on stupidity

This story courtesy of Justin (his words, from an email):

"It's like this brilliant test, where some professor asked participants to guess a number from 1 to 100, and try to be closest to 2/3 of the mean number guessed by all participants. So this brilliant participant worked out that if numbers were randomly chosen from 1 to 100, the mean should be close to 50, and the answer closest to 33. However, that should be obvious to everyone, so the answer would be reduced to 2/3 of that, which is 22. It shouldn't stop there however, but be repeated ad inifinitum. He cleverly found the right answer of 0.

The professor revealed the results, where a sprinkling of people guessed 50 (or higher) [say hello to the brain dead], a few people had guessed 0, and the majority of people had guessed 33. Hence some person in the low twenties won, which was about the same as other times the professor had tried the experiment apparently.

It should be quite obvious to us both to have guessed 22. Why? We know only too well people are idiots, but let's give them some credit, in classes like that, people should usually be of above average intelligence. That means they have just about enough brains to go through step 1. "Hmm, random numbers from 1 to 100 should generate 50 as an average, and 2/3s of that is..." If you then take another step forward, knowing most participants (who aren't brain dead) would guess 33, you can easily guess 22. If you try to be clever, and reduce it "Logically, the answer should be 0, since it must repeat to infinity!", then you've made the very fatal assumption that people are absolutely rational, and put in the effort to think on more than a basic level. Thus outsmarting yourself. If you really thought things through (to make the guess of 22), you'd probably realise the braniacs and brain-dead should about balance each other out (as it apparently did), and thus not have to adjust your answer."

This is how I get through the days.