Dynamical organization towards consensus in the Axelrod model on complex networks

Polarization inhibits the phase transition of Axelrod's model

We study the effect of polarization in Axelrod's model of cultural dissemination. This is done through the introduction of a cultural feature that takes only two values, while the other features can present a larger number of possible traits. Our numerical results and mean-field approximations show that polarization reduces the characteristic phase transition of the original model to a finite-size effect, since at the thermodynamic limit only the ordered phase is present. Furthermore, for finite system sizes, the stationary state depends on the percolation threshold of the network where the model is implemented: a polarized phase is obtained for percolation thresholds below 1/2, and a fragmented multicultural one otherwise.

Dense and influential core promotion of daily viral information spread in political echo chambers

Despite the intensive study of the viral spread of fake news in political echo chambers (ECs) on social networking services (SNSs), little is known regarding the underlying structure of the daily information spread in these ECs. Moreover, the effect of SNSs on opinion polarisation is still unclear in terms of pluralistic information access or selective exposure to opinions in an SNS. In this study, we confirmed the steady, highly independent nature of left- and right-leaning ECs, both of which are composed of approximately 250,000 users, from a year-long reply/retweet network of 42 million Japanese Twitter users. We found that both communities have similarly efficient information spreading networks with densely connected and core-periphery structures. Core nodes resonate in the early stages of information cascades, and unilaterally transmit information to peripheral nodes. Each EC has resonant core users who amplify and steadily spread information to a quarter of a million users. In addition, we confirmed the existence of extremely aggressive users of ECs who co-reply/retweet each other. The connection between these users and top influencers suggests that the extreme opinions of the former group affect the entire community through the top influencers.

Dynamics of organizational culture: Individual beliefs vs. social conformity

The complex nature of organizational culture challenges our ability to infer its underlying dynamics from observational studies. Recent computational studies have adopted a distinctly different view, where plausible mechanisms are proposed to describe a wide range of social phenomena, including the onset and evolution of organizational culture. In this spirit, this work introduces an empirically-grounded, agent-based model which relaxes a set of assumptions that describes past work–(a) omittance of an individual’s strive for achieving cognitive coherence; (b) limited integration of important contextual factors—by utilizing networks of beliefs and incorporating social rank into the dynamics. As a result, we illustrate that: (i) an organization may appear to be increasingly coherent in terms of its organizational culture, yet be composed of individuals with reduced levels of coherence; (ii) the components of social conformity—peer-pressure and social rank—are influential at different aggregation levels.

Culture and cooperation in a spatial public goods game

We study the coevolution of culture and cooperation by combining the Axelrod model of cultural dissemination with a spatial public goods game, incorporating both noise and social influence. Both participation and cooperation in public goods games are conditional on cultural similarity. We find that a larger "scope of cultural possibilities" in the model leads to the survival of cooperation, when noise is not present, and a higher probability of a multicultural state evolving, for low noise rates. High noise rates, however, lead to both rapid extinction of cooperation and collapse into cultural "anomie," in which stable cultural regions fail to form. These results suggest that cultural diversity can actually be beneficial for the evolution of cooperation, but that cultural information needs to be transmitted accurately in order to maintain both coherent cultural groups and cooperation.

Diversity and Community Can Coexist

We examine the (in)compatibility of diversity and sense of community by means of agent-based models based on the well-known Schelling model of residential segregation and Axelrod model of cultural dissemination. We find that diversity and highly clustered social networks, on the assumptions of social tie formation based on spatial proximity and homophily, are incompatible when agent features are immutable, and this holds even for multiple independent features. We include both mutable and immutable features into a model that integrates Schelling and Axelrod models, and we find that even for multiple independent features, diversity and highly clustered social networks can be incompatible on the assumptions of social tie formation based on spatial proximity and homophily. However, this incompatibility breaks down when cultural diversity can be sufficiently large, at which point diversity and clustering need not be negatively correlated. This implies that segregation based on immutable characteristics such as race can possibly be overcome by sufficient similarity on mutable characteristics based on culture, which are subject to a process of social influence, provided a sufficiently large "scope of cultural possibilities" exists.

The structure and dynamics of multilayer networks

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.

How can you capture cultural dynamics?

Cross-cultural comparison is a critical method by which we can examine the interaction between culture and psychological processes. However, comparative methods tend to overlook cultural dynamics - the formation, maintenance, and transformation of cultures over time. The present article gives a brief overview of four different types of research designs that have been used to examine cultural dynamics in the literature: (1) cross-temporal methods that trace medium- to long-term changes in a culture; (2) cross-generational methods that explore medium-term implications of cultural transmission; (3) experimental simulation methods that investigate micro-level mechanisms of cultural dynamics; and (4) formal models and computer simulation methods often used to investigate long-term and macro-level implications of micro-level mechanisms. These methods differ in terms of level of analysis for which they are designed (micro vs. macro-level), scale of time for which they are typically used (short-, medium-, or long-term), and direction of inference (deductive vs. empirical method) that they imply. The paper describes examples of these methods, discuss their strengths and weaknesses, and point to their complementarity in inquiries about cultural change. Because cultural dynamics research is about meaning over time, issues deriving from interpretation of meaning and temporal distance between researchers and objects of inquiry can pose threats to the validity of the research and its findings. The methodological question about hermeneutic circle is recalled and further inquiries are encouraged.

Axelrod's model with surface tension

In this work we propose a subtle change in Axelrod's model for the dissemination of culture. The mechanism consists of excluding from the set of potentially interacting neighbors those that would never possibly exchange. Although the alteration proposed does not alter the state space topologically, it yields significant qualitative changes, specifically the emergence of surface tension, driving the system in some cases to metastable states. The transient behavior is considerably richer, and cultural regions become stable leading to the formation of different spatiotemporal patterns. A metastable "glassy" phase emerges between the globalized phase and the disordered, multicultural phase.

Ultrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination

The Axelrod model of cultural diffusion is an apparently simple model that is capable of complex behaviour. A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model. Here we quantify the degree of ultrametricity of the initial culture vectors and investigate the effect of varying degrees of ultrametricity on the absorbing state of both a simple and extended model. Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances. Further, we find that a scheme for evolving synthetic opinion vectors from cultural “prototypes” shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.

Reconciling long-term cultural diversity and short-term collective social behavior

An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and long-term cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are intensively studied, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a high-dimensional analysis of the scientific beliefs of thousands of Europeans. We find that interopinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space. When empirical data are used as inputs in models, ultrametricity has strong and counterintuitive effects. On short timescales, it facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long timescales, it suppresses cultural convergence by restricting it within disjoint groups. Moreover, ultrametricity implies that these results are surprisingly robust to modifications of the dynamical rules considered. Thus the empirical distribution of individuals in cultural space appears to systematically optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence in a diverse range of online and offline settings.

Coevolutionary network approach to cultural dynamics controlled by intolerance

Starting from Axelrod's model of cultural dissemination, we introduce a rewiring probability, enabling agents to cut the links with their unfriendly neighbors if their cultural similarity is below a tolerance parameter. For low values of tolerance, rewiring promotes the convergence to a frozen monocultural state. However, intermediate tolerance values prevent rewiring once the network is fragmented, resulting in a multicultural society even for values of initial cultural diversity in which the original Axelrod model reaches globalization.

Dynamical patterns of cattle trade movements

Despite their importance for the spread of zoonotic diseases, our understanding of the dynamical aspects characterizing the movements of farmed animal populations remains limited as these systems are traditionally studied as static objects and through simplified approximations. By leveraging on the network science approach, here we are able for the first time to fully analyze the longitudinal dataset of Italian cattle movements that reports the mobility of individual animals among farms on a daily basis. The complexity and inter-relations between topology, function and dynamical nature of the system are characterized at different spatial and time resolutions, in order to uncover patterns and vulnerabilities fundamental for the definition of targeted prevention and control measures for zoonotic diseases. Results show how the stationarity of statistical distributions coexists with a strong and non-trivial evolutionary dynamics at the node and link levels, on all timescales. Traditional static views of the displacement network hide important patterns of structural changes affecting nodes' centrality and farms' spreading potential, thus limiting the efficiency of interventions based on partial longitudinal information. By fully taking into account the longitudinal dimension, we propose a novel definition of dynamical motifs that is able to uncover the presence of a temporal arrow describing the evolution of the system and the causality patterns of its displacements, shedding light on mechanisms that may play a crucial role in the definition of preventive actions.

Selective advantage of tolerant cultural traits in the Axelrod-Schelling model

The Axelrod-Schelling model incorporates into the original Axelrod's model of cultural dissemination the possibility that cultural agents placed in culturally dissimilar environments move to other places, the strength of this mobility being controlled by an intolerance parameter. By allowing heterogeneity in the intolerance of cultural agents, and considering it as a cultural feature, i.e., susceptible of cultural transmission (thus breaking the original symmetry of Axelrod-Schelling dynamics), we address here the question of whether tolerant or intolerant traits are more likely to become dominant in the long-term cultural dynamics. Our results show that tolerant traits possess a clear selective advantage in the framework of the Axelrod-Schelling model. We show that the reason for this selective advantage is the development, as time evolves, of a positive correlation between the number of neighbors that an agent has in its environment and its tolerant character.

Effects of mass media action on the Axelrod model with social influence

The use of dyadic interaction between agents, in combination with homophily (the principle that "likes attract") in the Axelrod model for the study of cultural dissemination, has two important problems: the prediction of monoculture in large societies and an extremely narrow window of noise levels in which diversity with local convergence is obtained. Recently, the inclusion of social influence has proven to overcome them [A. Flache and M. W. Macy, e-print arXiv:0808.2710]. Here, we extend the Axelrod model with social influence interaction for the study of mass media effects through the inclusion of a superagent which acts over the whole system and has non-null overlap with each agent of the society. The dependence with different parameters as the initial social diversity, size effects, mass media strength, and noise is outlined. Our results might be relevant in several socioeconomic contexts and for the study of the emergence of collective behavior in complex social systems.