In an interesting research paper titled "Are birds smarter than mathematicians? Pigeons (Columba livia) perform optimally on a version of the Monty Hall Dilemma.", by Herbranson, Walter T. and Schroeder, Julia that appeared in Feb 2010 issue of Journal of Comparative Psychology (Vol 124(1), Feb 2010, 1-13), the authors claim that with pigeons used as subjects to solve the Monty Hall problem, the results showed that pigeons are better at it than humans (also interestingly maybe a lay man was better than a PhD).

What is a Monty Hall problem? A probability problem based on a popular American TV game show, "Let's Make a Deal", and named after its host Monty Hall. The results appear absurd but can be demonstrated to be true. So it is also called at times Monty Hall Paradox. Here is a problem statement:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

As the player can not be certain which of the two remaining unopened doors has a car, most humans believe that each door has an equal chance and conclude that switching does not alter their chance of winning and stay with their initial guess. The solution actually requires you to switch, as by switching you doubly increase your probability of winning from 1/3 to 2/3 !

A variation of the Monty hall problem was experimented with pigeons and it was found that the birds reached the optimum strategy, going from switching roughly 36% of time on day 1 to 96% on day 30. If that was not interesting enough, here is more evidence about humans. On the other hand, 12 undergraduate student volunteers failed to adopt the best strategy with a similar apparatus, even after 200 trials of practice each.

The Monty Hall problem, in one of its common formulations, is mathematically equivalent to the earlier Three Prisoners Problems published in Martin Gardner's *Mathematical Games* column in Scientific American in 1959, and both bear some similarity to the much older Bertrand's box paradox. These and other problems involving unequal distributions of probability are notoriously difficult for people to solve correctly, and have led to numerous psychological studies that address how the problems are perceived. Even when given a completely unambiguous statement of the Monty Hall problem, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief. The fact that people do badly at this problem is true across cultures, including Brazil, China, Sweden and the United States.

So are humans not superior? Actually they are, generally speaking; it is just that they are bad at certain types of problems than some of the other animal species!

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