The mathematics of making decisions
David Sumpter, Uppsala universitet
What is the first thing you do when deciding what brand of mobile
phone to buy? For many people, the answer is that they ask their
friends and are more likely than not make the same choice as they did.
Animals use similar rules in their decisions about what to do, the
more individuals that have made a particular choice about where to
live or where to eat, the more likely others are to copy
them. Decision-making can thus be described as positive feedback with
the probability of performing a particular action an increasing
function of those making the choices before. Depending on the shape of
this function there are different outcomes for decisions. For example,
I show that bi-stability can arise where the chosen option is
determined by a few initial choices and when we introduce different
qualities to the options it is not always the best one that is
chosen. I also look at the case where the two options change quality
in time and identify the best strategy for either exploring new
options or exploiting known choices. Finally, I look at ways of
weighting the actions of others so as to be able to detect arbitrarily
small changes in the quality of the choices. Mathematically, the talk
will lead take us from positive feedback and bifurcations to the
'one-sided' Ising model.
Last modified: some time ago.