Pub Date : 2020-01-12DOI: 10.1080/0022250x.2019.1704284
F. Bianchi, A. Flache, F. Squazzoni
ABSTRACT This article examines the emergence of solidarity from interactions between professionals competing for collaboration. Research on multiplex collaboration networks has shown that economic exchange can elicit solidarity when mediated by trust but did not consider the effect of competition. To fill this gap, we built an agent-based model that simulates the evolution of a multiplex network of collaboration, trust, and support expectations. Simulations show that while resource heterogeneity is key for collaboration, competition for attractive collaboration partners penalizes low-resource professionals, who are less connected and highly segregated. Heterogeneous resource distribution can trigger segregation because of preferential selection of resourceful peers and reciprocity. Interestingly, we also found that low-resource professionals can reduce their marginalization by building in-group mutual support expectations.
{"title":"Solidarity in collaboration networks when everyone competes for the strongest partner: a stochastic actor-based simulation model","authors":"F. Bianchi, A. Flache, F. Squazzoni","doi":"10.1080/0022250x.2019.1704284","DOIUrl":"https://doi.org/10.1080/0022250x.2019.1704284","url":null,"abstract":"ABSTRACT This article examines the emergence of solidarity from interactions between professionals competing for collaboration. Research on multiplex collaboration networks has shown that economic exchange can elicit solidarity when mediated by trust but did not consider the effect of competition. To fill this gap, we built an agent-based model that simulates the evolution of a multiplex network of collaboration, trust, and support expectations. Simulations show that while resource heterogeneity is key for collaboration, competition for attractive collaboration partners penalizes low-resource professionals, who are less connected and highly segregated. Heterogeneous resource distribution can trigger segregation because of preferential selection of resourceful peers and reciprocity. Interestingly, we also found that low-resource professionals can reduce their marginalization by building in-group mutual support expectations.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250x.2019.1704284","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43010316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-12DOI: 10.1080/0022250x.2020.1711753
Neng-pin Lu
ABSTRACT For measuring the centrality in a digraph, Bonacich and Lloyd summarized a vector, from the power series of an attenuated adjacency matrix, as the alpha centrality. However, scores of alpha centrality are usually dominated by nodes in the strongly connected component, which owns the largest eigenvalue of the adjacency matrix. In this paper, based on reachability between strongly connected components, we consider not only the largest eigenvalue but also the other smaller ones to attenuate the adjacency matrix hierarchically; and obtain a measure from the power series of the hierarchically attenuated adjacency matrix. Consequently, we propose the hierarchical alpha centrality, which can yield higher scores for nodes at higher hierarchies of reachability in a digraph.
{"title":"A hierarchical walk-based measure of centrality based on reachability between strongly connected components in a digraph","authors":"Neng-pin Lu","doi":"10.1080/0022250x.2020.1711753","DOIUrl":"https://doi.org/10.1080/0022250x.2020.1711753","url":null,"abstract":"ABSTRACT For measuring the centrality in a digraph, Bonacich and Lloyd summarized a vector, from the power series of an attenuated adjacency matrix, as the alpha centrality. However, scores of alpha centrality are usually dominated by nodes in the strongly connected component, which owns the largest eigenvalue of the adjacency matrix. In this paper, based on reachability between strongly connected components, we consider not only the largest eigenvalue but also the other smaller ones to attenuate the adjacency matrix hierarchically; and obtain a measure from the power series of the hierarchically attenuated adjacency matrix. Consequently, we propose the hierarchical alpha centrality, which can yield higher scores for nodes at higher hierarchies of reachability in a digraph.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250x.2020.1711753","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42364403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-09DOI: 10.1080/0022250X.2020.1818078
C. Blex, T. Yasseri
ABSTRACT Fragmentation, echo chambers, and their amelioration in social networks have been a growing concern in the academic and non-academic world. This paper shows how, under the assumption of homophily, echo chambers and fragmentation are system-immanent phenomena of highly flexible social networks, even under ideal conditions for heterogeneity. We achieve this by finding an analytical, network-based solution to the Schelling model and by proving that weak ties do not hinder the process. Furthermore, we derive that no level of positive algorithmic bias in the form of rewiring is capable of preventing fragmentation and its effect on reducing the fragmentation speed is negligible.
{"title":"Positive algorithmic bias cannot stop fragmentation in homophilic networks","authors":"C. Blex, T. Yasseri","doi":"10.1080/0022250X.2020.1818078","DOIUrl":"https://doi.org/10.1080/0022250X.2020.1818078","url":null,"abstract":"ABSTRACT Fragmentation, echo chambers, and their amelioration in social networks have been a growing concern in the academic and non-academic world. This paper shows how, under the assumption of homophily, echo chambers and fragmentation are system-immanent phenomena of highly flexible social networks, even under ideal conditions for heterogeneity. We achieve this by finding an analytical, network-based solution to the Schelling model and by proving that weak ties do not hinder the process. Furthermore, we derive that no level of positive algorithmic bias in the form of rewiring is capable of preventing fragmentation and its effect on reducing the fragmentation speed is negligible.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2020.1818078","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47752323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-04DOI: 10.1080/0022250X.2020.1746298
C. Butts
ABSTRACT Although it is well known that some exponential family random graph model (ERGM) families exhibit phase transitions (in which small parameter changes lead to qualitative changes in graph structure), the behavior of other models is still poorly understood. Recently, Krivitsky and Morris have reported a previously unobserved phase transition in the edge/concurrent vertex family (a simple starting point for models of sexual contact networks). Here, we examine this phase transition, showing it to be a first-order transition with respect to an order parameter associated with the fraction of concurrent vertices. This transition stems from weak cooperativity in the recruitment of vertices to the concurrent phase, which may not be a desirable property in some applications.
{"title":"Phase transitions in the edge/concurrent vertex model","authors":"C. Butts","doi":"10.1080/0022250X.2020.1746298","DOIUrl":"https://doi.org/10.1080/0022250X.2020.1746298","url":null,"abstract":"ABSTRACT Although it is well known that some exponential family random graph model (ERGM) families exhibit phase transitions (in which small parameter changes lead to qualitative changes in graph structure), the behavior of other models is still poorly understood. Recently, Krivitsky and Morris have reported a previously unobserved phase transition in the edge/concurrent vertex family (a simple starting point for models of sexual contact networks). Here, we examine this phase transition, showing it to be a first-order transition with respect to an order parameter associated with the fraction of concurrent vertices. This transition stems from weak cooperativity in the recruitment of vertices to the concurrent phase, which may not be a desirable property in some applications.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2020.1746298","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49144351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-02DOI: 10.1080/0022250X.2019.1630832
Paulo L. dos Santos, N. Wiener
ABSTRACT This paper applies information-theoretic measures to consider the systemic effects on individual incomes of complex patterns of social and economic discrimination by race, ethnicity, and gender in the U.S. It estimates non-parametric indices of joint, conditional or incremental, and mutual information between income, social identity, and observable economic characteristics obtained using large-scale cross-sectional data from that economy. The paper advances new conceptual and empirical approaches to the nature and measurement of economic discrimination and inequalities of opportunity, founded on the formal informativeness of measures of social identity on economic outcomes. Estimated values for indices of informational association also cast new light on the effects of the intersections of gender and race/ethnicity on income, perverse patterns in the effects of education across different groups, and a few notable dynamic changes in patterns of income distribution in that economy over the past 40 years.
{"title":"By the content of their character? Discrimination, social identity, and observed distributions of income","authors":"Paulo L. dos Santos, N. Wiener","doi":"10.1080/0022250X.2019.1630832","DOIUrl":"https://doi.org/10.1080/0022250X.2019.1630832","url":null,"abstract":"ABSTRACT This paper applies information-theoretic measures to consider the systemic effects on individual incomes of complex patterns of social and economic discrimination by race, ethnicity, and gender in the U.S. It estimates non-parametric indices of joint, conditional or incremental, and mutual information between income, social identity, and observable economic characteristics obtained using large-scale cross-sectional data from that economy. The paper advances new conceptual and empirical approaches to the nature and measurement of economic discrimination and inequalities of opportunity, founded on the formal informativeness of measures of social identity on economic outcomes. Estimated values for indices of informational association also cast new light on the effects of the intersections of gender and race/ethnicity on income, perverse patterns in the effects of education across different groups, and a few notable dynamic changes in patterns of income distribution in that economy over the past 40 years.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2019.1630832","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42651209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-02DOI: 10.1080/0022250X.2019.1611576
Lennon Ó Náraigh
ABSTRACT We introduce a model based on Ordinary Differential Equations to describe how two mutually exclusive groups progress through a career hierarchy, whether in a single organization, or in an entire economic sector. The intended application is to gender imbalance at the top of the academic hierarchy in European Universities; however, the model is entirely generic and may be applied in other contexts also. Previous research on gender imbalance in European universities has focused on large-scale statistical studies. Our model represents a point of departure, as it is deterministic (i.e., based on Ordinary Differential Equations). The model requires a precise definition of the progression rates for the different groups through the hierarchy; these are key parameters governing the dynamics of career progression. The progression rate for each group can be decomposed into a product: the proportion of group members at a low level in the hierarchy who compete for promotion to the next level a given year, multiplied by the in-competition success rate for the group in question. Either of these two parameters can differ across the groups under consideration; this introduces a group asymmetry into the organization’s composition. We introduce a glass-ceiling index to summarize this asymmetry succinctly. Using case studies from the literature, we demonstrate how the mathematical framework can pinpoint the proximate cause of the glass ceiling in European academia.
{"title":"A differential-equation-based model of the glass ceiling in career progression","authors":"Lennon Ó Náraigh","doi":"10.1080/0022250X.2019.1611576","DOIUrl":"https://doi.org/10.1080/0022250X.2019.1611576","url":null,"abstract":"ABSTRACT We introduce a model based on Ordinary Differential Equations to describe how two mutually exclusive groups progress through a career hierarchy, whether in a single organization, or in an entire economic sector. The intended application is to gender imbalance at the top of the academic hierarchy in European Universities; however, the model is entirely generic and may be applied in other contexts also. Previous research on gender imbalance in European universities has focused on large-scale statistical studies. Our model represents a point of departure, as it is deterministic (i.e., based on Ordinary Differential Equations). The model requires a precise definition of the progression rates for the different groups through the hierarchy; these are key parameters governing the dynamics of career progression. The progression rate for each group can be decomposed into a product: the proportion of group members at a low level in the hierarchy who compete for promotion to the next level a given year, multiplied by the in-competition success rate for the group in question. Either of these two parameters can differ across the groups under consideration; this introduces a group asymmetry into the organization’s composition. We introduce a glass-ceiling index to summarize this asymmetry succinctly. Using case studies from the literature, we demonstrate how the mathematical framework can pinpoint the proximate cause of the glass ceiling in European academia.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2019.1611576","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48280308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-31DOI: 10.1080/0022250X.2020.1795652
C. Butts
ABSTRACT Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network models built on top of simple Bernoulli baseline (or reference) measures often behave unrealistically in this respect, leading to the development of sparse reference models that preserve features such as mean degree scaling. In this paper, we generalize recent work on the micro-foundations of such reference models to the case of sparse directed graphs with non-vanishing reciprocity, providing a dynamic process interpretation of the emergence of stable macroscopic behavior.
{"title":"A dynamic process reference model for sparse networks with reciprocity","authors":"C. Butts","doi":"10.1080/0022250X.2020.1795652","DOIUrl":"https://doi.org/10.1080/0022250X.2020.1795652","url":null,"abstract":"ABSTRACT Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network models built on top of simple Bernoulli baseline (or reference) measures often behave unrealistically in this respect, leading to the development of sparse reference models that preserve features such as mean degree scaling. In this paper, we generalize recent work on the micro-foundations of such reference models to the case of sparse directed graphs with non-vanishing reciprocity, providing a dynamic process interpretation of the emergence of stable macroscopic behavior.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2020.1795652","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46399521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-27DOI: 10.1080/0022250x.2023.2180002
P. Pramanik, A. Polansky
Mutually beneficial cooperation is a common part of economic systems as firms in partial cooperation with others can often make a higher sustainable profit. Though cooperative games were popular in 1950s, recent interest in non-cooperative games is prevalent despite the fact that cooperative bargaining seems to be more useful in economic and political applications. In this paper we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry fails to give a proper feedback Nash equilibrium. Cooperation occurs when two firms' strategies fall into each other's influence curvature in this strategy spacetime. Small firms in an economy dominated by large firms are subject to the influence of large firms. We determine an optimal feedback semi-cooperation of the small firm in this case using a Liouville-Feynman path integral method.
{"title":"Semicooperation under curved strategy spacetime","authors":"P. Pramanik, A. Polansky","doi":"10.1080/0022250x.2023.2180002","DOIUrl":"https://doi.org/10.1080/0022250x.2023.2180002","url":null,"abstract":"Mutually beneficial cooperation is a common part of economic systems as firms in partial cooperation with others can often make a higher sustainable profit. Though cooperative games were popular in 1950s, recent interest in non-cooperative games is prevalent despite the fact that cooperative bargaining seems to be more useful in economic and political applications. In this paper we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry fails to give a proper feedback Nash equilibrium. Cooperation occurs when two firms' strategies fall into each other's influence curvature in this strategy spacetime. Small firms in an economy dominated by large firms are subject to the influence of large firms. We determine an optimal feedback semi-cooperation of the small firm in this case using a Liouville-Feynman path integral method.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47998996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-06DOI: 10.1080/0022250X.2019.1664508
O. Stark
ABSTRACT Combining a standard measure of concern about low relative wealth and a standard measure of relative risk aversion leads to a novel explanation of variation in risk-taking behavior identified and documented by social psychologists and economists. We obtain two results: (1) Holding individual i’s wealth and his rank in the wealth distribution constant, the individual’s relative risk aversion decreases when he becomes more relatively deprived as a result of an increase in the average wealth of the individuals who are wealthier than he is. (2) If relative deprivation enters the individual’s utility function approximately linearly then, holding constant individual i’s wealth and the average wealth of the individuals who are wealthier than he is, the individual’s relative risk aversion decreases when he becomes more relatively deprived as a result of a decline in his rank. Our findings provide a theoretical support for evidence about the propensity of relatively deprived individuals to gamble and resort to other risky behaviors.
{"title":"Relative deprivation as a cause of risky behaviors","authors":"O. Stark","doi":"10.1080/0022250X.2019.1664508","DOIUrl":"https://doi.org/10.1080/0022250X.2019.1664508","url":null,"abstract":"ABSTRACT Combining a standard measure of concern about low relative wealth and a standard measure of relative risk aversion leads to a novel explanation of variation in risk-taking behavior identified and documented by social psychologists and economists. We obtain two results: (1) Holding individual i’s wealth and his rank in the wealth distribution constant, the individual’s relative risk aversion decreases when he becomes more relatively deprived as a result of an increase in the average wealth of the individuals who are wealthier than he is. (2) If relative deprivation enters the individual’s utility function approximately linearly then, holding constant individual i’s wealth and the average wealth of the individuals who are wealthier than he is, the individual’s relative risk aversion decreases when he becomes more relatively deprived as a result of a decline in his rank. Our findings provide a theoretical support for evidence about the propensity of relatively deprived individuals to gamble and resort to other risky behaviors.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2019.1664508","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43485658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-21DOI: 10.1080/0022250x.2019.1682802
Sandra González-Bailón
In his 1963 book Informal Sociology, William Bruce Cameron wrote the often-misattributed quote “not everything that can be counted counts, and not everything that counts can be counted”. With this ...
{"title":"Bit by bit: social research in the digital age","authors":"Sandra González-Bailón","doi":"10.1080/0022250x.2019.1682802","DOIUrl":"https://doi.org/10.1080/0022250x.2019.1682802","url":null,"abstract":"In his 1963 book Informal Sociology, William Bruce Cameron wrote the often-misattributed quote “not everything that can be counted counts, and not everything that counts can be counted”. With this ...","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250x.2019.1682802","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42567517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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