Cognitive Dissonance & Monty Hall

There have been some interesting articles in the Times over the last couple days that, on reflection, might have some relevance to what we do.

First, a classic study (from 1956) about cognitive dissonance (and consumer choice) has been overturned. In the study, monkeys were allowed to choose a red or blue M&M. Say it chooses red. Next, it’s given the chance to choose between blue and green – will it choose randomly? No, study after study shows the monkey is more likely to choose green. Why? The classic explanation is that it’s rationalized its previous rejection of blue by telling itself it doesn’t really like blue in the first place (it’s retroactively justifying its previous choice to avoid cognitive dissonance).

Implication – that if we arrange for consumers to make one random choice, that this will impact their future choices, that is, if we want our customers to pick that green M&M we can make it more likely by first offering them the choice of the red or blue, and then offering them the green along with whichever one they rejected before.

Not so fast, though – turns out the whole experiment is based on a statistical flaw, called the Monty Hall problem, from Let’s Make a Deal. Try this problem on for size:

You’re on Let’s Make a Deal. Monty Hall shows you three doors, and tells you there’s a car behind one door, and goats behind the other two. Pick the door with the car and you win. Say you choose door #1. Monty then opens one of the other two doors to reveal a goat, and asks you if you want to switch. Should you? (note: in real life Monty can manipulate the result, for the sake of this problem assume that he must always open exactly one door that’s hiding a goat)

This is a HUGELY contentious issue, when the columnist and self-described genius Marilyn Vos Savant published the correct answer in Parade magazine in 1991 she got a torrent of letters from professors, mathematicians, etc., telling her she was nuts, but she was right. John Tierney of the Times actually met with Monty Hall himself and proved it.

The answer is that you should switch.

Why? Wouldn’t the odds be 1 chance in 2 that either door is right? Nope. Think of it like this: imagine you chose Door #1, and Monty offered you BOTH doors #2 & #3. You’d take it, right? The odds are 2 in 3 that one of those two doors is the winner. Well, that’s exactly what’s happening – Monty’s offering you BOTH door #2 and door #3 (odds are 2 in 3 that one is the winner) and then simply revealing that one of the two is a goat, which we already knew (one of the 2 has to be a goat, there’s only 1 car). So the odds that door #2 hides the car is still 2 chances in 3, and the odds it’s behind #1 is still 1 chance in 3. Switch! Don’t believe me? The Times has as simulation where you can play for yourself.

Implications for us? Humans have a really hard time with probability. The way we arrange the available choices can strongly influence which selection people make. If we’re relying on them understanding the odds, then we need to be careful, and of course if we’re Monty Hall, then we’re controlling the game by taking advantage of difficult it is for people to process this sort of problem.

Further reading: http://www.nytimes.com/2008/04/08/science/08tier.html

ps – what’s that got to do with the monkeys? Tierney explains it on the above page, but basically the researchers were making the Monty Hall mistake and therefore misinterpreting their findings