The July 5 issue of Newsweek has an interesting piece (not online) about the weird interaction between money, the brain, and social psychology. Try this experiment: Take any two people. Give one of them (A) $10 and tell them they *have* to offer some of the money to the other person (B), who is free to accept or reject the offer. Game over. The goal is for both parties to walk away with as much money as possible.

As predicted by John (“A Beautiful Mind”) Nash, A *should* offer $1 to B, and B *should* accept the offer. But what in fact happens in the vast majority of cases where the experiment is tried is that low offers of $1 or $2 are almost universally *rejected* by B, even though it serves B’s best interests to accept the offer. This is where funny motivators like pride and dignity interlope, overriding pure reason. B is insulted that A would keep most of the money for themselves, and so rejects the offer altogether. And for similar reasons (sensitivity to the prospect of insulting another), most people playing A don’t offer $1 or $2, but something closer to a 50/50 split, e.g. $4.

It makes no mathematical sense for B to reject any offer, and it makes no mathematical sense for A to offer more than $1, but that’s how humans interact. Interestingly, people *will* offer or accept just $1 when playing the same game against a computer. But the part that I found really fascinating is that there is one group of people who play the game “rationally” (I put rational in quotes, because I do think that treating humans fairly is a rational thing to do, even if not mathematically sensible) — autistics will generally offer or accept $1, since they lack the sense of social fabric that most people experience.

Can I borrow a dollar?

I’ve just finished reading The Curious Incident of the Dog and the Night Time by Mark Haddon – an excellent story and also very good on both mathematical puzzles and autistics.

One that really threw me was this, the “Monty Hall Problem”: you’re on a game show, you’re presented with three doors. Two have goats behind, the third a car. You pick one of the doors. The host opens one of the other two doors to reveal a goat. You are then given the opportunity to switch your choice of doors before the final two are opened. Do you do it?

This seems really counter-intuitive, but if you switch to the other unopened door then you actually double your chance of winning the prize! The reason is that there is still only a 1 in 3 possibility of the prize being behind the door you first picked, but there is now a 2/3 possibility of it being behind the other unopened door. When this problem was first published, it attracted ridicule from many prominent mathematicians and scientists who insisted there was a 50/50 chance of the prize being behind either door, but they were actually wrong. Weird.

Dan, the more I think about this, the less I understand it.

> The reason is that there is still only a 1 in 3 possibility of the prize being behind the door you first picked,

How can this be true? At this point, you can forget all about the first goat/door. Throw it away. It’s as if the game started fresh and you are given two doors and you know that one of them has a car and one has a goat. I really can’t understand how your first choice now has a 1/3 chance. It clearly seems 1/2.

> but there is now a 2/3 possibility of it being behind the other unopened door.

Again, same problem. Can you explain this more?

“The Prisoner’s Dilemma shares with many other social science “models” a socially remote set of suppositions and nonsuppositions. It contains, and excludes, just enough data to enshrine the axioms of the discipline in question (a peculiarly predatory version of “economic” or “rational” man in the case of economists), but not enough to plausibly represent any real social situation. Thus the prisoners in the problem are assumed to have enough social reality to prefer freedom to prison, but not enough to feel brotherly devotion, or to be concerned for the effect on their mother if one betrays the other, or to take any account of the culture of crime in which both brothers have previously lived. Such “models” are emblems of disciplinary assumption rather than algorithms of viable computation, and computations made with them are nugatory.”

http://www.umass.edu/wsp/statistics/lesson/01/prisoner.html