Protest formulas

Mobiles expose the maths behind protest marches

Student protest in South-Africa, in 2016. ‘Let’s say I want to organise a protest march: should I rent vans, or should I call people?’

Where do protesters come from? Sociologist and mathematician Vincent Traag has produced mathematical models based on data from mobile phones.

Somewhere, in a certain country, at least 39 protest marches were held in one year during the last decade. Some of them might even have been riots – the information is not very specific. But why the protests were held is a secret, and so is the number of people who took part. However, we do know this: 1,105 mobile phones were on during the largest of the gatherings.

All that Vincent Traag will say about that country is that it is somewhere in Africa. The researcher from Leiden’s Centre for Science and Technology (CWTS) cannot divulge how he came by the mobile phone data. “I would really like to publish everything, but that’s not possible with a subject as sensitive as this. That’s why we’re very cautious about where and when it happened too. We’d hate it if anyone with malicious intent got their hands on that information somehow.”

“In my previous studies on mobile phone data”, he adds, “we could reveal which country we had researched and in which period, but we still faced the same problem: we can’t release the data. Not all academic journals are happy with that, but luckily it wasn’t a problem for Physica A.”

In that journal, Traag , who trained as a sociologist and mathematician, describes a number of theoretical models for protest marches based on the African data. “I have done things with telephone data before, but many social scientists thought the subjects – such as the number of concert-goers or the size of an audience at a football match – were not very relevant. They are interested in demonstrations, but it’s hard to obtain any data about that sort of thing. It’s difficult to make estimates of how many people were at a given place – just look at the discussion about Donald Trump’s inauguration – but my approach helps us to acquire more insight into such events.”

The revelation that distance has a very large impact on protest marches is a prime example, as Traag explains: “It’s immediately obvious from our data, but the question is how best to convert it into formulas.” An exponential formula with a “half-life distance” seems to describe the data quite well. It means that that for every nine kilometres, the chances of a person attending diminish by fifty per cent.

There are two possible explanations. The first is that protesting is primarily a social activity: research on demonstrations shows that people almost always only attend if someone else has asked them along. If Dutch scientists were to organise a March for Science in Amsterdam, you would be more likely to hear about it if you lived in Amsterdam than if you lived in Terneuzen, Zeeland. The second reason for distance’s large influence is even more fundamental: it takes four hours to travel from Terneuzen to Museumplein – travel is usually expensive too.

“Both explanations apply”, continues Traag, “though the network effect seems to be a bit more important. But even if you adjust for contacts, the chances drop drastically according to the distance. It can be useful to know how these things are related. Let’s say I want to organise a protest march but only have a few resources: should I rent vans to get people there or ring people to ask if they’ll come?”

Well? “Distance is tricky, at any rate, so I would make sure it can be bridged. If you make it easier for people to come, it will make a big difference.” Mind you, the distances in Africa can’t really be compared to those in the Netherlands. “That half-value distance depends on the transport infrastructure. In the Netherlands, it will be bigger than those nine African kilometres, but I couldn’t say by how much. Perhaps something like twenty to a hundred kilometres?”

In the article, Traag and his fellow authors stress that their models are merely a first step. “I would love to map out urban boundaries and natural borders and find out whether there are any differences between people. If we knew who contacted whom, we could study how the attendance of a protest spreads via a social network. That knowledge can, of course, be applied to other things too, such as people who help with a clean-up campaign or shoppers who visit the sales, but that’s awkward data to collect.”

That’s one reason why Traag’s study on mobile phone data is on the back burner now. “It’s hard to get access to the data, it’s hard to handle it properly and responsibly and it’s hard to publish any work on it – and that’s how it should be, of course, but it obstructs our research. It’s a pity, because we could learn lots of interesting things from that sort of data.”

At CWTS, he mainly focuses on researching how academics use citations from each other’s articles – citation networks instead of protesters’ networks. “The mathematical tools I have designed can be used for all sorts; I once co-wrote an article about the distribution of coral larvae acrossa reef. Seen from a mathematical angle, we can apply tools to all sorts of networks; in those terms, it’s all the same thing.”

Bart Braun

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Protest formulas

Where do protesters come from? Sociologist and mathematician Vincent Traag has produced …