The Monty Hall problem is one oft quoted by fundamentalist economists to ‘prove’ that mere humans cannot recognise a rational course of action when it is staring them in the face
It is based on a familiar kind of television game show. The contestant is offered three locked boxes, in one of which lurks a valuable prize. The other 2 contain mere trinkets. The contestant gets to choose which box to unlock
The twist is that Monty Hall the quiz master first opens one of the others to reveal - a trinket (he of course knows what is in each box)
And offers the contestant a chance - change their mind or stick with the original choice
Which box should a rational contestant choose?
The economist’s answer is that a rational man would always change his mind & go for the box which Monty did not open, because the odds are 2 to 1 that the prize lurks in there
There are several ways of working out this ‘correct’ answer.
There was a 1/3 chance that the contestant chose the right box in the first place, so there were 2 chances in 3 that the prize was in one of the other boxes, at least one of which must contain a trinket. The fact that Monty revealed the trinket does not alter the original 1/3 probability that the first box the contestant chose contains the prize versus 2/3 that it did not
For those who really need some convincing it is quite a good idea to take the frequentist approach of listing all the possible outcomes
Many people might think it ought to be 50:50, because at that stage of the game the original box either does, or does not, contain the prize, & the same applies to the box which Monty did not open
The producers of the show, or those who finance it, must hope that most contestants will stick with their original choice, for they will pay out less in the long run of the show
If contestants could get together to agree a strategy they might agree always to change their mind, & divi up the winnings afterwards – though this would require a large degree of trust between them
In reality however each contestant gets only one chance at the game. This is not the long run, it is now or never. Maybe this is the one time in 3
And in a sense the 50:50 assessment is right – he is either right or he is wrong, he picked the prize first time or he did not
If he just chose wrong first time, well that is just the luck of the draw, the rub of the green, plain bad luck
If it does turn out that he was right first time, but that Monty persuaded him to change his mind, then there is a very real chance that the contestant will feel that he was tricked, bamboozled, somehow talked out of his prize
Maybe the rational economist knows that he was right to change his mind
Funnily enough scientists have discovered that the feeling of being cheated evokes the same revulsion response as foul-tasting food & drink. They even have an evolutionary explanation for it
So unless the economist knows he can resist the feeling of being cheated, even when his friends make a point of sympathising with him, why then he is a rational masochist
Because Monty knew all along - there's the rub
