Bruce Hood - The Self Illusion

Consider an egocentric bias that blinds us to important changes in the world when it comes to decision-making. If you have not already heard of it, then let me introduce you to the Monty Hall problem. The problem is named after the presenter of the American game show, Let’s Make a Deal , where the climax was to choose a prize from behind one of three doors. Try to imagine your self in this situation. You have made it all the way through to the final part of the show and have a chance of winning the jackpot. Behind two doors are booby prizes but behind one door is a fabulous prize. For the sake of argument, let’s say that it is a £250,000 Ferrari. You hesitate initially and then choose door A. The host of the show, Monty, says, ‘You chose door A, but let me show you what’s behind door C.’ He then opens door C to reveal one of the booby prizes. Monty says, ‘You chose door A initially, but do you want to change your decision to door B?’ What should you do? Most people who encounter this problem for the very first time think that it makes no difference, because they reason that it is a 50-50 chance to win the Ferrari with only two doors left to chose from. Indeed, people are reluctant to change their minds once they have made a choice. Some may say that we stubbornly stick with our decisions because we have the courage of our conviction. After all, it is important to be decisive.

What do you think you should do – switch or stick? If you don’t already know, the correct answer is to switch, but if you don’t know why, it is incredibly hard to understand. The Monty Hall problem has become a somewhat famous cognitive illusion appearing both in bestselling books and even in the Hollywood movie 21 (2008), about a bunch of mathematically minded Massachusetts Institute of Technology students who counted cards at the blackjack tables of Las Vegas to beat the casinos. The correct solution to the Monty Hall problem is to switch because you are more likely to win than if you stick with your first choice. It is difficult to see at first and when it initially appeared in the popular magazine, Parade , in 1990, the problem created a storm of controversy and disagreement among both the general public and experts. Over 10,000 people (1,000 with PhDs) wrote in complaining the switch decision was false!

The reason you should switch is that, when you first choose a door, you have a chance of one out of three that you are correct. Now, after Monty has revealed one of the booby prizes, with two doors left, the remaining door that you did not select has a one out of two chance, which has better odds than the door you first chose, which remains at one out of three. Remember, Monty always shows you an empty door. Simple – except that it is not simple for most people.

An easier way to solve the Monty Hall problem is to consider a variation in which there are 100 doors instead of three. 9Again you get to pick one door. Now Monty opens ninety-eight out of the remaining ninety-nine doors to show you that they are all empty. There are now only two remaining unopened doors. Would you switch now? Here we can see that our door is unlikely to be the correct one. What are the odds that I correctly selected the right door on my first chance? Actually, it’s odds of 100-1 to be precise. That’s why we immediately twig that Monty is up to no good. There is something deeply counterintuitive about the Monty Hall problem, which reflects our limited capacity to think outside of the box – or to be more precise, to think in an unselfish way.

Another reason that people fail to switch in the Monty Hall problem is a general bias not to tempt fate. When it comes to making decisions, inherently we fear loss greater than we value the prospect of a win. Despite the so-called rationality of the modern era, people still think that if they change their decision then there is more chance that they will regret doing so. It’s not so much stubbornness or superstition but rather that we fear loss greater than the potential for gains. For example, the social psychologist Ellen Langer sold $1 lottery tickets to fifty-three office workers. Each stub of the ticket was put into a box from which one lucky winner would receive the whole $53. Just before the lottery-draw a couple of days later, Ellen approached each worker and asked them for how much they would sell their ticket. If they had just been handed a ticket by the experimenter so they had exercised no choice, the average price for resale was $2, but if they had chosen the ticket themselves it was $8! Moreover, ten of the choosers and five of the non-choosers refused to sell their ticket. 10It turns out that it is the fear of regret that looms large in our minds. How many times have you deliberated over an expensive purchase only to hear the salesperson reassure you, ‘Go on, you’ll not regret it!’

Risky Analysis

What the Monty Hall problem illustrates so clearly is the limitations of human reasoning – especially when it comes to probability. Probability is all about external information. Reasoning in terms of probable outcomes is very difficult because most of us think in a very self-centred way. We make decisions from our own perspective and often fail to take into consideration the external information that is most relevant.

In fact, most complex science is based on probabilities and not absolute known truths about the universe. After the age of Newton and the scientific revolution of the seventeenth century, it was assumed that the universe was one big clockwork mechanism that could be understood by measurement and prediction. It was thought that if we improved the accuracy of our measurements, then we would understand better how the universe worked. The opposite happened. The universe became more complex. With increasing efficiency, we discovered that the universe was much messier than we had previously imagined. There was more noise in the system and less certainty. This noise gave birth to the age of statistical modelling in which mathematicians tried to discover the workings of the universe using procedures that accounted, as best as possible, for all the variation that was observed. This is why the language of science is mathematics and its truths are based on probabilities. 11

Unfortunately, statistical analysis is not natural for the average man in the street. Our bodies and brains, for that matter, may operate in statistically predictable ways, but few of us explicitly understand statistical principles. This is why the general audience gets so frustrated when they hear scientists in the media refusing to give a straight ‘yes’ or ‘no’ answer to the questions that concern them. They want to know what to do about global warming, the dangers associated with childhood vaccination or how to prevent pandemic viruses. When answering, scientists talk in terms of probabilities rather than absolute certainties because they look at the big picture in which they know there is going to be some variation. That’s not what the general public wants to hear. They want to know whether vaccination will harm their children. They are less interested in the group because that is not the way individuals think.

The other problem with probability is that humans have not evolved to consider likelihood based on large amounts of data. Rather, we operate with heuristics – fast and dirty rules of thumb that generally serve us well. The German psychologist Gerd Gigerenzer has argued that humans have not evolved to work out probabilities such as those operating in the Monty Hall problem. 12We focus on the task as relevant to our self, and how it applies on an individual basis rather than on populations of people. We tend to only evaluate our own choices, not what is best for the group. Faced with two doors, my chances seem even. It’s only when I am faced with two doors a hundred times, or a hundred different people take the Monty Hall challenge, that the patterns become obvious.