Intuition, and why pigeons may be smarter than us.

[Michael]

Hey!
So by now most of you know that I am (for lack of a better layman's term) a "video person".

Anyway, this forum has been dead recently so I thought I would add something. It's the script for a video I've started animating. Any thoughts feel free to add! Or just photos of pigeons if you have nothing else. Though honestly, I think you can do better than that.


"INTUITION (and why pigeons may be smarter than us)"

Intuition is a funny thing. For seemingly good reasons, we have developed an innate trust of our intuition, our "gut feelings", to the point that we will often trust them even over the logical choice staring us in the face.

But before we can see why, we're going to have to play a little game. Even if you know this one, play along, we'll talk more after.


Welcome to "let's rip off a game show", the amazing and totally original quiz show not based on "let's make a deal" hosted by Monty Hall...

Okay, fine. It is. So much so, in fact, that the common name for this mathematical problem is called the "monty Hall Dilemma". But that's not important. Let's move on.


So, you've got 3 doors in front of you. One contains a prize. For fun, let's make it......a (season 5 boxset of medium. Because who can't love mediumshipnesness?). Behind the other two doors is nothing.

So we mix up the doors......

Now, take your pick. Since this isn't actually interactive, let's go ahead and pretend you picked door #2.


At this point, your all-knowing host - in this case, me, opens one of the empty doors. (open door 3)

So at this point you have a choice. You can keep what is behind your door, or you can switch doors, and take whatever is behind that door. So, what do you do?

If you figured 2 doors? it's a 50-50 chance that I'm right now. So switching isn't going to achieve anything. Plus I clearly missed at least one of the empty doors so maybe my instincts were right.

If you thought that then congratulations, you are among the staggering majority of people who have never heard this problem before.

You're also completely WRONG.

Let's look at it.

So let's say the prize was behind door number 1. That means that doors 1 and 2 were empty. Now, when we pick our first door, there is a 1 in 3 chance that the prize will be behind it. That means there is a 2 in 3 chance that we will choose a door without a prize. When we reveal the first door, we create a situation where switching doors will result in either going from a losing door to a winning door, or a winning door to a losing door. BUT because we were twice as likely to have chosen a losing door, the chances of going from a losing door to a winning door is also twice as likely.

It's a pretty simple math problem, really. What's interesting though, is that even though you've just had it explained to you, a lot of you will still be sitting there, scratching your heads and wondering what the hell? It's 50-50 dammit!

It's not. Try it for yourself, there are plenty of Monty Hall simulators out there.


In fact, so much do we rely on our intuition over facts that when this problem was first presented in [parade magazine], it's reported that over 10,000 people wrote in to dispute the fact, including a large number of scientists and mathematicians who should know better.


Well that's all fascinating, I hear you say, but where do pigeons come into it? Hold on, I'm getting there.

Scientists from Whitman university performed a study involving having pigeons run a simulated monty hall 5 times a day for 30 days. By the end of the trial, the pigeons had figured out to switch, and were doing so 96.33% of the time, an almost perfectly optimal strategy.

In contrast, when the same scientists ran a similar test using undergraduates, the results showed that human subjects were almost a third less likely to choose to switch, having not discerned the pattern.

so why is this? There are a few suggestions.

Throughout our life we are presented with a lot of situations where we have to make choices. quite often we're required to make choices rather quickly.
As such, over time we develop a large set of "rules of thumb" or intuitions, if you will that help us to make those decisions.
One of those "intuitions" is how we evaluate probability. Now, whilst it may be best to track the outcomes of a given problem over time and make predictions based on those [empirical probability], it turns out we generally don't do this.

Instead, we are constantly evaluating and re-evaluating our situations, and trying to predict all possible outcomes of a situation.

Another factor is our ability to ignore seemingly irrelevant data. So when the first incorrect door is opened, and thus seemingly removed from the equation, our minds update our probability predictions to a 1-in-2 chance, forgetting that when we made our initial choice the door was in play and as such remains an important factor in the subsequent outcome.

Pigeons, it seems, don't have this problem.

So do they know something we don't? Are pigeons smarter than us?

No. At the end of the day, the reason why have these rules of thumb is that over time, we have learnt that it is generally better to use this intuition to come to a quick conclusion, rather than the slower empirical method.

It is important to remember, however, that even when we think we are right, and every bone in our body says to trust our intuition, we may just be wrong. Maybe in those cases it's best to take a step back, look at all the data, and make a choice from there.

In short, maybe on occasions it's better to think like a pigeon.

[Smellyoldgit]

Michael wrote

it's a 50-50 chance that I'm right now.

It's 50-50 dammit!

I have visions of Jerry creaming his cassock ....

[Professor Chaos]

Show me the study where human subjects were also used 5 times a day for 30 days for comparison, then we'll talk.

[Michael]

This is the paper that came from -
Are Birds Smarter Than Mathematicians? Pigeons (Columba livia) Perform
Optimally on a Version of the Monty Hall Dilemma
http://people.whitman.edu/~herbrawt/HS_JCP_2010.pdf

It appears I may have also subconsciously gotten the name for my stuff from that paper, so I might need to change it. Anyway, from the paper, regarding grad students in the experiment -

An experimental session consisted of a series of 200 trials organized into four blocks of 50. Between each block, participants were allowed to rest for as long as they wished before continuing to the next block.

One participant in Condition 1 was eliminated due to prior familiarity with the Monty Hall Dilemma, leaving 6 participants in each condition.

I'm not sure doing grad the students over 30 days is really neccessary. Besides, doing it in that time period increases the chances of them discovering the monty hall dillemma on their own and tainting the results with pre-knowledge.

[ghoulslime]

I've always thought that chickens are more intelligent than most Christians. Pigs are certainly more intelligent than Muslims.

[Professor Chaos]

Michael wrote

I'm not sure doing grad the students over 30 days is really neccessary. Besides, doing it in that time period increases the chances of them discovering the monty hall dillemma on their own and tainting the results with pre-knowledge.

Well, eliminating humans for having "knowledge" kind of ruins the premise question, "Are pigeons smarter than humans," no?

Anyways, if the pigeons were given 30 days to figure it out, it certainly doesn't make a fair comparison if the humans aren't also given the 30 days.

Does the study cite the pigeons success rate each day or just at the end? (Can't click.)

[Michael]

Professor Chaos wrote

Well, eliminating humans for having "knowledge" kind of ruins the premise question, "Are pigeons smarter than humans," no?

Not when the question is "how long will it take for them to figure out the answer to this problem" and the knowledge is "the answer to this problem". That kind of ruins it if you let them stay.

Anyways, if the pigeons were given 30 days to figure it out, it certainly doesn't make a fair comparison if the humans aren't also given the 30 days.

Does the study cite the pigeons success rate each day or just at the end? (Can't click.)

I honestly can't remember exactly what numbers they give on the success rates. I'll have to re-look at it later.

As for that whole it being unfair thing, I don't have anything to say in defence or against it. I think they outline something about it in the paper, I can't remember exactly(I'm not an academic, so it took damn near all of my concentration just to get through the thing first time around).
There are undoubtably explanations for it, just not sure exactly what they outline them as being. Though like I said before, one good reason I can think of for not having it over a longer period of time is that it increases (a great deal) the chances that they will discover the monty hall dillemma and subsequently taint the results.

[Professor Chaos]

You said "taint." Heh.