“Ben, suppose you’re on a game show. And you are given a chance to choose from three different doors, all right? Now, behind one of the doors is a new car. Behind the other two, goats. Which door would you choose, Ben?”
Imagine yourself at the final game of a TV quiz; the host Monty asks you to choose among three doors. However, once you have made your choice, Monty, who knows very well what’s behind every door, does not open it immediately, but opens another one showing you the goat behind it. And then he asks you: do you want to change your initial choice?
The paradox of Monty Hall, host of TV show “Let’s make a deal”, is a probabilistic mathematical problem, which has always been exciting psychologists and scholars of the decision making process.
Should we change our choice? What is the probability that changing our initial decision makes us win the car of our dreams?
In the movie “21”, Kevin Spacey is a professor who submits a version of this famous problem to his students, in order to test their ability to reason rationally in a counter-intuitive situation.
Even in the simplest decisions, we have to consider a whole number of influential factors. A number of management models were created over the years, in order to limit the complexity of the interactions in making a choice. Emotional and psychological factors are involved too, depending on individual, situation, and time needed for our decision.
Watching this clip we point out that there are two different decision-making moments: the first is when you have to choose among three doors, the second when the host asks if you want to change option. At first there is a choice of instinct:
“when I was originally asked to choose a door, I had a 33.3/ chance of choosing right”
We use intuition, because we have no other point to start from: any door could be the right one. And then?
-“Variable change? But he just asked you a simple question”
-“Yeah, which changed everything”
Many people believe that, whether they change their choice or not, the chance of winning will always be 50%. We let our heuristic instinctive belief in “equal probability”, or worse, in “I stand firm on my decision”, take over. We do not consider the variables and information that we now have at our disposal: we tend to solve the problem by relying on previous beliefs and thought patterns, leaving aside logic and analytical thought.
The misfortune is generally due to a miscalculation (B. Brecht, Life of Galileo), and if we do not stop and think better about the data we have in front of us, we will find ourselves going home on the back of a goat!
We can’t even console ourselves because we are not alone: Monty Hall paradox also gives a rough time to a lot of mathematics. But I wonder: any time we make a choice, maybe we are in front of closed doors too. Maybe the prize is not a sports car, but job satisfaction, creation of winning relationships, getting the desired result. So we cannot help but wondering how much of our decisions is given by reason and how much by intuition. But is it right to create a “scheme”? A model that, if applied to a situation, can make us decide?
In fact, we already do that, even if we do not realize it. When our mind has to handle the chaos of our thoughts, it develops systems to organize it, observe it and try to look beyond. Models help us reduce its complexity as we try to dissolve most of it and focus on the essential. This an attitude comes from the subconscious, so let’s not think that analyzing the data and organizing it according to our goal equals “standardizing” the problem; having a ”thought path” is indeed the result of owning an “active thought”.
Frederic Vester popularized branched thinking in the 1970s. Since then, the theme of “management of complex decisions and systems” has developed: complexity, chaos theories and self-organization have been required for managers for years.
So if our intuitions and sensations are also a manifestation of thought patterns implemented by our subconscious, which are communicated to us through the senses, why should we let our brain be limited in its potential? Why do we create our own models that only deceive us?
-“Remember, the host knows where the car is so how do you know he’s not playing a trick on you? Trying to use reverse psychology to get you to pick a goat?”
-“Well, I wouldn’t really care. I mean, my answer’s based on statistics”
Our mind inevitably suffers from heuristic patterns, more and more crowded as years an experience grow. Some experiments in which seven years old children were confronted with the resolution of the Monty Hall paradox, showed that 10% more kids than the same number of adult successfully solve the problem. This fact makes you think.
When we make a decision, we should give increasing weight to all factors: the first is the emotional one, the second is the logical-deductive one, and then increase the value as new data is added to our case. The most common error in the resolution of the paradox is not considering what happened before you remained with two doors, but focusing on the moment when only two doors remain in play: the past influences our thinking in probabilistic terms.
“ [ … ] most people wouldn’t take the switch out of paranoia, fear, emotions. But Mr. Campbell, he kept emotions aside and let simple math get his ass into a brand-new car!”
What about you?