Parameter Evaluation of a Simple Mean-Field Model of Social Interaction

Abstract

The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean-field discrete models is introduced and discussed both from the theoretical and phenomenological point of view. We propose a parameter evaluation procedure and test it by fitting the model against three families of data coming from different cases: the estimated interaction parameters are found to have similar positive values, giving a quantitative confirmation of the peer imitation behavior found in social psychology. Furthermore, all the values of the interaction parameters belong to the phase transition regime suggesting its possible role in the study of social systems

Fluctuation Results for General Block Spin Ising Models

“…Later, they were rediscovered as interesting models for statistical mechanics systems, see [18], [15], [8], [26], [24], as well as models for social interactions between several groups, e.g. in [17], [1], [28]. This latter approach follows very much the social re-interpretation for one group of the Curie-Weiss model in [6] or of the Hopfield model in [9] or [25].…”

How integrated are immigrants?

“…A detailed theoretical analysis performed with mathematical modelling in Barra et al (2014), see also (McFadden 2001;Gallo, Barra, and, Contucci 2009), suggests that a linear increase in cross-group couplings over immigrant density of the type we observe for labour market integration, is due to a stochastic independence of individual choices. This implies that employer-employee decisions, whether to engage in a mixed nativeimmigrant labour contract, are made independently from other employer-employee decisions.…”

“…The observed non-linear (square root) growth of the probability for cross-group couplings against immigrant density is due to the fact that individual choices are interdependent. Brock and Durlauf 2001;Contucci, Gallo, and Menconi 2008;Contucci and Giardina 2008;Gallo, Barra, and, Contucci 2009). That is, the action of inter-marrying (or having a child) are decisions that are contingent on how others (natives and immigrants) in the environment have acted in this context before (Weber 1978;Barra et al 2014;Kalmijn 1998).…”

An artificial neural network approach for modeling the ward atmosphere in a medical unit

“…Generalized kinetic models transfer the methodology developed for systems of a great number of interacting particles (such as Boltzmann and Vlasov equations, with direct interactions among the particles or mean field terms and external forces [17]) to various other fields of research, such as traffic dynamics (see, for instance, the review paper [11]), cellular dynamics (see, among others, [18,9,10,13,11]), social and population dynamics [27,14,[32][33][34]11,24] and biological systems in general [8,11]. Various models of the classical mathematical kinetic theory have been investigated and generalized in several contexts, [22,2]. The interested reader can find thorough reviews of the theory and applications of generalized kinetic models in [25,12,11].…”