The Dynamics of Continuous Cultural Traits in Social Networks

Büchel B, Hellmann T, Pichler M. The Dynamics of Continuous Cultural Traits in Social Networks. Working Papers. Institute of Mathematical Economics. Vol 457. Bielefeld: Center for Mathematical Economics; 2012.We consider an OLG model (of a socialization process) where continuous traits are transmitted from an adult generation to the children. A weighted social network describes how children are influenced not only by their parents but also by other role models within the society. Parents can invest into the purposeful socialization of their children by strategically displaying a cultural trait (which need not coincide with their true trait). Based on Nash equilibrium behavior, we study the dynamics of cultural traits throughout generations. We provide conditions on the network structure that are sufficient for long–run convergence to a society with homogeneous subgroups. In the special case of quadratic utility, the condition is that each child is more intensely shaped by its parents than by the social environment. Our model also represents an extension of the classical DeGroot model of opinion formation for which we introduce strategic interaction in choice of expressed opinions (in our setup: traits). We show that under strategic interaction convergence is slower and for convergence we need more restrictive necessary and sufficient conditions than in the DeGroot model

The dynamics of continuous cultural traits in social networks

We consider an overlapping generations model where continuous cultural traits are transmitted from an adult generation to the children. A weighted social network describes how children are influenced not only by their parents but also by other role models within the society. Parents can invest into the purposeful socialization of their children by strategically displaying a cultural trait (which need not coincide with their true cultural trait). We observe a cultural substitution effect when parents choose their behavior optimally. Based on Nash equilibrium behavior, we then study the dynamics of cultural traits throughout generations. These converge if parent’s influence on their children is large enough compared to the social environment’s influence. Under convergent dynamics, closed subgroups fully assimilate, while heterogeneous traits prevail in the other groups. Speed of convergence is low when parents' incentives to socialize their children to the own trait are high

Homophily, Cultural Drift and the Co-Evolution of Cultural Groups

In studies of cultural differentiation, the joint mechanisms of homophily and influence have been able to explain how distinct cultural groups can form. While these mechanisms normally lead to cultural convergence, increased levels of heterogeneity can allow them to produce global diversity. However, this emergent cultural diversity has proven to be unstable in the face of "cultural drift"- small errors or innovations that allow cultures to change from within. We develop a model of cultural differentiation that combines the traditional mechanisms of homophily and influence with a third mechanism of 2network homophily", in which network structure co-evolves with cultural interaction. We show that if social ties are allowed to change with cultural influence, a complex relationship between heterogeneity and cultural diversity is revealed, in which increased heterogeneity can reduce cultural group formation while simultaneously increasing social connectedness. Our results show that in certain regions of the parameter space these co-evolutionary dynamics can lead to patterns of cultural diversity that are stable in the presence of cultural drift.Comment: (8 pages, 8 figures

Binary and Multivariate Stochastic Models of Consensus Formation

A current paradigm in computer simulation studies of social sciences problems by physicists is the emergence of consensus. The question is to establish when the dynamics of a set of interacting agents that can choose among several options (political vote, opinion, cultural features, etc.) leads to a consensus in one of these options, or when a state with several coexisting social options prevail. We consider here stochastic dynamic models naturally studied by computer simulations. We will first review some basic results for the voter model. This is a binary option stochastic model, and probably the simplest model of collective behavior. Next we consider a model proposed by Axelrod for the dissemination of culture. This model can be considered as a multivariable elaboration of the voter model dynamics.Comment: (16 pages, 8 figures; for simililar work visit http://www.imedea.uib.es/physdept

Cultural transmission and optimization dynamics

We study the one-dimensional version of Axelrod's model of cultural transmission from the point of view of optimization dynamics. We show the existence of a Lyapunov potential for the dynamics. The global minimum of the potential, or optimum state, is the monocultural uniform state, which is reached for an initial diversity of the population below a critical value. Above this value, the dynamics settles in a multicultural or polarized state. These multicultural attractors are not local minima of the potential, so that any small perturbation initiates the search for the optimum state. Cultural drift is modelled by such perturbations acting at a finite rate. If the noise rate is small, the system reaches the optimum monocultural state. However, if the noise rate is above a critical value, that depends on the system size, noise sustains a polarized dynamical state.Comment: 11 pages, 10 figures include

Signs of universality in the structure of culture

Understanding the dynamics of opinions, preferences and of culture as whole requires more use of empirical data than has been done so far. It is clear that an important role in driving this dynamics is played by social influence, which is the essential ingredient of many quantitative models. Such models require that all traits are fixed when specifying the "initial cultural state". Typically, this initial state is randomly generated, from a uniform distribution over the set of possible combinations of traits. However, recent work has shown that the outcome of social influence dynamics strongly depends on the nature of the initial state. If the latter is sampled from empirical data instead of being generated in a uniformly random way, a higher level of cultural diversity is found after long-term dynamics, for the same level of propensity towards collective behavior in the short-term. Moreover, if the initial state is randomized by shuffling the empirical traits among people, the level of long-term cultural diversity is in-between those obtained for the empirical and uniformly random counterparts. The current study repeats the analysis for multiple empirical data sets, showing that the results are remarkably similar, although the matrix of correlations between cultural variables clearly differs across data sets. This points towards robust structural properties inherent in empirical cultural states, possibly due to universal laws governing the dynamics of culture in the real world. The results also suggest that this dynamics might be characterized by criticality and involve mechanisms beyond social influence.Comment: 16 pages, 7 figures; the same results as in version 3, but a shorter Introduction, Discussion and Conclusio

Opinion dynamics: models, extensions and external effects

Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainability and protection. Opinion formation is a complex process affected by the interplay of different elements, including the individual predisposition, the influence of positive and negative peer interaction (social networks playing a crucial role in this respect), the information each individual is exposed to, and many others. Several models inspired from those in use in physics have been developed to encompass many of these elements, and to allow for the identification of the mechanisms involved in the opinion formation process and the understanding of their role, with the practical aim of simulating opinion formation and spreading under various conditions. These modelling schemes range from binary simple models such as the voter model, to multi-dimensional continuous approaches. Here, we provide a review of recent methods, focusing on models employing both peer interaction and external information, and emphasising the role that less studied mechanisms, such as disagreement, has in driving the opinion dynamics. [...]Comment: 42 pages, 6 figure

Robustness of cultural communities in an open-ended Axelrod's model

We consider an open-ended set of cultural features in the Axelrod's model of cultural dissemination. By replacing the features in which a high degree of consensus is achieved by new ones, we address here an essential ingredient of societies: the evolution of topics as a result of social dynamics and debate. Our results show that, once cultural clusters have been formed, the introduction of new topics into the social debate has little effect on them, but it does have a significant influence on the cultural overlap. Along with the Monte-Carlo simulations, we derive and numerically solve an equation for the stationary cultural overlap based on a mean-field approach. Although the mean-field analysis reproduces qualitatively the characteristic phase transition of the Axelrod's model, it underestimates the cultural overlap, highlighting the role of the local interactions in the Axelrod's dynamics, as well as the correlations between the different cultural features.Comment: 6 pages and 5 figure

Behavioral Modernity and the Cultural Transmission of Structured Information: The Semantic Axelrod Model

Cultural transmission models are coming to the fore in explaining increases in the Paleolithic toolkit richness and diversity. During the later Paleolithic, technologies increase not only in terms of diversity but also in their complexity and interdependence. As Mesoudi and O'Brien (2008) have shown, selection broadly favors social learning of information that is hierarchical and structured, and multiple studies have demonstrated that teaching within a social learning environment can increase fitness. We believe that teaching also provides the scaffolding for transmission of more complex cultural traits. Here, we introduce an extension of the Axelrod (1997} model of cultural differentiation in which traits have prerequisite relationships, and where social learning is dependent upon the ordering of those prerequisites. We examine the resulting structure of cultural repertoires as learning environments range from largely unstructured imitation, to structured teaching of necessary prerequisites, and we find that in combination with individual learning and innovation, high probabilities of teaching prerequisites leads to richer cultural repertoires. Our results point to ways in which we can build more comprehensive explanations of the archaeological record of the Paleolithic as well as other cases of technological change.Comment: 24 pages, 7 figures. Submitted to "Learning Strategies and Cultural Evolution during the Paleolithic", edited by Kenichi Aoki and Alex Mesoudi, and presented at the 79th Annual Meeting of the Society for American Archaeology, Austin TX. Revised 5/14/1