Abstract

We investigate the impact of noise and topology on opinion diversity in social networks. We do so by extending well-established models of opinion dynamics to a stochastic setting where agents are subject both to assimilative forces by their local social interactions, as well as to idiosyncratic factors preventing their population from reaching consensus. We model the latter to account for both scenarios where noise is entirely exogenous to peer influence and cases where it is instead endogenous, arising from the agents’ desire to maintain some uniqueness in their opinions. We derive a general analytical expression for opinion diversity, which holds for any network and depends on the network’s topology through its spectral properties alone. Using this expression, we find that opinion diversity decreases as communities and clusters are broken down. We test our predictions against data describing empirical influence networks between major news outlets and find that incorporating our measure in linear models for the sentiment expressed by such sources on a variety of topics yields a notable improvement in terms of explanatory power.

Highlights

  • There is considerable value in understanding how opinions are formed, distributed and spread within a society, and how they evolve over time

  • While intermedia influence networks are only one of many possible empirical social networks, the fact that there is a strong relationship between the influence networks and the resultant dynamics validates that network topology has a measurable impact on the level of discord

  • Building on a popular model of opinion formation, we investigate the impact of both noise and network topology on discord

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Summary

Introduction

There is considerable value in understanding how opinions are formed, distributed and spread within a society, and how they evolve over time. Modelling society as a social network provides a useful mathematical framework for understanding how opinion dynamics leads to differing outcome behaviours. The remainder of the paper is structured as follows: §2 provides background and discusses relevant 3 recent advances in noisy opinion dynamics models and opinion diversity. The vector of opinions spanning all N nodes at time t is yt

Noisy opinion dynamics
Quantifying discord
Noisy opinion dynamics model
Opinion diversity
Noisy DeGroot model
Noisy FJ model
Results
Impact of susceptibility
Impact of topology on opinion diversity
Connectivity
Clustering
Communities
Adaptive noise
Empirical evaluation
Conclusion
Undirected case
Directed case
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