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Published on: August 22, 2018
Opinion formation models on a gradient
Michael T Gastner1, Nikolitsa Markou2, Gunnar Pruessner3
1Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Budapest, Hungary; Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom; Department of Mathematics, Imperial College London, London, United Kingdom.
Abstract:
Statistical physicists have become interested in models of collective social behavior such as opinion formation, where individuals change their inherently preferred opinion if their friends disagree. Real preferences often depend on regional cultural differences, which we model here as a spatial gradient g in the initial opinion. The gradient does not only add reality to the model. It can also reveal that opinion clusters in two dimensions are typically in the standard (i.e., independent) percolation universality class, thus settling a recent controversy about a non-consensus model. However, using analytical and numerical tools, we also present a model where the width of the transition between opinions scales proportional g(-1/4), not proportional g(-4/7) as in independent percolation, and the cluster size distribution is consistent with first-order percolation.
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