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.

我们调查了噪声和拓扑结构对社交网络中意见多样性的影响。为此，我们将公认的观点动态模型扩展到随机的环境，在这种环境中，代理人既会因其本地社会互动而受到同化作用力的影响，又会受到阻碍其人口达成共识的特殊因素的影响。我们对后者进行建模，以解决噪声完全来自同伴影响的情况以及噪声来自内因的情况，这两种情况都是由于代理商希望保持其观点的唯一性而产生的。我们为意见多样性推导了一个通用的分析表达式，该表达式适用于任何网络，并且仅通过其频谱属性就取决于网络的拓扑。使用该表达式，我们发现，随着社区和集群的破裂，意见多样性下降。