Choose a number between one and a hundred (1 - 100) that is two thirds ( 2/3 ) of the average of the numbers to be chosen by everyone in a room. (It could also be everyone in a town, a country or on a website.)
You can imagine that there are a few people with you in the room, or many people. You could choose a number at random, say 95.
But 95 is unlikely to be the average of all the numbers chosen by the people in the room. 50 is quite likely to be the average, or it would be if the numbers were being chosen at random.
But the numbers are not being chosen at random. They are being chosen by people who are trying to guess 2/3 of the average of everyone's numbers.
They should guess 33, if 50 was to be the average. So, 33 is more likely to be the average than 50. But, now if 33 is going to be the average, then we should choose 2/3 of 33, which is 22. However, if everyone is thinking like us, then we should go down to 15. It goes on like this. I'm now down to 10. But, perhaps you will stay on 22, because you think other people will say 33.
I've only met one person who ever went down to 0, who is someone in my family, and who knows how I think. Actually, I know I'm more likely to win if I stop at a higher number. And this is because other people usually choose a number between 20 and 40. We might ask why.
I think it's because if people are unfamiliar with the game, for whatever reason, they don't think too much about it. And, even if I offer a prize, it doesn't make much difference. Even with a large number of people the 2/3 of the average number averages to about 22. And even if the people are very well informed already, it very rarely gets down to as low as 15.
What is going on here? Initially I found the results to be quite astonishing. After all, we ought to think about how others are thinking. It's called a "theory of mind". If the others average on 30 in this game, then we should think 20, etc. But, then I developed my own "theory of mind". I have to admit that some people are not as interested in these games, as I am. They may not be listening. Others 'game' the game, by choosing a minus number, or even a very large number. Should we count these, even though they have broken the 'rules'? Others might be sleepy, bored, or just creative. Some people like the number 100, after all.
I now have a new "theory of mind". When we evolved on the savanna, or on a tropical beach with coconuts, or wherever we ended up for millennia, we learned to think about what the others might be thinking; hence taking us down to 33. And we also had to learn to think about what the others might be thinking about what we were thinking; now down to 22. It gets very useful in love and negotiations. But, beyond that we simply didn't have much time or use for further analysis. We were better off thinking about something else.
