Combinatorics debunks psychology

I found this NYT article via The Skeptics' Guide to the Universe Podcast.

About 50 years ago a bunch of psychologists decided they had support for the theory of cognitive dissidence because they had an experiment where monkeys showed their preference for m&m colours. What they did was let the monkey choose between a red and blue m&m. If he preferred red the monkey would be then be given the choice between blue and green. In this scenario the monkeys end up choosing green 2/3s of the time.

The conclusion was that the bias was because the monkey was urged to continue to reject the blue m&m in order to be consistent. And since psychology is complicated it's alright that rejecting blue once didn't always predict rejecting blue a second time. 2/3s is certainly statistically significant over very few trials, and I would guess is probably a pretty high correlation in psychology.

The news is that a simpler alternate solution has been pointed out by economist M. Keith Chen (ok, so he's neither a combinatorist nor does he debunk). Chen asks what if the Monkey has already decided on a preference order for m&m colours. And what if each of the six preference orders are equally represented among the monkeys. Then by choosing the red m&m over the blue m&m the monkey has eliminated three of the orders: leaving two possible orders where blue is his least favourite, and one where green is his least favourite.

Chen points out that this is just the Monty Hall problem. In this case the monkey is Monty Hall, the least favourite m&m is the prize you are trying to find, and the green m&m is the contestants original guess.

So not only does Chen's theory explain the bias it also explains the degree of the bias.