Pub Date : 2025-05-01Epub Date: 2025-05-12DOI: 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 : 2025-05-01Epub 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":"2025-05-01","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 : 2025-03-01Epub 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":"2025-03-01","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}
Pub Date : 2025-03-01Epub Date: 2025-01-03DOI: 10.1016/j.mathsocsci.2024.12.004
Ratul Lahkar
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.
{"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":"2025-03-01","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}
Pub Date : 2025-03-01Epub 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":"2025-03-01","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 : 2025-03-01Epub 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":"2025-03-01","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 : 2025-03-01Epub Date: 2024-12-20DOI: 10.1016/j.mathsocsci.2024.12.003
Grégory Ponthière , Nicolas Stevens
Dewatripont and Tirole (2024) defend the morality of markets on the ground of an irrelevance result: the social production of moral actions is independent from competitive pressure on markets. No matter how strong competitive pressure is, markets perform well in diffusing signals about moral values and in coordinating suppliers of moral actions. In this article, we argue, on the contrary, that markets lead to a double crowding out of moral values: first, imperfect transmission of moral values on markets leads to an underproduction of moral actions despite the presence of highly ethical suppliers; second, competitive pressure on markets favors the eviction of highly ethical suppliers by less ethical suppliers. Furthermore, we highlight that this double crowding-out restricts the normative scope of the irrelevance result, and raises the question of what the division of moral labor should be between citizens, firms and States.
{"title":"The morality of markets. A critique","authors":"Grégory Ponthière , Nicolas Stevens","doi":"10.1016/j.mathsocsci.2024.12.003","DOIUrl":"10.1016/j.mathsocsci.2024.12.003","url":null,"abstract":"<div><div>Dewatripont and Tirole (2024) defend the morality of markets on the ground of an irrelevance result: the social production of moral actions is independent from competitive pressure on markets. No matter how strong competitive pressure is, markets perform well in diffusing signals about moral values and in coordinating suppliers of moral actions. In this article, we argue, on the contrary, that markets lead to a double crowding out of moral values: first, imperfect transmission of moral values on markets leads to an underproduction of moral actions despite the presence of highly ethical suppliers; second, competitive pressure on markets favors the eviction of highly ethical suppliers by less ethical suppliers. Furthermore, we highlight that this double crowding-out restricts the normative scope of the irrelevance result, and raises the question of what the division of moral labor should be between citizens, firms and States.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"134 ","pages":"Pages 14-19"},"PeriodicalIF":0.5,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143175366","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 : 2025-03-01Epub 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":"2025-03-01","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 : 2025-03-01Epub 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":"2025-03-01","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 : 2025-01-01Epub Date: 2024-11-23DOI: 10.1016/j.mathsocsci.2024.11.003
Aditya Vikram
We investigate the stability of internet platform trading mechanisms using the notion of ex-ante incentive compatible core defined by Forges et al. (2002) in the context of an exchange economy. A mechanism can be blocked by a single buyer and seller pair if they can find an interim incentive-compatible trading mechanism that gives them higher ex-ante expected utilities. Standard double auction mechanisms like the trade reduction mechanism and McAfee double auction mechanism may not be single-buyer–single-seller (SBSS) ex-ante stable. We characterize interim incentive-compatible, interim individually-rational, symmetric and revenue-maximizing mechanisms that are SBSS ex-ante stable using methods in Myerson and Satterthwaite (1983).
{"title":"Stability and optimal double auction design for a two-sided market","authors":"Aditya Vikram","doi":"10.1016/j.mathsocsci.2024.11.003","DOIUrl":"10.1016/j.mathsocsci.2024.11.003","url":null,"abstract":"<div><div>We investigate the stability of internet platform trading mechanisms using the notion of ex-ante incentive compatible core defined by Forges et al. (2002) in the context of an exchange economy. A mechanism can be blocked by a single buyer and seller pair if they can find an interim incentive-compatible trading mechanism that gives them higher ex-ante expected utilities. Standard double auction mechanisms like the trade reduction mechanism and McAfee double auction mechanism may not be single-buyer–single-seller (SBSS) ex-ante stable. We characterize interim incentive-compatible, interim individually-rational, symmetric and revenue-maximizing mechanisms that are SBSS ex-ante stable using methods in Myerson and Satterthwaite (1983).</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"133 ","pages":"Pages 1-12"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743600","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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