Nonequilibrium phase transition in the coevolution of networks and opinions.

Models of the convergence of opinion in social systems have been the subject of considerable 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.

[1]  G. Yule,et al.  A Mathematical Theory of Evolution Based on the Conclusions of Dr. J. C. Willis, F.R.S. , 1925 .

[2]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[3]  P. Clifford,et al.  A model for spatial conflict , 1973 .

[4]  R. Holley,et al.  Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model , 1975 .

[5]  T. Schelling.  Micromotives and Macrobehavior , 1978 .

[6]  T. Liggett.  Interacting Particle Systems , 1985 .

[7]  S. Bikhchandani,et al.  You have printed the following article : A Theory of Fads , Fashion , Custom , and Cultural Change as Informational Cascades , 2007 .

[8]  Marsili,et al.  Nonequilibrium phase transition in a model for social influence , 2000, Physical review letters.

[9]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[10]  M. McPherson,et al.  Birds of a Feather: Homophily in Social Networks , 2001 .

[11]  D. Zanette,et al.  Vertical transmission of culture and the distribution of family names. , 2000, nlin/0009046.

[12]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[13]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[14]  Guillaume Deffuant,et al.  How can extremism prevail? A study based on the relative agreement interaction model , 2002, J. Artif. Soc. Soc. Simul..

[15]  B. Söderberg.  General formalism for inhomogeneous random graphs. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  S. Levin,et al.  Comparing Classical Community Models: Theoretical Consequences for Patterns of Diversity , 2002, The American Naturalist.

[17]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[18]  A General Formalism for Inhomogeneous Random Graphs , 2002, cond-mat/0211063.

[19]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Dynamic critical behavior of the XY model in small-world networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Claudio Castellano,et al.  Incomplete ordering of the voter model on small-world networks , 2003 .

[22]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[23]  Víctor M Eguíluz,et al.  Coevolution of dynamical states and interactions in dynamic networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  A. Arenas,et al.  Models of social networks based on social distance attachment. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  F. Amblard,et al.  The role of network topology on extremism propagation with the Relative Agreement opinion dynamics , 2004 .

[26]  Dietrich Stauffer,et al.  The coevolution of individual economic characteristics and socioeconomic networks , 2004 .

[27]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[28]  S. Redner,et al.  Voter model on heterogeneous graphs. , 2004, Physical review letters.

[29]  Vittorio Loreto,et al.  Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment Sharp transition towardsshared vocabularies in multi-agent systems , 2006 .

[30]  Petter Holme,et al.  A Network-Based Threshold Model for the Spreading of fads in Society and Markets , 2005, Adv. Complex Syst..