Pub Date : 2025-05-01DOI: 10.1016/j.mathsocsci.2025.102422
Federico Fioravanti
We consider the problem where a set of individuals has to classify objects into categories and does so by aggregating the individual classifications. We show that if , , 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 .
{"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}
Pub Date : 2025-05-01DOI: 10.1016/j.mathsocsci.2025.102417
Salvatore Barbaro
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.
{"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}
Pub Date : 2025-04-15DOI: 10.1016/j.mathsocsci.2025.102410
Marc Dubois
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.
{"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}
Pub Date : 2025-04-02DOI: 10.1016/j.mathsocsci.2025.102409
Toyotaka Sakai
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 ratio preservation, order preservation, and positivity. An alternative characterization based on reallocation-proofness is also obtained.
{"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}
Pub Date : 2025-03-22DOI: 10.1016/j.mathsocsci.2025.102405
Clinton Gubong Gassi , Frank Steffen
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 committee, 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 top-counting rules as multi-winner analogous to the Plurality rule, that does not contain the classical -Plurality rule.
{"title":"Multi-winner rules analogous to the Plurality rule","authors":"Clinton Gubong Gassi , 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}
Pub Date : 2025-02-11DOI: 10.1016/j.mathsocsci.2025.01.005
Elliott Hughes , Richard Watt
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.
{"title":"Bargaining theory and the copyright royalty board’s rate setting decisions for interactive streaming of music","authors":"Elliott Hughes , 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}
Pub Date : 2025-01-31DOI: 10.1016/j.mathsocsci.2025.01.004
Yoko Kawada , Yuta Nakamura , Noriaki Okamoto
We propose a new measure of population ageing, and introduce a new condition called the working-age principle, which is a sensitivity condition to the “thickness” of the working-age population. Then, we characterize our measure by working-age principle 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.
{"title":"A measurement of population ageing: From the perspective of thickness of the labor force","authors":"Yoko Kawada , Yuta Nakamura , 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}
Pub Date : 2025-01-22DOI: 10.1016/j.mathsocsci.2025.01.003
Florian Navarro
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.
{"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}
Pub Date : 2025-01-15DOI: 10.1016/j.mathsocsci.2025.01.002
Gianni Bosi, Gabriele Sbaiz
Let be an arbitrary nonempty set. Then a topology on is said to be completely useful (or upper useful) if every upper semicontinuous total preorder on the topological space can be represented by an upper semicontinuous real-valued order-preserving function (i.e., utility function). In this paper the structures of completely useful topologies on will be deeply studied and clarified. In particular, completely useful topologies will be characterized through the new notions of super-short and strongly separable topologies. Further, the incorporation of the Souslin Hypothesis and the relevance of these characterizations in mathematical utility theory will be discussed. Finally, various interrelations between the concepts of complete usefulness and other topological concepts that are of interest not only in mathematical utility theory are analyzed.
{"title":"Upper semicontinuous utilities for all upper semicontinuous total preorders","authors":"Gianni Bosi, Gabriele Sbaiz","doi":"10.1016/j.mathsocsci.2025.01.002","DOIUrl":"10.1016/j.mathsocsci.2025.01.002","url":null,"abstract":"<div><div>Let <span><math><mi>X</mi></math></span> be an arbitrary nonempty set. Then a topology <span><math><mi>t</mi></math></span> on <span><math><mi>X</mi></math></span> is said to be <em>completely useful</em> (or <em>upper useful</em>) if every upper semicontinuous <em>total</em> preorder <span><math><mo>≾</mo></math></span> on the topological space <span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math></span> can be represented by an upper semicontinuous real-valued order-preserving function (i.e., utility function). In this paper the structures of completely useful topologies on <span><math><mi>X</mi></math></span> will be deeply studied and clarified. In particular, completely useful topologies will be characterized through the new notions of super-short and strongly separable topologies. Further, the incorporation of the <em>Souslin Hypothesis</em> and the relevance of these characterizations in mathematical utility theory will be discussed. Finally, various interrelations between the concepts of complete usefulness and other topological concepts that are of interest not only in mathematical utility theory are analyzed.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"134 ","pages":"Pages 31-41"},"PeriodicalIF":0.5,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175367","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}
Pub Date : 2025-01-08DOI: 10.1016/j.mathsocsci.2025.01.001
Naomi M. Utgoff
The distribution of a single college’s incoming freshman cohort by high school of origin differs from the population distribution of high school seniors (Bernhard, 2013), a fact typically attributed to taste-based or statistical discrimination. This paper models a third explanation which I call information-based discrimination: information asymmetries between a college and high schools incentivize the formation of a relationship between the college and one ex ante randomly selected high school, resulting in de facto discriminatory admissions even in the absence of taste-based and statistical discrimination. I construct an admissions game between one college and identical in expectation high schools. The game features a perfect Bayesian equilibrium in which the ex ante randomly chosen high school provides truthful information to the college in exchange for future favorable admission treatment. When agents are sufficiently patient, this relationship between the college and the initially randomly chosen high school is sustained in equilibrium. This equilibrium increases overall admissions efficiency relative to but does not Pareto improve on a dominant strategy implementable alternative: the welfare gains accrue entirely to the college and high school in the relationship while harming students from all other high schools.
{"title":"Information-based discrimination","authors":"Naomi M. Utgoff","doi":"10.1016/j.mathsocsci.2025.01.001","DOIUrl":"10.1016/j.mathsocsci.2025.01.001","url":null,"abstract":"<div><div>The distribution of a single college’s incoming freshman cohort by high school of origin differs from the population distribution of high school seniors (Bernhard, 2013), a fact typically attributed to taste-based or statistical discrimination. This paper models a third explanation which I call <em>information-based discrimination</em>: information asymmetries between a college and high schools incentivize the formation of a relationship between the college and one <em>ex ante</em> randomly selected high school, resulting in <em>de facto</em> discriminatory admissions even in the absence of taste-based and statistical discrimination. I construct an admissions game between one college and <span><math><mi>N</mi></math></span> identical in expectation high schools. The game features a perfect Bayesian equilibrium in which the <em>ex ante</em> randomly chosen high school provides truthful information to the college in exchange for future favorable admission treatment. When agents are sufficiently patient, this relationship between the college and the initially randomly chosen high school is sustained in equilibrium. This equilibrium increases overall admissions efficiency relative to but does not Pareto improve on a dominant strategy implementable alternative: the welfare gains accrue entirely to the college and high school in the relationship while harming students from all other high schools.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"134 ","pages":"Pages 20-30"},"PeriodicalIF":0.5,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175365","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}
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