# Fitting In and Breaking Up: A Nonlinear Version of Coevolving Voter Models

## TL;DR

This paper introduces a nonlinear coevolving voter model where node rewiring and opinion adoption depend on local neighborhood fit, revealing that initial network topology and rewiring schemes significantly influence opinion spread and the majority illusion.

## Contribution

It develops a nonlinear model of coevolving voter dynamics incorporating neighborhood-dependent probabilities, extending prior linear models and highlighting the impact of initial topology and rewiring schemes.

## Key findings

- Initial network topology influences dynamics more than in linear models.
- Rewiring scheme choice has a smaller effect on opinion spread.
- Minority opinions can dominate if perceived as majority through the majority illusion.

## Abstract

We investigate a nonlinear version of coevolving voter models, in which node states and network structure update as a coupled stochastic dynamical process. Most prior work on coevolving voter models has focused on linear update rules with fixed and homogeneous rewiring and adopting probabilities. By contrast, in our nonlinear version, the probability that a node rewires or adopts is a function of how well it "fits in" within its neighborhood. To explore this idea, we incorporate a parameter $\sigma$ that represents the fraction of neighbors of an updating node that share its opinion state. In an update, with probability $\sigma^q$ (for some nonlinearity parameter $q$), the updating node rewires; with complementary probability $1-\sigma^q$, the updating node adopts a new opinion state. We study this mechanism using three rewiring schemes: after an updating node deletes a discordant edge, it then either (1) "rewires-to-random" by choosing a new neighbor in a random process; (2) "rewires-to-same" by choosing a new neighbor in a random process from nodes that share its state; or (3) "rewires-to-none" by not rewiring at all (akin to "unfriending" on social media). We compare our nonlinear coevolving model to several existing linear models, and we find in our model that initial network topology plays a larger role in the dynamics and the choice of rewiring mechanism plays a smaller role. A particularly interesting feature of our model is that, under certain conditions, the opinion state that is held initially by a minority of the nodes can effectively spread to almost every node in a network if the minority nodes view themselves as the majority. In light of this observation, we relate our results to recent work on the majority illusion in social networks.

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Source: https://tomesphere.com/paper/1907.11608