Thinking Slow About Thinking Fast – Part III – The Monty Hall Problemby Nisha Cooch, PhD | August 20, 2014
To wrap our minds around human behavior it’s helpful to consider why certain behaviors may have evolved. Natural selection tells us that behaviors that increase our chances of passing along our genes will continue to show up in future generations. It therefore follows that aspects of our behavioral tendencies at some point likely conferred an advantage over alternative behaviors. Efficiency may be the specific advantage afforded to us by our so-called irrational behaviors.
Before delving into classic examples of “irrational” behavior, I’d like to share my favorite example of how our brains are not built to choose optimally in certain scenarios wherein choosing optimally requires a large amount of energy.
In 1990, a magazine columnist named Marilyn vos Savant was approached with a question about the best strategy to use on the game show Let’s Make A Deal. On the show, a player is told that there is a large prize behind one of three doors, and if he chooses the correct door, he wins the prize. Once the player has selected a door, the host opens one of the two remaining doors, revealing no prize behind that door. The host then gives the player the option to change his guess as to which door leads to the prize.
If you were a contestant, would you stick with your original choice or switch your choice at the last minute, given the opportunity? According to Marilyn, switching to the other door would make you more likely to win the prize. Don’t believe it? Neither did dozens of mathematicians who read Marilyn’s response. But it turns out that Marilyn was right, and here’s why:
When the player originally chooses a door, there is a 1/3 probability that he has chosen the door that will win him the prize and a 2/3 probability that he has not. The key to the problem is that the host will always open a door that does not lead to the prize. Thus, regardless of where the prize actually is, the host, by eliminating one of the two doors that does not lead to the prize, gives the player the opportunity to switch their bet from a 1/3 probability of winning the prize to a 2/3 probability of winning.
So – the “rational” choice in Let’s Make A Deal is to switch doors before the door with the prize is revealed. But our brains do not readily identify the advantage associated with the switch. We have to almost turn off our fast brain to grasp the solution to this problem, which has come to be known as The Monty Hall Problem. Before Marilyn’s publication, Let’s Make A Deal players reliably defaulted to their original choice – an example of what is known as the “status quo bias”.
Why are there scenarios in which we tend to choose the seemingly less optimal option? My suspicion is that the relative advantage afforded by the “optimal” option does not outweigh the energy cost associated with fully assessing the options, particularly in light of the fact that the option we choose against in these scenarios does not guarantee a gain (remember, switching doors increases one’s chances of winning the prize but does not guarantee a win).
If we employ a rule of thumb, or heuristic, such as “go with your gut”, that can be applied habitually to all choice situations where outcomes are probabilistic, we can save an amount of energy that may be more valuable than forgone gains. And indeed, choosing the status quo is associated with increased activity in the parts of the brain that are active while performing habits, while choosing against the status quo activates the parts of the brain important for slow, laborious thinking. It therefore usually takes more effort and energy to NOT choose the status quo.
One last consideration – before moving on to the Framing Effect in the next post – is why our brains did not evolve to more efficiently identify advantageous choices like switching doors in Let’s Make A Deal. Throughout human history, we have dealt with the inundation of stimuli, the meaning of which we have learned through experience. However, gambling-type choices with known risk probabilities represent modern choices without obvious prehistoric analogues. Our brains thus likely did not evolve to assess such choices with high precision. Perhaps they would have had our ability to acquire food and other resources depended on identifying subtle statistical advantages.
Mental Context – A Delicate Subject
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