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The rates of learning with public and private signals 公共信号和私人信号的学习率
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-06-18 DOI: 10.1016/j.mathsocsci.2025.102433
Dengwei Qi
{"title":"The rates of learning with public and private signals","authors":"Dengwei Qi","doi":"10.1016/j.mathsocsci.2025.102433","DOIUrl":"10.1016/j.mathsocsci.2025.102433","url":null,"abstract":"<div><div>This paper presents a dynamic market-based learning model, in which agents trade a risky asset repeatedly while observing public and private endogenous signals about market prices and demands. We explicitly characterize the changes in precisions of agents’ beliefs about the market, and demonstrate that complete learning is achieved in the limit. Moreover, we show that the asymptotic learning rates of both public and private signals attain the highest possible rate in the model, which is linear, thereby establishing the asymptotic learning efficiency. Factors that influence the learning speed and asymptotic rates are also identified. We also prove that the asymptotic learning efficiency applies to other learning situations.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"136 ","pages":"Article 102433"},"PeriodicalIF":0.5,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313440","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
Aggregating incomplete rankings 汇总不完全排名
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-06-11 DOI: 10.1016/j.mathsocsci.2025.102423
Yasunori Okumura
{"title":"Aggregating incomplete rankings","authors":"Yasunori Okumura","doi":"10.1016/j.mathsocsci.2025.102423","DOIUrl":"10.1016/j.mathsocsci.2025.102423","url":null,"abstract":"<div><div>This study considers a method for deriving a ranking of alternatives by aggregating the rankings submitted by multiple individuals, each of whom need not evaluate all of the alternatives. We call the collection of subsets of alternatives that individuals can evaluate an evaluability profile. For a given evaluability profile, we define an aggregating ranking function whose inputs are the rankings provided by individuals on the alternatives that they evaluate. We investigate the properties of such functions, focusing on modified versions of the properties originally introduced by Arrow and his followers. Whether there exists an aggregating ranking function that satisfies a given combination of the properties depends on the evaluability profile. Accordingly, we identify the necessary and sufficient conditions on evaluability profiles to ensure the existence of functions that satisfy four different combinations of the properties. Finally, we discuss whether these properties are satisfied in a real-world scenario.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"136 ","pages":"Article 102423"},"PeriodicalIF":0.5,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279188","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
Existence of Berge equilibrium in finite games 有限对策中Berge均衡的存在性
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-05-21 DOI: 10.1016/j.mathsocsci.2025.102419
Hans Haller
{"title":"Existence of Berge equilibrium in finite games","authors":"Hans Haller","doi":"10.1016/j.mathsocsci.2025.102419","DOIUrl":"10.1016/j.mathsocsci.2025.102419","url":null,"abstract":"<div><div>This investigation is focused primarily on the existence of Berge equilibrium in finite games. A secondary concern is the comparison of Berge equilibrium existence and Nash equilibrium existence.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"136 ","pages":"Article 102419"},"PeriodicalIF":0.5,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195735","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
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
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