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Abstract

We study relaxational dynamics of social systems within a kinetic binary-choice (Ising-like) model. On the basis of the assumptions of the deterministic social-impact model in discrete time introduced by Nowak et al. (Psychol Rev 1990, 97, 362), we construct a probabilistic, continuous-time description. Although there are no stationary (equilibrium) solutions of the model in general, the presence of strong leaders maintaining their opinions for a long-time and strongly influencing other individuals leads to quasi-stable (steady-state) solutions. Analyzing closed individual chains, we discuss changes of the individual-opinion structure while varying a global parameter of the model. Such a kind of a “critical” behaviour is possible although there is no true phase equilibrium. © 2010 Wiley Periodicals, Inc. Complexity, 2010

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... This method can be motivated by much smaller value of the temperature of the fixed spin (a long time of its relaxation) than the temperature (or temperatures) of the rest of the spins. Such an analog of the two-temperature Ising model (of γ 1 = γ 2 = = γ N −1 < 1, γ N = 1) has been studied in [10]. ...
... In particular, similar dynamical equations to the ones presented in Subsection 3.1 govern the dynamics of multi-spin correlators of such a generalized kinetic Ising model. An example physical system of this type is discussed in Section 4 of [10]. ...
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We derive three system order parameters: dynamism, polarization, and clustering, to describe global states of attitude distribution and change for human social systems. Dynamism (f) captures the rate of change in a system, while polarization (Pt) refers to the increase or decrease of a minority position over time. Clustering (e) defines the spatial segregation of opinion based on system topography. These measures suggest a conception of human systems rooted in time and space that is distinct from other approaches. Their utility is illustrated through computer simulations showing that under a wide variety of circumstances, social influence models incorporating spatial distributions lead to unexpected outcomes of incomplete polarization and clustering, with alternative theories of how individuals encode information leading to quantitatively distinct results. A second set of simulations describes the intrusion of temperature, or unexplained randomness into these systems. Surprisingly, the self-organizational tendencies emerging from the iteration of simple laws of individual attitude change derived from Latané's (1981) metatheory of social impact appear to increase with moderate levels of randomness. We consider other approaches for measuring group level processes, among them network analysis-inspired indices and spatial autocorrelation, and suggest how our system order parameters could be used to predict political elections.
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The Nowak modification of the Sznajd opinion dynamics model on the square lattice assumes that with probability beta the opinions flip due to mass-media advertising from down to up, and vice versa. Besides, with probability alpha the Sznajd rule applies that a neighbour pair agreeing in its two opinions convinces all its six neighbours of that opinion. Our Monte Carlo simulations and mean-field theory find sharp phase transitions in the parameter space. (c) 2007 Elsevier B.V. All rights reserved.
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It has been suggested that Glauber (inflow) and Sznajd (outflow) zero-temperature dynamics for the one-dimensional Ising ferromagnet with nearest-neighbor interactions are equivalent. Here we compare the two dynamics from the analytical and computational points of view. We use the method of mapping an Ising spin system onto the dimer RSA model and show that already this simple mapping allows us to see the differences between inflow and outflow zero-temperature dynamics. Then we investigate both dynamics with synchronous, partially synchronous, and random sequential updating using the Monte Carlo technique and compare both dynamics in the number of persistent spins, clusters, mean relaxation time, and relaxation time distribution.
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A simple Ising spin model which can describe a mechanism of making a decision in a closed community is proposed. It is shown via standard Monte Carlo simulations that very simple rules lead to rather complicated dynamics and to a power law in the decision time distribution. It is found that a closed community has to evolve either to a dictatorship or a stalemate state (inability to take any common decision). A common decision can be taken in a "democratic way" only by an open community. Comment: 13 pages, 7 figures
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A simple Ising spin model which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among traders. It is shown via standard Monte Carlo simulations that very simple rules lead to dynamics that duplicate those of asset prices. Comment: Version 2: 4 pages, 4 figures; added more stringent statistical analysis; to appear in Int. J. Modern Physics C, Vol. 13, No. 1 (2002)
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We investigate models of opinion formation which are based on the social impact theory. The following approaches are discussed: (i) general mean field theory of social impact, (ii) a social impact model with learning, (iii) a model of a finite group with a strong leader, (iv) a social impact model with dynamically changing social temperature, (v) a model with individuals treated as active Brownian particles interacting via a communication field.
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A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models but that allows straightforward steady state solutions and, for small systems, development of the full time dependence for configuration probabilities. The model is easily accessible to upper-level undergraduate students, and also provides a good check for computer models of larger systems. 1 I.
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In this paper we will first discuss computer simulations of social processes as models of qualitative understanding. In the second part of the paper we will present the cellular automata model of dynamic social impact (Nowak et al. 1990) and its applications in the areas of the formation of public opinion and social change as an example of a model of qualitative understanding.
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The individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) which causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for any one spin depend on the values of the neighboring spins. This dependence is determined, in part, by the detailed balancing condition obeyed by the equilibrium state of the model. The Markoff process which describes the spin functions is analyzed in detail for the case of a closed N‐member chain. The expectation values of the individual spins and of the products of pairs of spins, each of the pair evaluated at a different time, are found explicitly. The influence of a uniform, time‐varying magnetic field upon the model is discussed, and the frequency‐dependent magnetic susceptibility is found in the weak‐field limit. Some fluctuation‐dissipation theorems are derived which relate the susceptibility to the Fourier transform of the time‐dependent correlation function of the magnetization at equilibrium.
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Techniques borrowed from sensory psychophysics were used in 2 studies examining nervousness and tension associated with the anticipation of performing in front of an audience. In Study 1 (60 undergraduates), a laboratory experiment, performance apprehension increased as a multiplicative power function of audience size and status but decreased as a power function of the number of performers. In Study 2, a correlational field study, performers in a university Greek Week talent show who appeared as members of large acts reported less nervousness and tension than performers who appeared in small acts, and again, an inverse power function provided a good fit to the data. Results support the combination of B. Latané's (in press) theory of social impact and A. Modigliani's (1968, 1971) theory of embarrassment. Implications for social facilitation and affiliation theories and for performers are discussed. (30 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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Reviews 2 traditional lines of research on social influence processes—research on conformity, which looks at the influence of the majority on a passive minority, and research on innovation, which considers the influence of active minorities on a silent majority. A new theory of social impact is examined that views social influence as resulting from forces operating in a social force field. It proposes that influence by either a majority or a minority will be a multiplicative function of the strength, immediacy, and number of its members. It is suggested that social impact theory offers a general model of social influence processes that integrates previous theoretical formulations and empirical findings and accounts for the reciprocal influence of majorities and minorities. Thus, by viewing social influence as a unitary concept, social impact theory permits comparisons between conformity and innovation and predicts the relative magnitude of their effects. (39 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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A computer simulation modeled the change of attitudes in a population resulting from the interactive, reciprocal, and recursive operation of B. Latané's (see record 1982-01296-001) theory of social impact, which specifies principles underlying how individuals are affected by their social environment. Surprisingly, several macrolevel phenomena emerged from the simple operation of this microlevel theory, including an incomplete polarization of opinions reaching a stable equilibrium, with coherent minority subgroups managing to exist near the margins of the whole population. Computer simulations, neglected in group dynamics for 20 years, may, as in modern physics, help determine the extent to which group-level phenomena result from individual-level processes. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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Proposes a theory of social impact specifying the effect of other persons on an individual. According to the theory, when other people are the source of impact and the individual is the target, impact should be a multiplicative function of the strength, immediacy, and number of other people. Furthermore, impact should take the form of a power function, with the marginal effect of the Nth other person being less than that of the ( N–2)th. When other people stand with the individual as the target of forces from outside the group, impact should be divided such that the resultant is an inverse power function of the strength, immediacy, and number of persons standing together. The author reviews relevant evidence from research on conformity and imitation, stage fright and embarrassment, news interest, bystander intervention, tipping, inquiring for Christ, productivity in groups, and crowding in rats. (27 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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We study the Deffuant et al model for continuous-opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending on a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce an order–disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. Using a linear stability analysis we can derive approximate conditions for the transition between opinion clusters and the disordered state. The master equation analysis is compared with direct Monte Carlo simulations. We find that the master equation and the Monte Carlo simulations do not always agree due to finite-size-induced fluctuations that we analyze in some detail.
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This study presents the outline of a model for collective phenomena. A symmetry-breaking model combines a number of well-established social psychology hypotheses with recent concepts of statistical physics. Specifically we start out from the regularities obtained in studies on the polarization of attitudes and decisions. From a strictly logical point of view, it is immediately clear that aggregation effects must be analysed separately from group effects as such. The conceptual analysis of the assumed mechanisms reveals that when we deal with phenomena that have until now been designated as polarization phenomena, we are faced not with a single phenomenon, as was believed hitherto, but with a whole class of phenomena. For this reason it would be appropriate to deal with them differentially both from an empirical and from a theoretical point of view. It is possible to show, moreover, that in principle polarization is a direct function of interaction and, beyond a critical threshold an inverse function of the differentiation between group members. A certain number of verifiable conjectures are presented on the basis of physio-mathematical-psychological considerations. It is to be hoped that these theoretical outlines will make it possible to give a new lease on life to a field of research that has established solid facts, but that became trapped in a dead-end road, for lack of a sufficiently broad analysis.
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We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions toward an average opinion, whereas low thresholds result in several opinion clusters. The model is further generalized to network interactions, threshold heterogeneity, adaptive thresholds, and binary strings of opinions. © 2002 Wiley Periodicals, Inc.
Article
The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie–Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability.
Article
We study phase transitions in models of opinion formation which are based on the social impact theory. Two different models are discussed: (i) a cellular-automata-based model of a finite group with a strong leader where persons can change their opinions but not their spatial positions, and (ii) a model with persons treated as active Brownian particles interacting via a communication field. In the first model, two stable phases are possible: a cluster around the leader, and a state of social unification. The transition into the second state occurs for a large leader strength and/or for a high level of social noise. In the second model, we find three stable phases, which correspond either to a “paramagnetic” phase (for high noise and strong diffusion), a “ferromagnetic” phase (for small nose and weak diffusion), or a phase with spatially separated “domains” (for intermediate conditions).
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As reported in summary form by W. Moede (1927), an unpublished study found that in a rope-pulling task, while collective group performance increased somewhat with group size, it was less than the sum of the individual efforts (IE). IE decreased as group size increased. The present 2 experiments with 84 undergraduates investigated this effect using clapping and shouting tasks. Results replicate the earlier findings. The decrease in IE, which is here called social loafing, is in addition to losses due to faulty coordination of group efforts. The experimental generality, theoretical importance, widespread occurrence, and negative social consequences of social loafing are examined, along with ways of minimizing it. (26 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Article
We present a general sequential probabilistic frame, which extends a series of earlier opinion dynamics models. In addition, it orders and classifies all of the existing two-state spin systems. The scheme operates via local updates where a majority rule is applied differently in each possible configuration of a local group. It is weighted by a local probability which is a function of the local value of the order parameter, i.e., the majority-to-minority ratio. The system is thus driven from one equilibrium state into another equilibrium state till no collective change occurs. A phase diagram can thus be constructed. It has two phases, one where the collective opinion ends up broken along one opinion, and another with an even coexistence of both opinions. Two different regimes, monotonic and dampened oscillatory, are found for the coexistence phase. At the phase transition local probabilities conserve the density of opinions and reproduce the collective dynamics of the Voter model. The essential behavior of all existing discrete two-state models (Galam, Sznajd, Ochrombel, Stauffer, Krapivsky-Redner, Mobilia-Redner, Behera-Schweitzer, Slanina-Lavicka, Sanchez ...) is recovered and found to depart from each other only in the value of their local probabilities. Corresponding simulations are discussed. It is concluded that one should not judge from the above model results the validity of their respective psycho-social assumptions.
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The use of equilibrium models in economics springs from the desire for parsimonious models of economicphenomenathat takehumanreasoning into account. This approach has been the cornerstone of modern economic theory.We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn’t be a question of dogma, and should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are alsomanysituations where the jury is still out,i.e.,where so far they fail to provide a good description of the world,but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models.We sketch some alternative approaches and discuss why they should play an important role in future research in economics.
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We discuss the mean-field theory for a class of probabilistic cellular automata that can describe the dynamics of social impact. The models exhibit complex intermittent behavior.
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This article explores the state of interplay between recent efforts to introduce complex systems methods into economics and the understanding of empirical phenomena. The empirical side of economic complexity may be divided into three general branches: historical studies, the identification of power and scaling laws, and analyses of social interactions. I argue that, while providing useful 'stylised facts', none of these empirical approaches has produced compelling evidence that economic contexts exhibit the substantive microstructure or properties of complex systems. This failure reflects inadequate attention to identification problems. Identification analysis should therefore be at the centre of future work on the empirics of complexity. Copyright 2005 Royal Economic Society.
Article
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow us to calculate the fluctuations and large deviations of the density and the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example, non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.
Opinion evolution in closed community 11, 1157; (b) Sznajd-Weron, K. Sznajd model and its applications
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Sznajd-Weron, K.; Sznajd, J. Opinion evolution in closed community. Int J Mod Phys C 2000, 11, 1157; (b) Sznajd-Weron, K. Sznajd model and its applications. Acta Phys Pol B 2005, 36, 2537; (c) Woloszyn, M.; Stauffer, D.; Kulakowski, K. Phase transitions in Nowak-Sznajd opinion dynamics. Physica A 2007, 378, 453.
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