To shed light on why humans often fall short of the best strategy with this kind of problem, scientists investigated pigeons, which often perform quite impressively on tasks requiring them to estimate relative probabilities, in some cases eclipsing human performance. Other animals do not always share the same biases as people, and therefore might help provide explanations for our behavior.
Scientists tested six pigeons with an apparatus with three keys. The keys lit up white to show a prize was available. After the birds pecked a key, one of the keys the bird did not choose deactivated, showing it was a wrong choice, and the other two lit up green. The pigeons were rewarded with bird feed if they made the right choice.
In the experiments, the birds quickly reached the best strategy for the Monty Hall problem - going from switching roughly 36 percent of the time on day one to some 96 percent of the time on day 30.
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.
It is a pity I did not have this paper in time for the big book. It would have been perfect!
The 12 undergraduates described here seem to have performed exceptionally badly. Other such experiments have shown higher rates of people learning the correct solution after repeated trials, as I describe in Chapter Six of the book. Still, ninety-six percent is pretty impressive.
The technical paper, published in The Journal of Comparative Psychology, has been printed out and is now sitting on my desk. Now to find time to read it!
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Oh yes that is one fun problem. What trips most people up is that they think the previous choice, 1 out of 3, is not important since they now have a 1 in 2 chance. Which is not true since the removal of a wrong choice still means that the original choice is only 1 in 3 to be right.
Well, pigeons have to be good at something
Or it could be that pigeons had approximately 2700 trials over 30 days compared to the peoples 200 total. Also, just skimming very briefly, the humans showed some learning, just not to the extent that the pigeons did.
Apparently pigeons are good at teamwork too:
http://www.couriermail.com.au/entertainment/weird/not-just-a-bunch-of-b…
Humans aren't very good at probability, so I guess it's not surprising that some animals evolved under conditions that would make them better. It would be interesting if the authors speculated about why pigeons would develop that ability. I wonder if they're better at not over rating low probability events or any of the other specific fallacies humans are prone to. Weren't pigeons also used in research with generating superstitious behaviors by rewarding them randomly?
A lot of responses to the MH problem involve the person getting it wrong, then explaining afterwards that they thought the host picked the second door at random. I'm still not sure I can imagine how that would work as either a game show or an interesting puzzle.
Host: I'm going to open Door 3. And⦠it's got the prize! A car filled with delicious bird seed! Knowing that the other two doors are empty, the big question is: are you going to switch to it?
I believe the mathematical answer to that is "duh".
One thing that may have helped the pigeons was not getting hung up on the motivations of the testers, instead dealing with the problem solely in a "computing" sense ("Hey, this strategy seems to work better, so I'll stick to it"). The human ability to think well is also an ability to overthinkâ¦
Now I'm wondering if the human group was likewise given the opportunity to play the game repeatedly. (If not, it's not really a fair comparison.)
Part of me wants to believe that there must be a point at which people (who may have misunderstood the problem before) eventually catch on to the best strategy. Of course, if that were actually how the human mind worked, we wouldn't have casinos. I wonder if pigeons can be motivated to irrationally gamble?
Aaand my question was already answered in an earlier post; I guess that paragraph was TSDR. Thanks mottaaf!
Humans know it's a test. Pigeons don't.
I still want to read your book Jason. It is on my list. However, I recently read a touching fiction book called "the curious incident of the dog in the night" about an autistic child. In the book, the main character spends about 3 pages discussing the Monty Hall problem--I thought of your book when I read this.
Hi Rich. I mention “the curious incident of the dog in the night&rdquo in my book. I loved that novel! Hope you enjoy the Monty Hall book.
Check this out: http://www.scribd.com/doc/20823892/Monty-Hall-Redux
Moral: There are pigeons and then there are "pigeons"
5 out of 4 pigeons, however, performed poorly at statistical analysis.
Hah! Looks like you jumped to conclusions yet again. Everyone knows that undergrads aren't human!
Does this mean that pigeons are Bayesians?
Having not read the paper, I'm wondering if the pigeons simply responded to something happening to one of the items not picked. That is, they picked an item, it just sat there, and then some other lucky hairy biped picked another item and something happened. So the "choice" is to "pick another item."