Maths in Psychology

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When Sue Street moved from engineering to psychology at Massey University, she brought with her an unusual approach for this people-focused social science – mathematical simulation of the interactions of autonomous individuals that calculates their effects on a system.

In her Masters, she used this agent-based modelling to explore the impact of income inequalities on people’s relationships; in her PhD, she modeled development of trust in people’s behavior on the internet auction site Trade Me.

As an engineer coming into psychology, I was struck by the relative absence of a dimension that is always present in electrical engineering: time. And when you think about time, you’re thinking about dynamics. Apart from certain fields like developmental psychology, time is curiously absent in psychology.”
For her masters, Street wanted to explore the impact of differences in income, which research has shown has much more impact on the health and mortality of populations than absolute levels of poverty or wealth.

“If two people grow up in Taita and one becomes a millionaire, do they stay friends? I wondered whether the increasing income differences strain existing relationships, and cause a cascading breakdown in relationships within a population. People tend to be friends with those who are similar, so increasing the difference in income is likely to reduce that similarity.”

She modelled friendships rather than marriages or sexual relationships, in a finite element structural simulation. She randomly allocated difference in wealth at two relating nodes, and how much time and effort (loading) each node put on the relationship.

“Reducing the similarity in some relationships caused some to break, and shifted the loading on other relationships, some of which also broke, so there were fewer relationships in the population. Reversing the differences didn’t recover the overall level of activity in relationships, which implies that closing the gaps in the real world might not work by itself – we’d have to do something to rebuild the effects of prolonged inequality.”

For her PhD, Street used Repast, which is free open-source agent-based modeling software, to create a group of traders with a randomly-assigned strategy for dealing with the limited information that Trade Me supplies. This includes the person’s number of trades, their trade rating, whether or not individual trades were successful and the reasons why some were not. This could be because someone didn’t respond, didn’t pay or didn’t send the goods. Some agents were randomly more likely to be dishonest and all could learn by getting random strategy information from traders who were doing better.

Street found that agents “got better at identifying and avoiding unreliable traders, but that learning the signs of dishonest traders and avoiding them was patchy at best. Overall, agents improved their trading success, and restricted unreliable traders, but left dishonest traders in circulation.” Dishonest traders tend to re-enter Trade Me with a new ID once their original rating deteriorates, but she did not build that into her model.

Street believes that mathematical simulations are a valuable approach that is underused in psychology for analysing very complex patterns of social behaviour.