Why do we fall for the Monty Hall problem?

After posting on the Monty Hall problem ten days ago, I’ve done a bit more reading. Mainly because you guys seemed so interested in it! (It’s been surprising how much traffic that post got.) Anyway, as I’ve been reading it’s become increasingly clear that the Monty Hall problem is a classic in both statistics and psychology.

Why is it a classic? Because we all seem to get it so wrong. In one study, (quoted in Krauss and Wang, “The psychology of the Monty Hall problem: discovering psychological mechanisms for solving a tenacious brain teaser”, Journal of Experimental Psychology, Vol 132, No. 1, 2003) only 13% of participants correctly chose to switch doors. Krauss and Wang commented on the literature: “Until now, all experimental studies have had similar results: The vast majority of participants think that switching and staying are equally good alternatives and decide to stay.”

“Only 13% of participants correctly chose to switch doors.”

This raises a really interesting question. If you think the remaining two doors are equally weighted, why does everyone (or 87% of people, anyway) choose to stay? Krauss and Wang go on to quote another study where: “Participants reported that they would feel worse if they switched from a door with the car behind it than if they stuck to a door with a goat behind it because, in the first case, they had picked the winning door but then decided against it.” (Note that in this description of the Monty Hall problem, the prize is a car and the non-prize doors aren’t empty, instead they have goats behind them).

“Participants reported that they would feel worse if they switched from a door with the car behind it…”

This is crucial. Participants say they would “feel worse” if they switched and then got it wrong. This is a classic example of “loss aversion”. Loss aversion simply means that as humans we dislike losing something more than we like gaining something. Daniel Kahneman gives a great example of loss aversion in “Thinking fast and slow” (Farrar, Straus and Giroux, 2011). He does this by way of example (p 283):

You are offered  a gamble on the toss of a coin.

If the coin shows tails, you lose $100.

If the coin shows heads, you win $150.

Is this gamble attractive? Would you accept it?

Most people don’t accept this bet. Even though it’s clear that the expected pay-off is positive. Why? Because the pain of losing $100 far outweighs the pleasure of winning $150. In fact, for most people you have to offer them a win of $200 for them to take on the risk of losing $100 (p 284).

This effect – loss aversion – runs through a lot of our world – certainly in investment decisions – but also in wage and salary negotiations. The pain of losing is greater than the pleasure of gaining.

And it’s this effect that seems to be at play in how we react to the Monty Hall problem. We aren’t going to switch, because the pain of getting it wrong after switching is worse than the pleasure of getting it right after switching.

Fundamentally, when it comes to decision making, we aren’t rational actors.

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