One of the more exciting uses of social network is to look for patterns of behaviour on networks such as Twitter that predict the behaviour of people in the real world.

Various groups have focused on purchasing behaviour in particular. Sure enough Twitter moods sometimes seem to predict things like stock market trends and movie box office revenues.

However, a detailed theory is still lacking that explains how these purchasing behaviours emerge when real people are influenced by forces such as word-of-mouth recommendations and commercial adverts.

That could be about to change thanks to a fascinating paper by Akira Ishii and buddies at Tottori University in Japan.

These guys have used ideas from statistical mechanics to model the behaviour of humans influenced by word-of-mouth interactions and advertisements. In this paper, Ishii and co derive a bunch of equations that they use to model the number of people who’ll turn up to see a movie or visit an art show.

Here’s how they do it. These guys think of humans as if they were atoms interacting with each other via three different forces. The first is advertising, which they think of as a general external force, like a magnetic field. The second is a word-of -mouth effect, which they model as a two-body interaction. Finally, they think of rumours as an interaction between three bodies.

With all these forces in play, they let the ‘atoms’ go and see what happens.

One important problem is how to calibrate such a model. This is where these guys’ work is different from many others. They use real data from an exhibition of art in Sakaiminato, a relatively remote town in Japan. The data consists of a daily record of the advertising spend by the local tourist office, a daily count of the number of visitors to the exhibition and a record of the number and frequency of blog postings about the exhibition.

Putting these numbers into their model, Ishii and co say they can predict the number of visitors in the near future, using only the advertising spend and number of visitors in the past. They’re also able to predict spikes in the number of blog postings too.

The result is a kind of weather forecast for visitors: cloudy with a chance of coach parties.

Various groups have tried to develop a kind of statistical mechanics of society before–the idea goes back at least a hundred years. However, nobody has come up with a model that has any serious predictive power.

That’s a result that could generate significant interest. It’ll be interesting to see whether Ishii and co’s model stands up to further scrutiny.

They certainly have broad hopes for it. They say it should work in general for any product or service in which advertising plays a significant role in the purchase decision. And they’ve already confirmed its efficacy by predicting the number of people who pay to see a movie, given a certain spend on adverts.

That’s significant because this model is predicting purchasing decisions.

One interesting question is whether it works just as well in other cultures and for many other products and services. Only one way to find out!

Ref: arxiv.org/abs/1112.0767: Revenue Prediction of Local Event using Mathematical Model of Hit Phenomena