The impact of noise and topology on opinion dynamics in social networks

Smaldino P, Moser D, Merico A. Noise and opinion dynamics: how ambiguity promotes pro-majority consensus in the presence of confirmation bias

Opinion dynamics are affected by cognitive biases and noise. While mathematical models have focused extensively on biases, we still know surprisingly little about how noise shapes opinion patterns. Here, we use an agent-based opinion dynamics model to investigate the interplay between confirmation bias-represented as bounded confidence-and different types of noise. After analysing where noise can enter social interaction, we propose a type of noise that has not been discussed so far, ambiguity noise. While previously considered types of noise acted on agents either before, after or independent of social interaction, ambiguity noise acts on communicated messages, assuming that socially transmitted opinions are inherently noisy. We find that noise can induce agreement when confirmation bias is moderate, but different types of noise require quite different conditions for this effect to occur. An application of our model to the climate change debate shows that at just the right mix of confirmation bias and ambiguity noise, opinions tend to converge to high levels of climate change concern. This result is not observed with the other types. Our findings highlight the importance of considering and distinguishing between the various types of noise and the unique role of ambiguity in opinion formation.

Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise

We introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents' movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents' spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM.

Opinion dynamics in social networks under competition: the role of influencing factors in consensus-reaching

The rapid development of information technology and social media has provided easy access to the vast data on individual preferences and social interactions. Despite a series of problems, such as privacy disclosure and data sensitivity, it cannot be denied that this access also provides beneficial opportunities and convenience for campaigns involving opinion control (e.g. marketing campaigns and political election). The profitability of opinion and the finiteness of individual attention have already spawned extensive competition for individual preferences on social networks. It is necessary to investigate opinion dynamics over social networks in a competitive environment. To this end, this paper develops a novel social network DeGroot model based on competition game (DGCG) to characterize opinion evolution in a competitive opinion dynamics. Social interactions based on trust relationships are captured in the DGCG model. From the model, we then obtain equilibrium results in a stable state of opinion evolution. We also analyse what role relevant factors play in the final consensus and competitive outcomes, including the resource ratio of both contestants, initial opinions, self-confidence and network structure. Theoretical analyses and numerical simulations show that these factors can significantly sway the consensus and even reverse competition outcomes.

Two sides of the same leader: an agent-based model to analyze the effect of ambivalent opinion leaders in social networks

Opinion leaders (OLs) are becoming increasingly relevant on social networking sites as their visibility can help to shape their followers' attitudes toward a variety of issues. While earlier research provided initial evidence on the effect of OLs using agent-based modeling, it remains unclear how OLs affect their network environment and, therefore, the opinion climate when: (a) they publicly hold ambivalent attitudes, and (b) they not only express support for their own stance but also discredit or 'debunk' the opposing side. This paper presents an agent-based model that determines the influence of OLs in social networks in relation to ambivalence and discreditation. The model draws on theoretical foundations of OLs as well as attitudinal ambivalence and was implemented using two network topologies. Results indicate that OLs have significant influence on the opinion climate and that an unequal number of OLs of different opinion camps lead to an imbalance in the opinion climate only in certain situations. Furthermore, OLs can dominate the opinion climate and turn their stance into a majority opinion more effectively when discrediting the opposing side. Ambivalent OLs, on the other hand, can contribute to greater balance in the opinion climate. These findings provide a more nuanced analysis of OLs in social networks by pointing to potential amplifications as well as boundaries of their influence. Implications are discussed with a focus on human and artificial key actors in online networks and their efficacy therein.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s42001-022-00161-z.

A general framework to link theory and empirics in opinion formation models

We introduce a minimal opinion formation model that is quite flexible and can reproduce a wide variety of the existing micro-influence assumptions and models. The model can be easily calibrated on real data, upon which it imposes only a few requirements. From this perspective, our model can be considered as a bridge, connecting theoretical studies on opinion formation models and empirical research on social dynamics. We investigate the model analytically by using mean-field approximation and numerically via Monte Carlo simulations. Our analysis is exemplified by recently reported empirical data drawn from an online social network. We demonstrate that the model calibrated on these data may reproduce fragmented and polarizing social systems. Furthermore, we manage to generate an artificial society that features properties quantitatively and qualitatively similar to those observed empirically at the macro scale. This ability became possible after we had advanced the model with two important communication features: selectivity and personalization algorithms.

The influence of community structure on opinion expression: an agent-based model

Social media has become important in shaping the public discourse on controversial topics. Many businesses therefore monitor different social media channels and try to react adequately to a potentially harmful opinion climate. Still, little is known about how opinions form in an increasingly connected world. The spiral of silence theory provides a way of explaining deviations between the perceived opinion climate and true beliefs of the public. However, the emergence of a spiral of silence on social media is hard to observe because only the thoughts of those who express their opinions are evident there. Recent research has therefore focused on modelling the processes behind the spiral of silence. A particular characteristic of social media networks is the presence of communities. Members of a community tend to be connected more with other members of the same community than with outsiders. Naturally, this might affect the development of public opinion. In the present article we investigate how the number of communities in a network and connectivity between them affects the perceived opinion climate. We find that higher connectivity between communities makes it more likely for a global spiral of silence to appear. Moreover, a network fragmented into more, smaller communities seems to provide more "safe spaces" for a minority opinion to prevail.