
Ana Mauleon , Mariam Nanumyan , Vincent Vannetelbosch
{"title":"Dynamics of ideal efforts and consensus in a multi-layer network game","authors":"Ana Mauleon ,&nbsp;Mariam Nanumyan ,&nbsp;Vincent Vannetelbosch","doi":"10.1016/j.mathsocsci.2025.102421","DOIUrl":"10.1016/j.mathsocsci.2025.102421","url":null,"abstract":"<div><div>We study a network game on a fixed multi-layer network of two types of relationships. The social interactions in the first layer carry a pressure to conform with the social norm within the layer. The second layer provides additional strategic complementarities from players’ interaction. Players are endowed with personal ideal efforts and are heterogeneous in their ideal efforts and productivity. Each player repeatedly chooses her effort level in the network game and updates her ideal effort based on the new effort choice. Each player suffers disutility when her effort differs from her neighbors’ efforts or is inconsistent with her ideal effort. We find the pure Nash equilibrium of the game in each period and provide conditions for the convergence of efforts and ideals to a steady state. Furthermore, we find that the sensitivity to cognitive dissonance and the taste for conformity have opposing effects on the speed of convergence to a consensus and the steady state.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"135 ","pages":"Article 102421"},"PeriodicalIF":0.5,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Condorcet efficiency: Weighted Bucklin vs. weighted scoring and Borda 孔多塞效率：加权巴克林vs加权得分和博尔达
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-05-01 DOI: 10.1016/j.mathsocsci.2025.102420
D. Marc Kilgour , Jean-Charles Grégoire , Angèle M. Foley
{"title":"Condorcet efficiency: Weighted Bucklin vs. weighted scoring and Borda","authors":"D. Marc Kilgour ,&nbsp;Jean-Charles Grégoire ,&nbsp;Angèle M. Foley","doi":"10.1016/j.mathsocsci.2025.102420","DOIUrl":"10.1016/j.mathsocsci.2025.102420","url":null,"abstract":"<div><div>We ask how good Bucklin-related procedures can be at identifying Condorcet winners in ranked-ballot, single-winner elections. Bucklin procedures can have a wide range of weighting vectors and thresholds; one, for example, applies Borda weights, analogous to the Borda Count in weighted scoring elections. Using simulation, we estimate the maximum Condorcet efficiency of both weighted Bucklin and weighted scoring elections as the number of voters becomes very large; these measures depend of course on the underlying distribution of ballots. For the impartial anonymous culture distribution, weighted Bucklin exhibits higher Condorcet efficiency than weighted scoring when there are 3 candidates, but is not as good when there are 4 candidates, and about equal when there are 5 or 6. We also compare them under the impartial culture distribution (equally good), and under a one-dimensional spatial model (weighted Bucklin is usually better, sometimes much better).</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"135 ","pages":"Article 102420"},"PeriodicalIF":0.5,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fuzzy classification aggregation 模糊分类聚合
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-05-01 DOI: 10.1016/j.mathsocsci.2025.102422
Federico Fioravanti
{"title":"Fuzzy classification aggregation","authors":"Federico Fioravanti","doi":"10.1016/j.mathsocsci.2025.102422","DOIUrl":"10.1016/j.mathsocsci.2025.102422","url":null,"abstract":"<div><div>We consider the problem where a set of individuals has to classify <span><math><mi>m</mi></math></span> objects into <span><math><mi>p</mi></math></span> categories and does so by aggregating the individual classifications. We show that if <span><math><mrow><mi>m</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, <span><math><mrow><mi>m</mi><mo>≥</mo><mi>p</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, and classifications are fuzzy, that is, objects belong to a category to a certain degree, then an optimal and independent aggregator rule that satisfies a weak unanimity condition belongs to the family of Weighted Arithmetic Means. We also obtain characterization results for <span><math><mrow><mi>m</mi><mo>=</mo><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"135 ","pages":"Article 102422"},"PeriodicalIF":0.5,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Election methods and political polarization 选举方法和政治两极分化
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-05-01 DOI: 10.1016/j.mathsocsci.2025.102417
Salvatore Barbaro
{"title":"Election methods and political polarization","authors":"Salvatore Barbaro","doi":"10.1016/j.mathsocsci.2025.102417","DOIUrl":"10.1016/j.mathsocsci.2025.102417","url":null,"abstract":"<div><div>Political polarization poses a significant challenge to democratic societies. While much of the scholarly focus has been on the socio-demographic factors that drive polarization, this paper focuses on voting rules and their effects on the incentives for candidates to be moderate or polarizing. It addresses the question: Which voting methods most impede the success of a polarizing candidate? Through a comparative analysis of plurality voting, the Condorcet method, and Borda’s rule, we find the Borda rule to be the most effective at discouraging extreme platforms. In a generalization, we show that a scoring rule is more effective at hindering the success of polarizing candidates the more weight that it places on voters’ second preferences in the tallying process.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"135 ","pages":"Article 102417"},"PeriodicalIF":0.5,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Competitive attractiveness measurement in sports leagues: Sequential procedures for heterogeneous competitors 体育联盟的竞争吸引力测量：异质竞争者的顺序程序
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-04-15 DOI: 10.1016/j.mathsocsci.2025.102410
Marc Dubois
{"title":"Competitive attractiveness measurement in sports leagues: Sequential procedures for heterogeneous competitors","authors":"Marc Dubois","doi":"10.1016/j.mathsocsci.2025.102410","DOIUrl":"10.1016/j.mathsocsci.2025.102410","url":null,"abstract":"<div><div>The paper proposes three dominance criteria that assess whether one seasonal outcome of a sports league is more attractive than another, taking into account their respective competitive balance levels. Seasonal outcomes are distributions of seasonal points involving heterogeneous competitors (having varying sizes of fan bases). The proposed criteria are the first-degree sequential downward (FSD), second-degree sequential upward (SSU), and third-degree sequential downward (TSD) dominance criteria. The FSD criterion is axiomatically characterized in line with two principles, which require that a famous competitor (with a large fan base) matters more for attractiveness than a common competitor (with a small fan base). The SSU criterion relies on the same principles that characterize the FSD criterion and on two additional ones. First, attractiveness should increase with respect to competitive balance. Second, balance among famous competitors is more important than balance among common competitors. The TSD criterion relies on all the aforementioned principles and incorporates upside sensitivity, emphasizing that a balanced race among many famous competitors enhances attractiveness. An illustrative application provides comparisons of seasonal outcomes of the English Premier League from 2014–2015 to 2018–2019.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"135 ","pages":"Article 102410"},"PeriodicalIF":0.5,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The probability smoothing problem: Characterizations of the Laplace method 概率平滑问题：拉普拉斯方法的表征
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-04-02 DOI: 10.1016/j.mathsocsci.2025.102409
Toyotaka Sakai
{"title":"The probability smoothing problem: Characterizations of the Laplace method","authors":"Toyotaka Sakai","doi":"10.1016/j.mathsocsci.2025.102409","DOIUrl":"10.1016/j.mathsocsci.2025.102409","url":null,"abstract":"<div><div>We formulate an axiomatic model to analyze the problem of probability smoothing in Naïve Bayes. We define several desirable properties of smoothing methods. Our main result shows that the Laplace smoothing method is the only one that satisfies <em>ratio preservation</em>, <em>order preservation</em>, and <em>positivity</em>. An alternative characterization based on <em>reallocation-proofness</em> is also obtained.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"135 ","pages":"Article 102409"},"PeriodicalIF":0.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-winner rules analogous to the Plurality rule 多赢家规则类似于多数规则
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-03-22 DOI: 10.1016/j.mathsocsci.2025.102405
Clinton Gubong Gassi , Frank Steffen
{"title":"Multi-winner rules analogous to the Plurality rule","authors":"Clinton Gubong Gassi ,&nbsp;Frank Steffen","doi":"10.1016/j.mathsocsci.2025.102405","DOIUrl":"10.1016/j.mathsocsci.2025.102405","url":null,"abstract":"<div><div>The aim of this paper is to identify the multi-winner voting rules that can be considered as extensions of the Plurality rule when voters’ preferences are expressed as linear rankings over the candidates. Multi-winner voting addresses the problem of selecting a fixed-size subset of candidates, called a <em>committee</em>, from a larger set of available candidates based on the voters’ preferences. In the single-winner setting, where each voter provides a strict ranking of the candidates and the goal is to select a unique candidate, Yeh (2008) characterized the Plurality rule as the only voting rule satisfying five independent axioms: anonymity, neutrality, consistency, efficiency, and top-only. In this paper, we demonstrate that a natural extension of these axioms to the multi-winner framework allows us to identify a class of <em>top-</em><span><math><mi>k</mi></math></span> <em>counting rules</em> as multi-winner analogous to the Plurality rule, that does not contain the classical <span><math><mi>k</mi></math></span>-Plurality rule.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"135 ","pages":"Article 102405"},"PeriodicalIF":0.5,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bargaining theory and the copyright royalty board’s rate setting decisions for interactive streaming of music 讨价还价理论和版权版税委员会的费率设置决策的交互式流媒体音乐
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-02-11 DOI: 10.1016/j.mathsocsci.2025.01.005
Elliott Hughes , Richard Watt
{"title":"Bargaining theory and the copyright royalty board’s rate setting decisions for interactive streaming of music","authors":"Elliott Hughes ,&nbsp;Richard Watt","doi":"10.1016/j.mathsocsci.2025.01.005","DOIUrl":"10.1016/j.mathsocsci.2025.01.005","url":null,"abstract":"<div><div>In the USA, the remuneration for songwriters whose copyrighted material is broadcast using online interactive music services is subject to a compulsory license with a rate that is regulated by the Copyright Royalty Board. On the other hand, an essentially equally necessary input to the interactive music services, namely the sound recording copyright, is freely negotiated between the parties. This sets up an interesting bargaining problem that is of interest to the regulator. The present paper sets out this problem formally, and resolves the equilibrium outcomes. The model is calibrated with the actual rates that have been set recently.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"134 ","pages":"Pages 58-65"},"PeriodicalIF":0.5,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A measurement of population ageing: From the perspective of thickness of the labor force 人口老龄化的测度：基于劳动力厚度的视角
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-31 DOI: 10.1016/j.mathsocsci.2025.01.004
Yoko Kawada , Yuta Nakamura , Noriaki Okamoto
{"title":"A measurement of population ageing: From the perspective of thickness of the labor force","authors":"Yoko Kawada ,&nbsp;Yuta Nakamura ,&nbsp;Noriaki Okamoto","doi":"10.1016/j.mathsocsci.2025.01.004","DOIUrl":"10.1016/j.mathsocsci.2025.01.004","url":null,"abstract":"<div><div>We propose a new measure of population ageing, and introduce a new condition called the <em>working-age principle</em>, which is a sensitivity condition to the “thickness” of the working-age population. Then, we characterize our measure by <em>working-age principle</em> and the other standard axioms. We also applied our measure to compute the degree of ageing in China, Japan, Niue, and Singapore, highlighting its importance in capturing the thickness of the labor force.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"134 ","pages":"Pages 50-57"},"PeriodicalIF":0.5,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cooperative games with types, outside options, and the egalitarian value 具有类型、外部选择和平等价值的合作游戏
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-22 DOI: 10.1016/j.mathsocsci.2025.01.003
Florian Navarro
{"title":"Cooperative games with types, outside options, and the egalitarian value","authors":"Florian Navarro","doi":"10.1016/j.mathsocsci.2025.01.003","DOIUrl":"10.1016/j.mathsocsci.2025.01.003","url":null,"abstract":"<div><div>This article introduces a new axiom of sub-game order preservation for TU-games as well as a model of cooperative games with types. The axiom, alongside efficiency, characterizes the egalitarian value. The model addresses situations where players of different types are needed. Each player has a specific type and coalitions are feasible only if it contains at most one player of each type. We use the new characterization of the egalitarian value for TU-games to obtain the following result in our class of problems: the egalitarian value is the only sharing rule that ensures that each player of the most productive group is better off joining this most productive group. We characterize the egalitarian value without fairness requirement and show that, for this new class of problems, egalitarianism can provide some form of incentives towards optimal cooperation.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"134 ","pages":"Pages 42-49"},"PeriodicalIF":0.5,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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