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The probability smoothing problem: Characterizations of the Laplace method
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
Bargaining theory and the copyright royalty board’s rate setting decisions for interactive streaming of music
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
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
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
Upper semicontinuous utilities for all upper semicontinuous total preorders
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-15 DOI: 10.1016/j.mathsocsci.2025.01.002
Gianni Bosi, Gabriele Sbaiz
{"title":"Upper semicontinuous utilities for all upper semicontinuous total preorders","authors":"Gianni Bosi,&nbsp;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}
引用次数: 0
Information-based discrimination
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-08 DOI: 10.1016/j.mathsocsci.2025.01.001
Naomi M. Utgoff
{"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}
引用次数: 0
Evolutionary implementation with partially effective institutions
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-03 DOI: 10.1016/j.mathsocsci.2024.12.004
Ratul Lahkar
{"title":"Evolutionary implementation with partially effective institutions","authors":"Ratul Lahkar","doi":"10.1016/j.mathsocsci.2024.12.004","DOIUrl":"10.1016/j.mathsocsci.2024.12.004","url":null,"abstract":"<div><div>We consider large population models of a public goods game and a tragedy of the commons. A planner applies externality pricing in these models. However, institutions in society are only partially effective. Hence, the externality price does not compel agents to internalize externalities fully. The resulting externality-adjusted game with partially effective institutions is a potential game. Evolutionary dynamics converge to its Nash equilibrium. More effective institutions bring this Nash equilibrium closer to the original Pareto efficient state. We trace the effectiveness of institutions to a primeval Tullock contest over natural resources in society. The society’s institutional structure arises from the contest’s Nash equilibrium. The institutional structure is more inclusive if natural resources in the contest are less appropriable. Institutions are then also more effective in implementing externality pricing.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"134 ","pages":"Pages 1-13"},"PeriodicalIF":0.5,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175364","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
Optimal top-n policy
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-01 DOI: 10.1016/j.mathsocsci.2024.12.001
Isa Hafalir , Siqi Pan , Kentaro Tomoeda
{"title":"Optimal top-n policy","authors":"Isa Hafalir ,&nbsp;Siqi Pan ,&nbsp;Kentaro Tomoeda","doi":"10.1016/j.mathsocsci.2024.12.001","DOIUrl":"10.1016/j.mathsocsci.2024.12.001","url":null,"abstract":"<div><div>A widely adopted affirmative action policy in the university sector is the “top-<span><math><mi>n</mi></math></span>” policy, where the universities guarantee admission to students in the top <span><math><mi>n</mi></math></span> fraction of their class from every high school. The efficacy of the top-<span><math><mi>n</mi></math></span> policy in university integration has been questioned because students strategically relocate to low-achieving high schools. We show that when minorities are less likely to strategize than others, the policy can even segregate minorities from the target university, compared to the school-blind policy. A suitably chosen eligibility requirement, featuring the minimum time students must spend at a high school in order to be eligible for top-<span><math><mi>n</mi></math></span> admissions, can restore the efficacy of this policy. However, the most stringent requirement is not always optimal. The optimal requirement depends on the original distribution of students across high schools.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"133 ","pages":"Pages 34-48"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143092906","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
Condorcet domains on at most seven alternatives
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-01 DOI: 10.1016/j.mathsocsci.2024.12.002
Dolica Akello-Egwel , Charles Leedham-Green , Alastair Litterick , Klas Markström , Søren Riis
{"title":"Condorcet domains on at most seven alternatives","authors":"Dolica Akello-Egwel ,&nbsp;Charles Leedham-Green ,&nbsp;Alastair Litterick ,&nbsp;Klas Markström ,&nbsp;Søren Riis","doi":"10.1016/j.mathsocsci.2024.12.002","DOIUrl":"10.1016/j.mathsocsci.2024.12.002","url":null,"abstract":"<div><div>A Condorcet domain is a collection of linear orders which avoid Condorcet’s paradox for majority voting. We have developed a new algorithm for complete enumeration of all maximal Condorcet domains and, using a supercomputer, obtained the first enumeration of all maximal Condorcet domains on <span><math><mrow><mi>n</mi><mo>≤</mo><mn>7</mn></mrow></math></span> alternatives.</div><div>We investigate properties of these domains and use this study to resolve several open questions regarding Condorcet domains, and propose several new conjectures. Following this we connect our results to other domain types used in voting theory, such a non-dictatorial and strategy-proof domains. All our data are made freely available on the web.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"133 ","pages":"Pages 23-33"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143092905","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
With a little help from my friends: Essentiality vs opportunity in group criticality
IF 0.5 4区 经济学
Mathematical Social Sciences Pub Date : 2025-01-01 DOI: 10.1016/j.mathsocsci.2024.11.004
M. Aleandri, M. Dall’Aglio
{"title":"With a little help from my friends: Essentiality vs opportunity in group criticality","authors":"M. Aleandri,&nbsp;M. Dall’Aglio","doi":"10.1016/j.mathsocsci.2024.11.004","DOIUrl":"10.1016/j.mathsocsci.2024.11.004","url":null,"abstract":"<div><div>We define a notion of the criticality of a player for simple monotone games based on cooperation with other players, either to form a winning coalition or to break a winning one, with an essential role for all the players involved. We compare it with the notion of differential criticality given by Beisbart that measures power as the opportunity left by other players.</div><div>We prove that our proposal satisfies an extension of the strong monotonicity introduced by Young, assigns no power to null players, does not reward free riders, and can easily be computed from the minimal winning and blocking coalitions. An application to the Italian elections is presented.</div><div>Our analysis shows that the measures of group criticality defined so far cannot weigh essential players while only remaining an opportunity measure. We propose a group opportunity test to reconcile the two views.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"133 ","pages":"Pages 13-22"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143092907","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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