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Modelling and simulation

Modelling and simulation

Voter model examines how opinions spread between social networks

12 Dec 2019
Voting
How do opinions spread between social networks? (Courtesy: iStock/stocknshares)

Michael Gastner and Kota Ishida at Yale-NUS College in Singapore have studied the voter model – a simple description of opinion formation and dynamics. They used the model to investigate social networks containing two communities that were highly connected internally, but with few connections between the two groups. Gastner describes how the number of connections between the two communities affects the time it takes for all members to reach agreement.

The research is reported in full in Journal of Physics A, published by IOP Publishing – which also publishes Physics World.

What was the motivation for the research?

A common perception about our digital age is that we live in “echo chambers”, where we mostly exchange opinions and ideas with people who are similar to us. In a society split into tightly knit communities that hardly reach out to each other, it appears ever less likely to reach a consensus on controversial issues. Brexit, immigration or climate change readily come to mind as topics that have revealed deep divisions in society. With our research, we wanted to develop a simple mathematical model that shows to what extent divisions in society lead to delays in reaching a consensus.

What did you do in the work?

We looked at a simple model of opinion formation – the “voter model”. We thought of society as a network in which people are linked to their friends. After some time has passed, people ask one of their friends about her or his current opinion and adopt it as their own. After we repeat this process often enough, everybody eventually agrees on the same opinion. This model is a classic in sociological research.

What was new in our study was the structure of the social network. While previous research assumed that society is homogeneous, we considered networks with two communities that were internally highly connected, but with few connections between the communities. In our model, the communities formed so-called “cliques”: every member of a community was connected to everybody else in the same community. This is more extreme than we find in real social networks, but it was a starting point to keep the maths tractable.

Voter model

What was the most interesting and/or important finding?

Initially we thought the time until the two cliques agree on a shared opinion would simply decrease with every additional link between the cliques. But it turns out the situation is much less straightforward than we had expected. It is true that a network in which there is only one link between the cliques needs on average twice as long to reach a consensus than a network with two such links. But when there are too many links, we found to our surprise that the consensus time increases again.

After analysing the maths carefully, we found the reason for this counterintuitive behaviour. On one hand, frequent opinion exchanges between the cliques are necessary to quickly agree on the same opinion. On the other hand, additional links give the minority clique greater influence, causing more self-doubt within the majority clique and consequently slower convergence towards a shared opinion.

Why is this research significant?

Some researchers have argued that the best way to overcome the polarization in today’s society is to develop bipartisan links that form bridges across the political divide. Our research shows that the situation is not quite so simple.  Of course, a society consisting of isolated communities will find it impossible to reach a compromise. But too many bipartisan links are in fact not necessarily helpful in this respect either. If communities lose their distinct identities, extreme opinions may make inroads into the mainstream. The result can be a prolonged tug of war between two opinions with about equally many supporters.

What do you plan to do next?

The present model allowed us to solve the maths, but real social networks are admittedly more nuanced than what we can currently account for. For example, some community members may have greater influence on the opinion dynamics than others. In the next stage of our research, we will study more sophisticated network models that mimic the heterogeneity of real societies.

The full results of the study are reported in Journal of Physics A: Mathematical and Theoretical. This research is part of Kota Ishida’s final-year capstone project in Mathematics and Computational Sciences.

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