Are You Smart Enough to Change Your Mind?
If you made the wrong choice, are you smart enough to change your mind?
Cognitive dissonance is when something you believe is true conflicts with something that you know is true. Psychology tells us that our mind will try to fix this conflict, even if it has to make something up that’s not true. For example, have you ever wanted something that you couldn’t get but then tell yourself you’re better off without it? Whether that’s true or not, that’s cognitive dissonance in action.
The Monty Hall Problem
Suppose you were on a game show and were given a choice of three doors - behind one of the doors is a new car and behind each of the other two doors is a goat. You are asked to pick one of the doors and before you find out if you picked the door with the car, the host goes to the other two doors and opens one of the doors that had a goat. Now the game show hosts asks if you still want to stick with your choice or to change you choice to the other remaining door. What should you do?
This classic problem was named after the game show host Monty Hall, who basically gave such a choice to his contestants. If you were like me, you would have stuck with your first choice because you would have seen that the odds were 50/50 that the car was behind your door and you’re not better off if you change your mind. If you were like me, you would have made the wrong decision.
When I first made the choice, I had a 1/3 chance I picked the car. The other two doors each had the same 1/3 chance, so if someone else picked the field (picking all the remaining choices), that person would have a combined 2/3 chance of having the car. When the game show host intervened and took away the door that had the goat, he caused the last door to have the 2/3 chance of having the car. Clearly, a 2/3 chance is better than a 1/3 chance, so I should have switched my choice instead of sticking to it.
[If you had the correct answer the first time around, congratulations! However, if you still don’t believe the answer, see Marilyn vos Savant’s article, who first published this problem in Parade magazine.]
Can You Handle the Truth?
Apparently a lot of people picked the wrong answer. Thousands of people - including mathematicians - wrote to the magazine trying to explain that the odds are really 50/50 and that the published answer was wrong, but only a few were brave enough to write in later to fess up that their original 50/50 answer was wrong. In my opinion, the Monty Hall problem is much more than just a neat puzzle because it touches on an important and common problem: if we were given new information, will we recognize it correctly and change our choices if needed?
I can’t speak for the rest of the thousands of people who tried to correct an answer that wasn’t wrong. However, I was so thoroughly convinced that the answer was 50/50 that it took me a long time to get past my initial thoughts to properly figure the problem out, even after I read its explanation. It took a while before I replaced my “old reality” with the “new reality.”
I feel embarrassed that it took me a while to figure out the answer, but what if I never figured it out? What if I was not just deciding on something that affected me now but also my future, such as picking a direction towards my goals? If I encountered a Monty Hall problem relating to my path in life, how long would it take for me to replace my “old reality” with the “new reality” and change course, or would I simply update my old, incorrect version of reality and find a reason to dismiss the correct choice?
The Cognitive Diss
The psychological term for this is “cognitive dissonance.” When we face a conflict with the truth, there is a natural instinct to somehow resolve the conflict so that the mind can be at peace. The fable of the fox deciding that the grapes he couldn’t reach were sour is an example.
It’s only human to make the wrong decision sometimes, but justifying the wrong decision, even after getting new information, is unfortunately also a common reaction. So now that we know that our minds can’t be trusted, what can we do?
Fortunately there are a number of ways to handle it (thanks to Aaron J. Louie for summarizing them):
- Attitude Changes: Completely change one of the perceived truths. For example, if I think all vegetarian dishes are bland, and I come across a vegetarian dish I really like, my outlook on vegetarian dishes is forever changed.
- Bolstering: Compensate for the conflicting truth that is more important. In one study, a non-sexist group was subjected to sexist comments, and the group later showed an even stronger bias against sexism.
- Trivialization: Reduce the importance of the conflicting truth that is less important. If you like traveling but have a fear of flying, you could downplay the fear of flying so that it won’t stop you from traveling.
- Emotional Expression: Get to the root of the conflicting truth and resolve it. Revisiting the fear of flying, figure out why the fear is there to begin with and try to resolve it.
- Distancing: Put yourself far away from the conflicting truth. For examples, a lot of entrepreneurs already know that 90% of all businesses fail, but they distance themselves from this thought and still plod through with unbridled optimism.
I think filling the gaping holes in our knowledge with made-up (and often wrong) information is some sort of a natural survival instinct. The key is to try and keep this instinctive behavior in check so that we can make the best choices when we have to.
Additional Info
- The Monty Hall Problem: The game show problem as explained by Marilyn vos Savant.
- Interactive Monty Hall Game: Don’t believe the answer to the Monty Hall problem? Try it out yourself!
- Cognitive Dissonance (and more): The Urban Monk describes a few psychology techniques, including cognitive dissonance.
- Cognitive Dissonance vs. Monty Hall: An article from NY Times regarding how the Monty Hall problem may have affected prior studies on cognitive dissonance.
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This is an awesome post, great depth! This is such a tough thing to crack because as humans we absolutely hate to admit when we’re wrong.
It’s funny though, the most successful people in the world are those who are willing to see they are wrong, make a change, then try again and again and again. I think entrepreneurs, artists and inventors seem to embody this characteristic quite well.
I once had a teacher who told us to be successful we must, “test fast, fail fast.” This process enables us to learn and grow, but it all depends on being able to admit when you’re wrong…in fact, it means embracing being wrong often.
Cameron
Hi Cameron - thanks for the positive feedback!
“Test fast, fail fast.” The advice from your teacher is worth millions. Failing is definitely tough on the ego, but if one sees failure for what it is - namely, a learning experience - then they are that much closer to success.
Thank you for the link. I loved this post, and learnt a lot especially from the summary of how to handle them!
Hi Albert - I’m glad you liked the article! I had to link to your article about psychological techniques, since it covered so much more than just cognitive dissonance. It’s always a pleasure to read your articles since they’re so content-rich.
Al, great post! I had to read Marylin’s article and all of the comments before I was convinced. I found that I was glossing over the fact that the host’s opening of the door was not a random act. If it had been, the odds would have stayed the same (well, gone to 50/50 anyway).
The important point is to be observant of non-random occurrences. Hunter Nuttall had a post on this same theme this week, coming at it from a different direction.
Hi Stephen, I’m glad you liked it!
That’s a great way of putting it as well… being observant of non-random occurrences. It’s a tough call whether to follow a disciplined path and not get swayed with ups and down, or to know that the changing situation calls for a different path. I think it’s a matter of being honest in interpreting the situation.
Btw - thanks for the link to Hunter Nuttall’s post. That was a very interesting read
Hi Al,
You write the most insightful stuff. Well done. This is a classic example of how switching frames (or perceptions) can result in real change other than imagined change.
Don’t worry I had to read the explanation page before I understood it! And yes, just about everything else comes at a snails pace too.
Great stuff
Luke
Hi Luke!
Thanks for the comment. Great point about how switching frames can result in real change. It’s one of those advice that you hear a lot of people say but doesn’t really mean anything until you experience it yourself.
[…] a discussion of why this is so, read “Are You Smart Enough to Change Your Mind?” from 7P Productions, which links to the vos Savant article and to a fun interactive version […]
[…] Mediation Channel, also wrote a short article about the Monty Hall problem, and she reference her article from 7P productions’ article which started off asking “If you made the wrong choice, are you smart enough to change […]
Hi, Al. I wrote a snail-mail letter to Marilyn about this problem back in 1990 but didn’t get a response (I’m sure she gets a lot of mail).
What I said is that the problem is not clearly defined, hence all the confusion. I think that’s still true today.
Let’s say the host is on your side and is helping you out by opening either door 2 or 3, whichever works to your advantage. In that case, yes, you’ll have a 2/3 chance of winning the car if you switch. If the car is behind either door 2 or 3, the host will guide you to the right door.
Let me see if I can illustrate this.
Possibility 1: The car is behind door 1 (probability: 1/3). The host can’t help you, so he just opens door 2. Switch and you lose.
Possibility 2: The car is behind door 2 (probability: 1/3). The host opens door 3 to help you. Switch and you win.
Possibility 3: The car is behind door 3 (probability: 1/3). The host opens door 2 to help you. Switch and you win.
Switching lets you win 2/3 of the time.
However, I think the original wording just said the host opened door 3 and it had a goat. There was no mention that the host was trying to help you, so it could be assumed that he was going to blindly open door 3 no matter what. In that case, there’s no benefit to switching.
Possibility 1: The car is behind door 1 (probability: 1/3). The host blindly opens door 3. Switch and you lose.
Possibility 2: The car is behind door 2 (probability: 1/3). The host blindly opens door 3. Switch and you win.
Possibility 3: The car is behind door 3 (probability: 1/3). The host blindly opens door 3 and reveals the car. You lose whether you stay or switch.
However, as soon as the host opens door 3 and reveals a goat, that changes possibility 3’s probability to 0. It just didn’t happen. That also changes the probability of possibilities 1 and 2 to 1/2 each, since they have to add up to 1.
So is the host trying to help you by eliminating a losing door, or did he just open an arbitrary door that happened to have a goat behind it? Nearly two decades later, we’re still arguing about the solution, when we don’t even know what the problem is!
Hi Hunter,
That’s pretty awesome that you saw this problem the first time around when Marilyn vos Savant published it.
I think you really got to the heart of the point that I tried to make - namely, that we will not get to the right answer if we incorrectly perceive the situation.
If the host randomly chose from door 2 or 3 without knowing which one had the car, then I agree with you. The problem never explicitly said whether the host knew which door had the car, but when I first read the problem, I assumed that the host knew which door had the car, since it’s his game! Also, because it’s a game show, I’m assuming that the reason the host opened the door isn’t to unselfishly help me out , but instead to confuse me for the sake of entertaining the audience - hence, I can’t assume that his actions are for my benefit. I think these were similar assumptions a lot of people may had, but these are all assumptions, so we all made the same mistake.
My main point is that our understanding of the situation may not in line with what really is going on. You made a very excellent point that the wording could and should have been better, but I think it’s also interesting that a lot of people didn’t ask for more explanation, but instead went straight to an answer (which frequently was wrong).
Al, have you seen the movie “21″ by any chance? I just saw it, and they discuss the Monty Hall problem.
Hunter - I have not seen “21″ yet. The premise of the movie about MIT kids outsmarting Vegas casinos sounds interesting to me, and you got me even more interested now.
Was it a good movie? Thanks for letting me know about that!
Yup, it was pretty good. Not as good as the book (which was called “Bringing Down the House,” but they didn’t dumb it down as much as I expected. I’d recommend it.
[…] a really interesting problem, and I read a number of articles on it before I figured out how to put it in terms that make it […]
You are right:) Nice post.
I went to the website in which they lay it out. And actually to me it becomes even more obvious they are wrong. She deceives herself by stacking the deck. Giving a chart in which there is 6 possible initial settings she assumes the picking of the same door for each example. In that case she is right but in real life that is not the case and you are dealing with an element of randomness. In each case the person will not have chosen the same door and as a consequence the logic being used does not apply. When you eliminate the third door you automaticaly change the scenario to a 50% chance.
I was so curious enough to write a small program to simulate it (I’m a programmer). It has shown as soon as I wrote the function that the result would be 2/3, and the simulation result is approximately correct accordingly.
I think the explanation can be simply put as, if your chance to win if you don’t switch is 1/3, the chance to win if you switch must be 2/3. There’s no other way round.