PIGEONS RULE AT THE MONTY HALL PROBLEM
January 4, 2017 7:03 PM   Subscribe

CHECK THIS OUT: PIGEONS VERY GOOD AT MONTY HALL. HERE'S THE PDF. HERE IS YOU CAN TRY IT, HUMAN. HERE IS BERT THE HUMAN DOING THAT DAMN DANCE WE ALL LOVE (THE PIGEON). HAVE A GREAT NIGHT EVERYBODY
posted by Greg Nog (34 comments total)

This post was deleted for the following reason: Poster's Request -- frimble



 
Do I get to keep the goat.
posted by mountmccabe at 7:25 PM on January 4, 2017 [5 favorites]


Why does the PDF describe the goat as "mangy"? Now I don't want to keep the goat. Which I won several times, vs one car.
posted by wallabear at 7:30 PM on January 4, 2017 [1 favorite]


A quick search of Ig Nobel Prize winners finds that pigeons are not unknown as subjects of strange research projects. This may be another contender.
posted by key_of_z at 7:33 PM on January 4, 2017


You get to keep the goat if you buy it a nice enough dinner first.
posted by mrgoat at 7:42 PM on January 4, 2017 [1 favorite]


Also, the goat's mane is glorious and long.
posted by mrgoat at 7:43 PM on January 4, 2017 [5 favorites]


All I got was a duck and a bag of grain.
posted by Mchelly at 7:49 PM on January 4, 2017 [1 favorite]


Wait, does the lettuce go in the boat with the wolf and the sheep gets to wander off with the pigeon? Confused.
posted by Eyebrows McGee at 7:50 PM on January 4, 2017 [2 favorites]


You get to keep the goat if you buy it a nice enough dinner first.

With all eponymously due respect, mrgoat, I'm pretty sure I could print the PDF and hand it to the goat and it would qualify as a nice enough dinner.
posted by maryr at 7:56 PM on January 4, 2017 [5 favorites]


Quote:

A second approach, empirical probability, involves collecting observa-
tions and making predictions based on the relative frequencies
with which events have occurred in the past. Strategies based
on empirical probability consequently take longer to learn
than those based on classical probability and are subject to
random fluctuations (especially in the short term). Despite
these limitations, pigeons effectively used empirical probabil-
ity to solve the Monty Hall Dilemma, as evidenced by the fact
that their responses were random at the beginning of the
experiment and changed as the pigeons gained experience,
eventually settling on the optimal approach. Humans also
learned from experience, but they fell short of the best strat-
egy. Thus, they must have been using something other than (or
in addition to) empirical probability.

posted by Brian B. at 7:56 PM on January 4, 2017 [3 favorites]


But what about the seagulls?
posted by Literaryhero at 7:58 PM on January 4, 2017 [1 favorite]


I have a question about the Monty Hall problem as it relates to the children's card game Rat-a-tat Cat: in Rat-a-tat Cat, one frequently has the option of taking a visible card of moderate value, or trying for a better number by taking the face down mystery card from the draw pile. Dos the Monty Hall problem say I should take the face down card?

My 14 year old has tried to explain the Monty Hall problem to me many times but I still don't understand. However, I am pretty good at Rat-a-tat Cat.
posted by latkes at 8:13 PM on January 4, 2017 [1 favorite]


Thus, they [humans] must have been using something other than (or
in addition to) empirical probability.


Yeah, I've met some humans who really want to be pigeons.
posted by polymodus at 8:22 PM on January 4, 2017


The thing with Monty Hall problem is that the person running the problem always picks a goat, instead of randomly opening a door, like one might assume. Apparently, this is to be evil and to mess with you so people can think you're dumb if you pick the sub-optimal strategy. But this is accomplished by making it easier for you to win, by making the "open the other door" and "choose randomly" options better, not by making the "stick with the same door" option worse, so it doesn't make any friggin' sense that even someone trying to be evil to you would do that sort of thing. Which is why it confuses the heck out of the human brain.

It's not just that the statistics are confusing, it's that the motivation doesn't make a lick of sense.
posted by Zalzidrax at 8:26 PM on January 4, 2017 [2 favorites]


The Monty Hall problem is great for tripping up people who like to think of themselves as smart, and also for ruining friendships.

The odds you pick the winning door are 1/3 in the show. Monty's actions do not effect the odds, you are given the choice to have a 2/3 odds instead.
posted by MikeWarot at 8:27 PM on January 4, 2017 [1 favorite]


Abstract argument about The Monty Hall problem is also great because the real Monty Hall had the option of whether or not to offer to switch at all depending on his mood, in spite of those who seem to think his actions don't matter or can't change the outcome.
posted by Earthtopus at 8:31 PM on January 4, 2017 [3 favorites]


Worth noting, at the bottom of this page is a link to a past discussion on common sense, featuring a video in the first post that used the Monty Hall problem to illustrate how common sense or "instinct" is misguided. It appears that pigeons unraveled this point, showing that humans were not necessarily using common sense, but a rational choice that put even odds on round two, perhaps conditioned to begin the problem there rather than carry assumptions forward. The Monty Hall problem should assume that our first choice has 1/3 probability of winning from the start, while the last/unpicked door that survived an elimination (which our pick was excluded from), thus had a 2/3 chance of winning from the start.
posted by Brian B. at 8:38 PM on January 4, 2017 [1 favorite]


Possible Origin of Cross-Species Differences: You peck at one button, and a light goes out or something. You don't get the prize. So, what you gonna do then smart guy? You peck at the other button. Maybe it's the good one. Common sense, innit?
posted by sfenders at 9:08 PM on January 4, 2017 [2 favorites]


The contest Isn't fair. That just means pigeons are immune to math goblins.
posted by Popular Ethics at 9:15 PM on January 4, 2017 [3 favorites]


how come nobody is questioning the idea of bert having legs
posted by not_on_display at 9:23 PM on January 4, 2017 [3 favorites]


Nice study. I always enjoy animal cognition findings in which the animal subjects outperform humans on an analogous task. But, there's often a fairly prosaic explanation. From the paper:
Pigeons completed up to 100 trials per day over 30 days (see Fig. 1). Human participants completed 200 trials using a computer display and touch-screen monitor.
(My emphasis.) In other words, pigeons had 15 times as much practice at the task as the humans did, and they had the benefit of sleeping in between practice sessions (which we know consolidates learning even more than just additional practice time). So comparing the learning outcomes between humans and pigeons here is really apples-and-oranges; perhaps if the humans had a similar amount of experience, they would have performed similarly well, or better. Conversely, perhaps the pigeons' early performance, which the researcher didn't present an analysis of, would show evidence of biased behavior similar to that of humans, and only the considerably greater training they received allowed them to overcome it. If this latter possibility were true, it could suggest that pigeons in fact have cognitive biases in making inferences about probability, just like humans.
posted by biogeo at 10:24 PM on January 4, 2017 [3 favorites]


Herzog informs me how the chicken wins at tic-tac-toe, but...
Leonard Mlodinow's||The Drunkard's Walk:How Randomness Ruins Our Lives was my primer for distinguishing probability and statistics (Monty Hall problem). Plus, he co-authors with Stephen Hawking and wrote Trek scripts.
posted by lazycomputerkids at 10:38 PM on January 4, 2017 [1 favorite]


I love the NYT article linked to by Earthtopus - firstly for going and tracking down the actual fucking Monty Hall and secondly for showing his penchant for stomping all over the dry world of the abstract problem. Would you opt not to switch to the second door if he gave you $3000 to stay where you were? What about $5000? Or maybe he just opens the door you selected in the first place and gives you the goat - it was your choice buddy!

Pigeon intelligence is something much more studied then one might assume: they can pick a Monet from a Picasso, for example. But their world is concerned about finding grain, churning our squabs and carrying the odd message for the Rothchilds - no need to waste energy working out whether somebody might be trying to con them. Here it is that focus that makes them effective: there are 3 fields that have corn in them, you are on your way to the first of them when you notice that the second one has no corn in it - that means its time to head to the third field without any further delay.

On the other hand, pigeons don't have such a successful track record with decoys - so I think the dovey equivalent $3000 side offer might be their undoing.
posted by rongorongo at 10:55 PM on January 4, 2017 [1 favorite]


I can recommend Pigeons: The Fascinating Saga of the World's Most Revered and Reviled Bird
Probably because I was a kid when The Flintstones was in heavy, afternoon syndication, I've always said if humans were so smart, we'd have trained squirrels and pigeons to remedy our litter.
posted by lazycomputerkids at 11:10 PM on January 4, 2017


if you play the game multiple times you might get both a goat AND a car and then you can forge them to upgrade to GoatKart

Mr. Nog is clearly trying to establish a car-goat cult.
posted by GenjiandProust at 5:20 AM on January 5, 2017 [12 favorites]


I hear they are very supertitious; perhaps they think it is good luck to switch doors.
posted by thelonius at 5:44 AM on January 5, 2017 [1 favorite]


Monty Hall's still alive, too!
posted by Earthtopus at 6:11 AM on January 5, 2017


Conversely, perhaps the pigeons' early performance, which the researcher didn't present an analysis of, would show evidence of biased behavior similar to that of humans, and only the considerably greater training they received allowed them to overcome it.

Thanks. Your post reminds us that with randomness from Monty Hall, or choosing a random door for first round elimination and not bypassing the winning door, there would be no Monty Hall Problem, because the winning door would be picked right away and not avoided. The pigeons applied brute force with no human shortcuts exploiting their miscalculation. Humans naturally tried to avoid the learning curve by applying a rule, but they wrongly assumed randomness from Monty.
posted by Brian B. at 7:21 AM on January 5, 2017


In case you were wondering, the molecular biology equivalent of the Monty Hall problem is that if you and your spouse both carry a embryogenic lethal gene, the chance of you progeny carrying it is 2/3 which is DEVESTATING to learn on a bloody exam which is why you walk students through early probability so slowly that everyone thinks biologists can't do math when REALLY we are the ones who do math because we use NUMBERS and you snotty engineers can go infinitely sum yourselves.
posted by maryr at 10:08 AM on January 5, 2017 [2 favorites]


But you weren't wondering, were you?
posted by maryr at 10:08 AM on January 5, 2017


oh no pigeons
posted by beerperson at 10:14 AM on January 5, 2017 [1 favorite]


Did the research control for the fact that chickens, as theropod dinosaurs, belong to a suborder with well-known goat-eating proclivities?
posted by tobascodagama at 10:42 AM on January 5, 2017


That's awesome. I suppose it makes sense that we're hobbled by biases and incorrect abstractions. I wonder if you could design a version that's opaque enough we don't bother trying to think it through and successfully develop the correct superstitions.

> if you and your spouse both carry a embryogenic lethal gene, the chance of you progeny carrying it is 2/3

What, I'm totally wondering now.
posted by lucidium at 3:06 PM on January 5, 2017


Your progeny only survive to birth if they didn't inherit the 1/4 chance double recessive trait. So remember your Punnett square and cross out a quarter.
posted by maryr at 8:20 PM on January 5, 2017 [2 favorites]


Ah.
posted by lucidium at 11:08 AM on January 6, 2017


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