Mathematical Psychology: from financial modelling to election strategy

Abstract

A mathematical model for characterising the state of mind of a person is given by the probability assignment of the totality of choices available to that person. What would be interesting then is to understand how a person’s point of view changes in time. Noticing that the change is generated by information acquisition, one finds that techniques of communication theory can be applied to explain cognitive behaviours of people. A simple application of this idea is found in financial modelling — prices of financial assets change in accordance with how market participants view the future returns generated by those assets. One can also explain the statistics of how people might vote in a future election, and identify optimal strategies to enhance the likelihood of winning an election. But going beyond, it turns out that the mathematics of probability theory famously axiomatised by Kolmogorov is insufficient to describe many of the common day-to-day behaviours. Psychologists had previously thought that such empirical behaviours represent irrationality. But now we know better — it is not that people are irrational (although some are), but it has to do with the limitation of probability theory. Perhaps surprisingly, it is the rule of probability assignment in quantum theory for explaining atoms and particles that turns out to offer an accurate description of cognitive psychology.