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# Statistical Physics Models of Opinion Spread: Theory and Empirical Tests

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### Abstract

We investigate a set of discrete-spin statistical physics models for opinion spread in social networks and explore how suitable they are for predicting real-world belief change on both the individual and group levels. Our studies center on the degree and rate of consensus formation in inhomogeneous models that take into account different individual preferences or set beliefs. We investigate the effects of different social interaction rules (voter, majority, and expert rule), a variety of both artificial and realistic social network structures, different distributions of initial information, dependence on clustering of intrinsic preferences, the effects of having only two choices vs.~multiple choices, and different weightings of social information input relative to intrinsic preferences. We find that the many combinations of model inputs results in a smaller, manageable set of consensus formation patterns. We then compare the predictions of these models to empirical social science studies, one done at MIT on 80~individuals living in a dorm during the 2008 presidential election season, and another conducted online by us with 94~participants during the 2016 presidential election primary season. We find that these relatively simple statistical physics-based models contain predictive value on both the individual and group levels. The results underscore the sensitivity of opinion spread to the underlying social network structure and the number of available belief options, and to a somewhat lesser (but still relevant) degree to the social interaction rules.

### Most cited references2

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### Scaling behavior in a proportional voting process

(1999)
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### Nature vs. Nurture: Predictability in Low-Temperature Ising Dynamics

(2013)
Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state ("nature") vs. the realization of the stochastic dynamics ("nurture") in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from $$T=\infty$$ to $$T=0$$. We performed Monte Carlo studies on the overlap between "identical twins" raised in independent dynamical environments, up to size $$L=500$$. Our results suggest an overlap decaying with time as $$t^{-\theta_h}$$ with $$\theta_h = 0.22 \pm 0.02$$; the same exponent holds for a quench to low but nonzero temperature. This "heritability exponent" may equal the persistence exponent for the 2D Ising ferromagnet, but the two differ more generally.
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### Author and article information

###### Journal
2017-06-06
###### Article
1706.02287