Pub Date : 2019-07-03DOI: 10.1080/0022250x.2019.1695608
D. Haw, S. Hogan
ABSTRACT We present a complete analysis of the Schelling dynamical system of two connected neighborhoods, with or without population reservoirs, for different types of linear and nonlinear tolerance schedules. We show that stable integration is only possible when the minority is small and combined tolerance is large. Unlike the case of the single neighborhood, limiting one population does not necessarily produce stable integration and may destroy it. We conclude that a growing minority can only remain integrated if the majority increases its own tolerance. Our results show that an integrated single neighborhood may not remain so when a connecting neighborhood is created.
{"title":"A dynamical systems model of unorganized segregation in two neighborhoods","authors":"D. Haw, S. Hogan","doi":"10.1080/0022250x.2019.1695608","DOIUrl":"https://doi.org/10.1080/0022250x.2019.1695608","url":null,"abstract":"ABSTRACT We present a complete analysis of the Schelling dynamical system of two connected neighborhoods, with or without population reservoirs, for different types of linear and nonlinear tolerance schedules. We show that stable integration is only possible when the minority is small and combined tolerance is large. Unlike the case of the single neighborhood, limiting one population does not necessarily produce stable integration and may destroy it. We conclude that a growing minority can only remain integrated if the majority increases its own tolerance. Our results show that an integrated single neighborhood may not remain so when a connecting neighborhood is created.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250x.2019.1695608","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45940993","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 : 2019-04-30DOI: 10.1080/0022250X.2019.1606806
B. Cornwell, Jake Burchard
ABSTRACT The detection of structural cohesion is a key utility of social network analysis, but little work has been done to refine the detection of structural cohesion in two-mode networks. Most work on cohesion in two-mode networks either: (1) attempts to detect cohesion in such networks using one-mode projections (which can be problematic for reasons we discuss); or (2) focuses on restrictive substructures like bi-cliques to identify cohesive subgroups. We propose a new strategy for two-mode networks that follows the general reasoning of approaches to detecting structural cohesion in one-mode networks. Our approach identifies the number of actors from one node set that may be removed before disconnecting actors in the opposite set. We also develop a definition of embeddedness that draws on Moody and White’s hierarchical nesting approach.
{"title":"Structural cohesion and embeddedness in two-mode networks","authors":"B. Cornwell, Jake Burchard","doi":"10.1080/0022250X.2019.1606806","DOIUrl":"https://doi.org/10.1080/0022250X.2019.1606806","url":null,"abstract":"ABSTRACT The detection of structural cohesion is a key utility of social network analysis, but little work has been done to refine the detection of structural cohesion in two-mode networks. Most work on cohesion in two-mode networks either: (1) attempts to detect cohesion in such networks using one-mode projections (which can be problematic for reasons we discuss); or (2) focuses on restrictive substructures like bi-cliques to identify cohesive subgroups. We propose a new strategy for two-mode networks that follows the general reasoning of approaches to detecting structural cohesion in one-mode networks. Our approach identifies the number of actors from one node set that may be removed before disconnecting actors in the opposite set. We also develop a definition of embeddedness that draws on Moody and White’s hierarchical nesting approach.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2019.1606806","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46236107","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 : 2019-04-15DOI: 10.1080/0022250X.2019.1602045
R. A. W. Bradford
ABSTRACT The shift to a genetic basis of evolution in the 1960s, and away from group selection, created a problem in regard to the origin of cooperative behavior in human societies. The resolution essentially involves mutual recognition of individuals, thus permitting the phenomena of reputation, reciprocation, and retribution to arise, these being key to stable cooperative societies. The analysis presented, based on evolutionary game theory, serves to emphasize the crucial role of individual recognition by illustrating the consequences of assuming the opposite. It is shown that where tribal membership is apparent, but individuals are not recognizable, evolving mistrust leads to tribal extinction in an evolutionary game theory model. Moreover, a single tribe is also unstable to schism. Subsequently, the extinction of one schismatic group occurs. Failure to recognize individuals therefore facilitates a mechanism which leads to increasing conformity.
{"title":"Group Extinction in Iterated Two Person Games with Evolved Group-Level Mixed Strategies","authors":"R. A. W. Bradford","doi":"10.1080/0022250X.2019.1602045","DOIUrl":"https://doi.org/10.1080/0022250X.2019.1602045","url":null,"abstract":"ABSTRACT The shift to a genetic basis of evolution in the 1960s, and away from group selection, created a problem in regard to the origin of cooperative behavior in human societies. The resolution essentially involves mutual recognition of individuals, thus permitting the phenomena of reputation, reciprocation, and retribution to arise, these being key to stable cooperative societies. The analysis presented, based on evolutionary game theory, serves to emphasize the crucial role of individual recognition by illustrating the consequences of assuming the opposite. It is shown that where tribal membership is apparent, but individuals are not recognizable, evolving mistrust leads to tribal extinction in an evolutionary game theory model. Moreover, a single tribe is also unstable to schism. Subsequently, the extinction of one schismatic group occurs. Failure to recognize individuals therefore facilitates a mechanism which leads to increasing conformity.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2019.1602045","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48958687","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 : 2019-03-14DOI: 10.1080/0022250X.2019.1593522
A. van de Rijt
{"title":"“How behavior spreads: the science of complex contagions","authors":"A. van de Rijt","doi":"10.1080/0022250X.2019.1593522","DOIUrl":"https://doi.org/10.1080/0022250X.2019.1593522","url":null,"abstract":"","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2019.1593522","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45691660","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 : 2019-03-05DOI: 10.1080/0022250X.2019.1583226
M. Sanz, Vicente Díaz Gandasegui, Begoña Elizalde-San Miguel
ABSTRACT This paper presents a stochastic dynamic mathematical model, in which a Family Policy Index (XFPI) is included to measure and compare two different models of provision of resources to support families with children from 0 to 3 years old. The main variables in this model are the XFPI, fertility, mortality, emigration and immigration rates. This mathematical model was validated in two different countries, Spain and Norway, during the 2007–2015 period. A sensitivity analysis was applied to simulate the future trend (2016–2030), examining the influence of providing public pre-school services (0 to 3 years) on (XISF). The results obtained show that these services may indeed have an influence on fertility rates, as long as they are developed extensively.
{"title":"Sense and sensibility: using a model to examine the relationship between public pre-school places and fertility","authors":"M. Sanz, Vicente Díaz Gandasegui, Begoña Elizalde-San Miguel","doi":"10.1080/0022250X.2019.1583226","DOIUrl":"https://doi.org/10.1080/0022250X.2019.1583226","url":null,"abstract":"ABSTRACT This paper presents a stochastic dynamic mathematical model, in which a Family Policy Index (XFPI) is included to measure and compare two different models of provision of resources to support families with children from 0 to 3 years old. The main variables in this model are the XFPI, fertility, mortality, emigration and immigration rates. This mathematical model was validated in two different countries, Spain and Norway, during the 2007–2015 period. A sensitivity analysis was applied to simulate the future trend (2016–2030), examining the influence of providing public pre-school services (0 to 3 years) on (XISF). The results obtained show that these services may indeed have an influence on fertility rates, as long as they are developed extensively.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2019.1583226","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42132981","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 : 2019-01-02DOI: 10.1080/0022250X.2018.1470511
Paolo Rungo, Atilano Pena-López
ABSTRACT This paper studies the influence of individual social capital on the persistence of socioeconomic inequality. The set of social relations constitute a form of capital that provides the individual with a wide range of resources. Social capital interacts with other forms of capital, particularly with human capital, to enhance inequality. The overlapping-generations model proposed here focuses on the long-term investment processes in human and social capital. When these effects are considered, a society may end up divided into two groups. The first comprises people stuck in a trap of low intergenerational mobility resources. The second group includes people with increasing levels of education and social capital. Within the last group, income inequalities persist due to initial differences in social capital.
{"title":"Persistent inequality and social relations: An intergenerational model","authors":"Paolo Rungo, Atilano Pena-López","doi":"10.1080/0022250X.2018.1470511","DOIUrl":"https://doi.org/10.1080/0022250X.2018.1470511","url":null,"abstract":"ABSTRACT This paper studies the influence of individual social capital on the persistence of socioeconomic inequality. The set of social relations constitute a form of capital that provides the individual with a wide range of resources. Social capital interacts with other forms of capital, particularly with human capital, to enhance inequality. The overlapping-generations model proposed here focuses on the long-term investment processes in human and social capital. When these effects are considered, a society may end up divided into two groups. The first comprises people stuck in a trap of low intergenerational mobility resources. The second group includes people with increasing levels of education and social capital. Within the last group, income inequalities persist due to initial differences in social capital.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2018.1470511","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45607870","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 : 2018-12-30DOI: 10.1080/0022250X.2018.1555828
Benjamin R. Chisholm, P. Muller, A. J. Horn, Zachary S. Ellis
ABSTRACT We develop a non-network, deterministic, competing infections model for the spread of two competing viewpoints of a divisive idea that incorporates external factors in addition to interpersonal interactions. We consider divisive ideas to have polarizing support, i.e. there are no “shades of grey.” The proposed model for the spread of the competing support and skepticism of such an idea within a population is based on both epidemiological and competing species models. The model is then analyzed qualitatively and quantitatively in a case study of the 2016 Republican primary polls. Parameter fitting to this data shows the proposed model is plausible for the spread of viewpoints of a divisive idea.
{"title":"A competing infection model for the spread of different viewpoints of a divisive idea","authors":"Benjamin R. Chisholm, P. Muller, A. J. Horn, Zachary S. Ellis","doi":"10.1080/0022250X.2018.1555828","DOIUrl":"https://doi.org/10.1080/0022250X.2018.1555828","url":null,"abstract":"ABSTRACT We develop a non-network, deterministic, competing infections model for the spread of two competing viewpoints of a divisive idea that incorporates external factors in addition to interpersonal interactions. We consider divisive ideas to have polarizing support, i.e. there are no “shades of grey.” The proposed model for the spread of the competing support and skepticism of such an idea within a population is based on both epidemiological and competing species models. The model is then analyzed qualitatively and quantitatively in a case study of the 2016 Republican primary polls. Parameter fitting to this data shows the proposed model is plausible for the spread of viewpoints of a divisive idea.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2018.1555828","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41643451","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 : 2018-12-17DOI: 10.1080/0022250X.2018.1555827
Neng-pin Lu
ABSTRACT Principal eigenvectors of adjacency matrices are often adopted as measures of centrality for a graph or digraph. However, previous principal-eigenvector-like measures for a digraph usually consider only the strongly connected component whose adjacency submatrix has the largest eigenvalue. In this paper, for each and every strongly connected component in a digraph, we add weights to diagonal elements of its member nodes in the adjacency matrix such that the modified matrix will have the new unique largest eigenvalue and corresponding principal eigenvectors. Consequently, we use the new principal eigenvectors of the modified matrices, based on different strongly connected components, not only to compose centrality measures but also to identify bowtie structures for a digraph.
{"title":"Using principal eigenvectors of adjacency matrices with added diagonal weights to compose centrality measures and identify bowtie structures for a digraph","authors":"Neng-pin Lu","doi":"10.1080/0022250X.2018.1555827","DOIUrl":"https://doi.org/10.1080/0022250X.2018.1555827","url":null,"abstract":"ABSTRACT Principal eigenvectors of adjacency matrices are often adopted as measures of centrality for a graph or digraph. However, previous principal-eigenvector-like measures for a digraph usually consider only the strongly connected component whose adjacency submatrix has the largest eigenvalue. In this paper, for each and every strongly connected component in a digraph, we add weights to diagonal elements of its member nodes in the adjacency matrix such that the modified matrix will have the new unique largest eigenvalue and corresponding principal eigenvectors. Consequently, we use the new principal eigenvectors of the modified matrices, based on different strongly connected components, not only to compose centrality measures but also to identify bowtie structures for a digraph.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2018.1555827","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45503032","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 : 2018-12-13DOI: 10.1080/0022250X.2020.1756285
J. Bruggeman, R. Sprik, Rick Quax
ABSTRACT Cooperation for public goods poses a dilemma, where individuals are tempted to free ride on others’ contributions. Classic solutions involve monitoring, reputation maintenance and costly incentives, but there are important collective actions based on simple and cheap cues only, for example, unplanned protests and revolts. This can be explained by an Ising model with the assumption that individuals in uncertain situations tend to conform to the local majority in their network. Among initial defectors, noise such as rumors or opponents’ provocations causes some of them to cooperate accidentally. At a critical level of noise, these cooperators trigger a cascade of cooperation. We find an analytic relationship between the phase transition and the asymmetry of the Ising model, which in turn reflects the asymmetry of cooperation and defection. This study thereby shows that in principle, the dilemma of cooperation can be solved by nothing more than a portion of random noise, without rational decision-making.
{"title":"Spontaneous cooperation for public goods","authors":"J. Bruggeman, R. Sprik, Rick Quax","doi":"10.1080/0022250X.2020.1756285","DOIUrl":"https://doi.org/10.1080/0022250X.2020.1756285","url":null,"abstract":"ABSTRACT Cooperation for public goods poses a dilemma, where individuals are tempted to free ride on others’ contributions. Classic solutions involve monitoring, reputation maintenance and costly incentives, but there are important collective actions based on simple and cheap cues only, for example, unplanned protests and revolts. This can be explained by an Ising model with the assumption that individuals in uncertain situations tend to conform to the local majority in their network. Among initial defectors, noise such as rumors or opponents’ provocations causes some of them to cooperate accidentally. At a critical level of noise, these cooperators trigger a cascade of cooperation. We find an analytic relationship between the phase transition and the asymmetry of the Ising model, which in turn reflects the asymmetry of cooperation and defection. This study thereby shows that in principle, the dilemma of cooperation can be solved by nothing more than a portion of random noise, without rational decision-making.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2020.1756285","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43986387","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 : 2018-12-12DOI: 10.1080/0022250X.2018.1545769
K. Sawyer, André F. Gygax
ABSTRACT This paper constructs a new theory of social networks based on reputation. The model assumes that reputation is an asset and that individuals connect by buying options on the reputation of others. In networking, individuals construct portfolios of call options to leverage the reputations of others and put options to hedge the connections with others. A network then consists of portfolios of reputation options. The option model confers advantages not present in existing models. First, the payoff to connecting is the payoff on a portfolio of reputation options. Second, the network forms as individuals take option positions; the network evolves as individuals adjust those positions. Third, networking strategies become option strategies. The model allows for insights into network structure, the price of connecting and the value of connecting.
{"title":"An option-theoretic model of a reputation network","authors":"K. Sawyer, André F. Gygax","doi":"10.1080/0022250X.2018.1545769","DOIUrl":"https://doi.org/10.1080/0022250X.2018.1545769","url":null,"abstract":"ABSTRACT This paper constructs a new theory of social networks based on reputation. The model assumes that reputation is an asset and that individuals connect by buying options on the reputation of others. In networking, individuals construct portfolios of call options to leverage the reputations of others and put options to hedge the connections with others. A network then consists of portfolios of reputation options. The option model confers advantages not present in existing models. First, the payoff to connecting is the payoff on a portfolio of reputation options. Second, the network forms as individuals take option positions; the network evolves as individuals adjust those positions. Third, networking strategies become option strategies. The model allows for insights into network structure, the price of connecting and the value of connecting.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2018.1545769","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49605525","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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