Pub Date : 2023-11-25DOI: 10.1007/s00355-023-01490-2
Chun-Ting Chen, Wei-Torng Juang, Ching-Jen Sun
In this paper we propose a simple axiom which, along with the axioms of additivity (transfer) and dummy player, characterizes the Shapley value (the Shapley–Shubik power index) on the domain of TU (simple) games. The new axiom, cross invariance, demands payoff invariance on symmetric players across “quasi-symmetric games,” that is, games where excluding null players, all players are symmetric. Additionally, we demonstrate that the axiom of additivity can be replaced by a new axiom called strong monotonicity, or it can be completely dropped if a stronger version of cross invariance is employed. We also show that the weighted Shapley values can be characterized using a weighted variant of cross invariance. Efficiency is derived rather than assumed in our characterizations. This fresh perspective contributes to a deeper understanding of the Shapley value and its applicability.
{"title":"Cross invariance, the Shapley value, and the Shapley–Shubik power index","authors":"Chun-Ting Chen, Wei-Torng Juang, Ching-Jen Sun","doi":"10.1007/s00355-023-01490-2","DOIUrl":"https://doi.org/10.1007/s00355-023-01490-2","url":null,"abstract":"<p>In this paper we propose a simple axiom which, along with the axioms of additivity (transfer) and dummy player, characterizes the Shapley value (the Shapley–Shubik power index) on the domain of TU (simple) games. The new axiom, cross invariance, demands payoff invariance on symmetric players across “quasi-symmetric games,” that is, games where excluding null players, all players are symmetric. Additionally, we demonstrate that the axiom of additivity can be replaced by a new axiom called strong monotonicity, or it can be completely dropped if a stronger version of cross invariance is employed. We also show that the weighted Shapley values can be characterized using a weighted variant of cross invariance. Efficiency is derived rather than assumed in our characterizations. This fresh perspective contributes to a deeper understanding of the Shapley value and its applicability.</p>","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"11 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503900","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 : 2023-11-16DOI: 10.1007/s00355-023-01492-0
Xiangyu Qu
Measuring inequality is a challenging task, particularly when data is collected in a coarse manner. This paper proposes a new approach to measuring inequality indices that considers all possible income values and avoids arbitrary statistical assumptions. Specifically, the paper suggests that two sets of income distributions should be considered when measuring inequality, one including the highest income per individual and the other including the lowest possible income per individual. These distributions are subjected to inequality index measures, and a weighted average of these two indices is taken to obtain the final inequality index. This approach provides more accurate measures of inequality while avoiding arbitrary statistical assumptions. The paper focuses on two special cases of social welfare functions, the Atkinson index and the Gini index, which are widely used in the literature on inequality.
{"title":"Inequality measurement with coarse data","authors":"Xiangyu Qu","doi":"10.1007/s00355-023-01492-0","DOIUrl":"https://doi.org/10.1007/s00355-023-01492-0","url":null,"abstract":"<p>Measuring inequality is a challenging task, particularly when data is collected in a coarse manner. This paper proposes a new approach to measuring inequality indices that considers all possible income values and avoids arbitrary statistical assumptions. Specifically, the paper suggests that two sets of income distributions should be considered when measuring inequality, one including the highest income per individual and the other including the lowest possible income per individual. These distributions are subjected to inequality index measures, and a weighted average of these two indices is taken to obtain the final inequality index. This approach provides more accurate measures of inequality while avoiding arbitrary statistical assumptions. The paper focuses on two special cases of social welfare functions, the Atkinson index and the Gini index, which are widely used in the literature on inequality.</p>","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"60 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516847","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 : 2023-11-02DOI: 10.1007/s00355-023-01491-1
Sarvesh Bandhu, Abhinaba Lahiri, Anup Pramanik
{"title":"Stochastic same-sidedness in the random voting model","authors":"Sarvesh Bandhu, Abhinaba Lahiri, Anup Pramanik","doi":"10.1007/s00355-023-01491-1","DOIUrl":"https://doi.org/10.1007/s00355-023-01491-1","url":null,"abstract":"","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"61 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934779","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 : 2023-11-02DOI: 10.1007/s00355-023-01487-x
Agustín G. Bonifacio
{"title":"Variable population manipulations of reallocation rules in economies with single-peaked preferences","authors":"Agustín G. Bonifacio","doi":"10.1007/s00355-023-01487-x","DOIUrl":"https://doi.org/10.1007/s00355-023-01487-x","url":null,"abstract":"","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"37 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135934435","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 : 2023-11-01DOI: 10.1007/s00355-023-01489-9
Alexander Usvitskiy
{"title":"A dynamic model of endogenous development: the role of pioneers","authors":"Alexander Usvitskiy","doi":"10.1007/s00355-023-01489-9","DOIUrl":"https://doi.org/10.1007/s00355-023-01489-9","url":null,"abstract":"","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"360 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135321149","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 : 2023-10-27DOI: 10.1007/s00355-023-01488-w
Jean Baccelli
Abstract It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology.
{"title":"Ordinal utility differences","authors":"Jean Baccelli","doi":"10.1007/s00355-023-01488-w","DOIUrl":"https://doi.org/10.1007/s00355-023-01488-w","url":null,"abstract":"Abstract It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology.","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"10 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263144","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 : 2023-10-10DOI: 10.1007/s00355-023-01486-y
Sacha Bourgeois-Gironde, João V. Ferreira
Abstract Different voting rules are commonly used to settle collective decisions. A promising way to assess voting rules, for which little is known, is to compare the expressive utility that voters derive from voting with each rule. In this paper, we first propose a simple ordinal model of expressive voting that allows us to compare voting rules in terms of the expressive utility that voters can derive from voting (their expressive power ). Our model provides a novel testable implication according to which expected turnout increases with expressive power. We then ran an online experiment testing this implication in a controlled environment. We find that if voters are made aware of alternative voting rules, turnout is higher in voting rules with higher expressive power. Our results also show that higher expressive power is associated with a better representation of voters’ actual preferences and, according to our model, higher expressive utility. This suggests that the expressive power of voting rules is a relevant criterion when choosing between voting rules for economic and political decisions.
{"title":"The expressive power of voting rules","authors":"Sacha Bourgeois-Gironde, João V. Ferreira","doi":"10.1007/s00355-023-01486-y","DOIUrl":"https://doi.org/10.1007/s00355-023-01486-y","url":null,"abstract":"Abstract Different voting rules are commonly used to settle collective decisions. A promising way to assess voting rules, for which little is known, is to compare the expressive utility that voters derive from voting with each rule. In this paper, we first propose a simple ordinal model of expressive voting that allows us to compare voting rules in terms of the expressive utility that voters can derive from voting (their expressive power ). Our model provides a novel testable implication according to which expected turnout increases with expressive power. We then ran an online experiment testing this implication in a controlled environment. We find that if voters are made aware of alternative voting rules, turnout is higher in voting rules with higher expressive power. Our results also show that higher expressive power is associated with a better representation of voters’ actual preferences and, according to our model, higher expressive utility. This suggests that the expressive power of voting rules is a relevant criterion when choosing between voting rules for economic and political decisions.","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295096","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 : 2023-10-04DOI: 10.1007/s00355-023-01484-0
Steven J. Bosworth, Dennis J. Snower
Abstract This paper models the welfare consequences of social fragmentation arising from technological advance. We start from the premise that technological progress falls primarily on market-traded commodities rather than prosocial relationships, since the latter intrinsically require the expenditure of time and thus are less amenable to productivity increases. Since prosocial relationships require individuals to identify with others in their social group whereas marketable commodities are commonly the objects of social status comparisons, a tradeoff arises between in-group affiliation and inter-group status comparisons. People consequently narrow the bounds of their social groups, reducing their prosocial relationships and extending their status-seeking activities. As prosocial relationships generate positive externalities whereas status-seeking activities generate negative preference externalities, technological advance may lead to a particular type of “decoupling” of social welfare from material prosperity. Once the share of status goods in total production exceeds a crucial threshold, technological advance is shown to be welfare-reducing.
{"title":"Technological advance, social fragmentation and welfare","authors":"Steven J. Bosworth, Dennis J. Snower","doi":"10.1007/s00355-023-01484-0","DOIUrl":"https://doi.org/10.1007/s00355-023-01484-0","url":null,"abstract":"Abstract This paper models the welfare consequences of social fragmentation arising from technological advance. We start from the premise that technological progress falls primarily on market-traded commodities rather than prosocial relationships, since the latter intrinsically require the expenditure of time and thus are less amenable to productivity increases. Since prosocial relationships require individuals to identify with others in their social group whereas marketable commodities are commonly the objects of social status comparisons, a tradeoff arises between in-group affiliation and inter-group status comparisons. People consequently narrow the bounds of their social groups, reducing their prosocial relationships and extending their status-seeking activities. As prosocial relationships generate positive externalities whereas status-seeking activities generate negative preference externalities, technological advance may lead to a particular type of “decoupling” of social welfare from material prosperity. Once the share of status goods in total production exceeds a crucial threshold, technological advance is shown to be welfare-reducing.","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"302 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547703","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 : 2023-09-19DOI: 10.1007/s00355-023-01485-z
Dimitrios Xefteris, Nicholas Ziros
{"title":"The “invisible hand” of vote markets","authors":"Dimitrios Xefteris, Nicholas Ziros","doi":"10.1007/s00355-023-01485-z","DOIUrl":"https://doi.org/10.1007/s00355-023-01485-z","url":null,"abstract":"","PeriodicalId":47663,"journal":{"name":"Social Choice and Welfare","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135060931","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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