Better thinking
I've been thinking a lot lately about how we think about value. And how and why we get it wrong so often. Maybe it is because of the supposedly ideological and philosophical debates raging about the the state of the world and our future, maybe because I am around a bunch of college students for the first time in 25 years. Maybe it's because I'm teaching them Economics. Maybe all of the above and more.
I believe our perception of value is a large part of how we choose.
I believe that choices we make today will affect how things will be tomorrow. And the collective impact of many. many days and years of choosing will affect how things are going to be years from now. Not just the "butterfly affect" but that and more. Exponentially more.
For a demonstration of our inability to establish value and to make sub-optimum choices see TED talks for Dan Gilbert, Michael Shermer and Al Seckel. (And probably several others- check my favorites (I'm MDarling) or follow the links TED suggests.)
But here is something that is either really dumb or really brilliant. I have been staring at the answer for thirty minutes. And when I keep looking at it, I get it. But as soon as I look away (like now to publish this) I slip back and start thinking nahhh....it has got to be 50/50...Gotta be!
So, suppose you're on a game show and you're given the choice of three doors to win the prize behind each door. Behind one door is a car or a box with a million dollars or something valuable that you want; behind the other two doors, goats; that is, junk of no value. The car and the goats were placed randomly behind the doors before the show.
The rules of the game show are this: After you have chosen a door, that door remains closed for the time being. The game show host, who knows what is behind all three doors, now must open one of the two remaining doors, and he must open a door with a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After the host opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last unchosen door. Example: imagine that you chose Door 1 and the host opens Door 3, revealing a goat. The host will ask you Do you want to switch to Door Number 2?
Is it valuable for you to change your choice?
Why or why not?
Warning: Just because my head did not hurt yet form looking at this does not mean your head will be likewise unaffected.
This is the kind of thinking that I believe affects our choosing. Confuses our choosing, more often than not. And this is exactly the kind of choosing that I would expect AI to get right, assuming we can frame the problem correctly and define our desired outcomes correctly.
Comments
This is why poker is so valuable -- developing a winning strategy requires embracing a good deal of counter-intuitive math, such as situations where it's okay to raise or fold, but calling is a big mistake.
Bet $0, good. Bet $10, good. Bet $5, bad.
Or say you're playing limit hold 'em and on two successive hands (in early position) you get a pair of Jacks and then a pair of fives. On which hand do you want as many opponents as possible, and on which do you want to keep the number of opponents down?
It's backwards!
BTW, completely OT, the Monty Hall thing reminds me of a birthday card I got once. On the front it said CHOOSE YOUR BIRTHDAY GIFT with a picture of a car, a boat, and a frog. When you opened it, it was just the frog, saying, "You know, it's not easy living with all this rejection."
Posted by: Phil Bowermaster | April 7, 2009 09:57 PM
Just imagine there are two candidates, A and B. A and B both choose the same door. After the moderator picked one door A always stays with his first choice, B always changes his choice to the remaining third door. Now imagine you run this experiment 999 times. What will happen? Because A always stays with his initial choice, he will win 333 cars. But where are the remaining 666 cars? Of course B won them!
Another illustration:
Let us conduct the experiment with 100 doors! Now let's say the candidate picks door 8. By rule of the game the moderator now has to open 98 of the remaining 99 doors behind which there is no car. Afterwards there is only one door left besides door 8 that the candidate has chosen. Obviously you would change your decision now! The same should be the case with only 3 doors!
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Basically by switching, your chance of picking the car is reduced from 1/3 to 1/2 since when you change your choice it means that the moderator picked one of two doors for you, when you picked one of three doors at the beginning.
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This stuff just shows that we are probability and statistic illiterate. If you really want to do what is right in regard to what you want, you better become an AI. You can basically start doubting everything, because so much is counter-intuitive.
You think about how to invest your money but don't think about how much more important and easier it might be to wear a helmet while driving a car...
Posted by: XiXiDu | April 8, 2009 03:43 AM
Car helmets
Funny you mention that one- I've been shopping for one recently.
Realizing in the world of data I'm just an an anecdote - here's how stoopid I am.
Once upon a time almost 20 years ago I was a daily motorcycle rider. Always wore a helmet, long pants, gloves, jacket, sunglasses if sunny, etc. My bike was in good to great shape- tires, brakes, lights, horn, etc. I never rode drunk. I avoided riding and driving after 7pm on Fri & Sat to avoid the other drunks out there. I was careful.
I was living in CA at the time and the CA legislature was inspired to take up a helmet law for motorcyclists. I wore a helmet- but opposed the law.*
And almost every social argument made to support the proposed law was peeled apart in the larger context of cars and trucks. Head injuries? Car and truck drivers and passengers have way more avoidable head injuries- if the law was really motivated to minimize head injuries, it would require car and truck drivers and passengers to wear helmets.
I opposed the law. I understood the data. I wore a helmet when riding my motorcycle. I wore a helmet while skiing (I was early on that one). I wore a helmet when flying jets. But it still was only recently I started looking for a helmet suitable for driving a car.
I've just about boiled it down to a bicycle style helmet- need something that does not interfere with hearing or visibility. A constant tradeoff in motorcycle land.
*I opposed the law even though I knew it was good policy for three reasons.
1) imposing the requirement on motorcycles reinforced bad thinking. See the data on avoidable head injuries and cars and trucks.
2) Legislating what I wear and how I manage my personal bio-space when it's not infringing on yours seemed too intrusive.
3) Over time, those who choose to ride helmetless will either be very, very good riders or they'll be injured. If injured prior to breeding - Darwin award. If injured/killed after- well, maybe the next generation will figure it out anyway and resist the genetic urge to be stupid.
Posted by: MDarling | April 8, 2009 09:18 AM
Blah, I meant of course 2/3...
Posted by: XiXiDu | April 8, 2009 09:42 AM
figured- but it just goes to show- all that careful and correct non-intuitive thinking and it still comes out wrong
Posted by: MDarling | April 8, 2009 04:00 PM
Hey MDarling, don't overlook the supply of organs for transplant that helmetless bike riders provide.
Posted by: Mark Parker | April 9, 2009 08:54 AM