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Monty Hall for Projects: To Switch or Not to Switch?

Categories: Bias, Probability

I was wondering about the internet and I found yet another discussion about the Monty Hall problem. For those who are not following, a quick recap. There is a game show where you can choose between three doors. One has a prize, the others do not. After you make your choice, the host opens a door (without the prize, of course) and says that you have the opportunity to make a move, or maintain your position. Although most people thing that changing does not improve your odds, there is probability proof that changing actually doubles your chances! I won’t post a link, but you can search for texts and videos online if you wish to do so.

It is completely counterintuitive, but it is true! So I started considering how would we deal with a Monty Hall Problem in the project management environment. Let us suppose, as an exercise, that you have five equally adequate companies that could carry the work you need to procure. You choose one, but your reasons are not really strong ones. All of them have the same credit risk, status in the industry and other indicators you might have looked at to make your decision.

Now consider that, just before you take your decision to the executive board for a final recommendation, three of those companies have a financial setback, removing them from your potential list. You are now faced with two companies, the one you chose, and the other one. You have the power to switch decisions, and you still evaluate both companies the same way. Should you switch? Would you switch?

You should do the switch, but probably you won’t. There are some strong assumptions behind the Monty Hall problem:

  1. You have a prize and the other doors have nothing (or a goat, in most versions I’ve seen online). So you don’t have two successes, two companies who would carry out the work well. Only one winner here, and several losers. Binary, all the way home.
  2. Human factors are set aside, that is, you would not have the bias for maintaining the decision you took earlier, which is a total fallacy.

Put those things on hold now, let us examine the question in the pristine light of the numbers. Let us boringly call the companies A, B, C, D and E. Suppose you chose company A. The odds that you made the right choice are 1 out of 5, that is, 20%.

Consider now that financial distress took place, and companies B, C and D got swallowed whole by the ruthless economic situation. All you have left are companies A and E. Seems like you got a fifty-fifty shot, one might say. However, since you have a single best answer, and you voided three that you did not choose a priori, the chances that you may win are still 20%, if you do not change your decision. Switching multiplies by four (reaching a massive 80%) your chances of winning this game. Most people do not contemplate this and switch, and keep their position.

If you consider the mindset of the average person, it is completely understandable that no one would change their decision because of this turn of events. The psychological, it seems, gets in the way of the logical and mathematical reasoning.

A takeaway for me, looking into this, is that you have to look at each situation individually and remember why you made that choice. If you are confident, go ahead with your decision. The numbers game is amusing, but it doesn’t apply, in my opinion, to the discrete and singular situations of a project.

What about you? Ever been to this kind of situation? Did you switch or sustained your position? Let me know! Thank you!

Posted on: January 29, 2019 11:01 AM | Permalink | Comments (10)
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