...Prove Their Worth...

"Problems worthy of attack
prove their worth
by hitting back." - Piet Hein

A kind of running diary and rambling pieces on my struggles with assorted books, classes, and other things, as they happen. You must be pretty bored to be reading this...

Saturday, June 08, 2002

underthumb reports on an interesting (though, from my amateurish perspective, fatally flawed) experiment in psychology. People are presented with a box with a known ratio of black/white marbles (.5), and a box with an unknown ratio of marbles. Experiments then show that people tend to pick the known-ratio box over the unknown box. There is then the claim that this is stupid and irrational. The argument goes like this: if, say the 'win condition' is getting a black ball, people tend bet on the known-ratio box. You've thereby made a bet that the ratio for the unknown box is worse (that is, more white than black) than in the known box. Put the ball back. Then make people pick again, this time making a white ball the win condition. People still pick the known box, 'betting that the ratio in the unknown box is worse', in the opposite direction. So you've just made two 'opposing' bets about the same damn box. Irattional? Stupid? Um, hell no. I'm going to try to make the argument that it is perfectly rational, and smart to go with the known, rather than the unkown, and to claim otherwise is ... unwise.

First, the flaw in the experiment. It's good, in setting up the experiment, to keep it simple, and strip away the irrelevant. It's possible to strip away essential variables, however, and the marble problem is an example. Let's try a slightly more complicated setup. Say you're given some win condition, and two choices of 'path' to that condition. One path is described to you prior to an attempt to get to the win condition, the other is undescribed. Say futher that the win condition and paths are complex enough to allow on-the-fly and pre-op choices in moving toward the win condition (I suspect that's one of the big things that makes the 'evolutionary' approach that underthumb refers to work). Concrete example: two sets of road networks, with the objective of getting a certain distance in a certain time.

In this case, it's completely bloody obvious that it's a good idea to pick the road network that you know about. You can plan a route ahead of time with it, and make informed on-the-fly choices. With the 'unknown' road network, you can't. You might get to your destination faster (it might be a much straighter path, for instance), but betting that way is stupid - it might just as easily be worse, and you've got no planning or information benefits.

The marble experiment strips away the utility of the given information, thereby making it a stupid test of the 'better a known than an unknown' phenomenon -- after all, in Real Life, information does tend to be useful. But forget that. Even with the problem as stated, it's smart to go for the known.

When you make that first choice of known box to get a marble from, you aren't making any bets as to the other box. All you're stating is that you don't know the ratios for the unknown. Could be worse for you, could be the same, or could be better. You don't know, and it's a given that you can't know. So, because you want to win, and you don't want to take the chance that the unknown has no 'win balls' at all or something, you go for the known. In the second experiment, nothing has changed. You still don't know anything about the unknown. So the very same reasoning applies to the second draw as to the first one. It's not unlike coin tosses - the outcome of one flip has no effect on the probabilities of subsequent flips. Basic fact of statistics.

I'm a rank amateur. It's possible I Just Don't Get It, or I'm missing something important. But as it stands, it seems to me that any psychologist that claims people are wrong in this marble experiment hasn't thought about it very carefully.

Counter-arguments welcomed.


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