Schelling segregation in an open city: a kinetically constrained Blume-Emery-Griffiths spin-1 system

In the 70's Schelling introduced a multi-agent model to describe the segregation dynamics that may occur with individuals having only weak preferences for 'similar' neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city-lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a new variety of "phases" whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socio-economic correlates.Comment: 10 pages, 7 figures, final version accepted for publication in PR

A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure

Residential segregation and cultural dissemination: An Axelrod-Schelling model

In the Axelrod's model of cultural dissemination, we consider mobility of cultural agents through the introduction of a density of empty sites and the possibility that agents in a dissimilar neighborhood can move to them if their mean cultural similarity with the neighborhood is below some threshold. While for low values of the density of empty sites the mobility enhances the convergence to a global culture, for high enough values of it the dynamics can lead to the coexistence of disconnected domains of different cultures. In this regime, the increase of initial cultural diversity paradoxically increases the convergence to a dominant culture. Further increase of diversity leads to fragmentation of the dominant culture into domains, forever changing in shape and number, as an effect of the never ending eroding activity of cultural minorities

Local interaction scale controls the existence of a non-trivial optimal critical mass in opinion spreading

We study a model of opinion formation where the collective decision of group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value, a \textit{critical mass}. We find that there exists a unique, non-trivial critical mass giving the most efficient convergence to consensus. In addition, we observe that for small critical masses, the characteristic time scale for the relaxation to consensus splits into two. The shorter time scale corresponds to a direct relaxation and the longer can be explained by the existence of intermediate, metastable states similar to those found in [P.\ Chen and S.\ Redner, Phys.\ Rev.\ E \textbf{71}, 036101 (2005)]. This longer time-scale is dependent on the precise condition for consensus---with a modification of the condition it can go away.Comment: 4 pages, 6 figure

Effective Free Energy for Individual Dynamics

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc

Nonequilibrium phase transition in the coevolution of networks and opinions

Models of the convergence of opinion in social systems have been the subject of a considerable amount of recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. We characterize the static and dynamical properties of this transition

Role of Activity in Human Dynamics

The human society is a very complex system; still, there are several non-trivial, general features. One type of them is the presence of power-law distributed quantities in temporal statistics. In this Letter, we focus on the origin of power-laws in rating of movies. We present a systematic empirical exploration of the time between two consecutive ratings of movies (the interevent time). At an aggregate level, we find a monotonous relation between the activity of individuals and the power-law exponent of the interevent-time distribution. At an individual level, we observe a heavy-tailed distribution for each user, as well as a negative correlation between the activity and the width of the distribution. We support these findings by a similar data set from mobile phone text-message communication. Our results demonstrate a significant role of the activity of individuals on the society-level patterns of human behavior. We believe this is a common character in the interest-driven human dynamics, corresponding to (but different from) the universality classes of task-driven dynamics.Comment: 5 pages, 6 figures. Accepted by EP

Role of social environment and social clustering in spread of opinions in co-evolving networks

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for the asymmetric influences in relationships among individuals in a social group. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of the simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus leading to the existence of diverse set of opinions and the other having one single dominant connected component with each node within it having the same opinion. Furthermore, and more importantly, we found that the initial clustering in network can also induce similar transitions. Our investigation also brings forward that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes. [1] P. Holme and M. Newman, Phys. Rev. E 74, 056108 (2006)

Co-evolutionnary 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