Assessing risk is impacted by how easily you can change your mind

[Extract from “Risky Strategy” to be published in 2016]

Cognitive inertia (a.k.a in long form Cognitive Dissonance Reduction) is our inability to evaluate a situation objectively, or to come up with new creative solutions,  when we face conflicts with decisions we have already taken.  We experience  Cognitive Dissonance  when we encounter evidence that conflicts with a decision that we have already made and it feels uncomfortable, so we try to minimise that dissonance.  So, we tend to find it hard to evaluate the new evidence objectively or rationally.  This can affect both risk averse and risk taking behaviour.

Let me illustrate with the Game Show Host conundrum. Try and do this without looking at the answer below, because your response to the answer is important.   Then once you have completed the exercise,  read on.

In a game show, contestants are asked to pick between three doors. Behind one of the doors is a prize. As a contestant you pick one door. The Game Show Host then opens a second door, one of the doors you didn’t pick, to reveal the prize is not behind that door. The rules of the game is that the Host will always open another door which doesn’t have the prize.  You are then asked if you would like to switch your choice to the last remaining door. What do you do?

a)  Stick with your original choice, or

b)  Switch your choice to the remaining door

THE ANSWER: Having selected your choice , I will now tell you that the majority of respondents answer ‘a’  But I also need to tell you that you double your chances of winning if you change your choice… you have a 2 in 3 chance of winning if you switch doors, compared to a 1 in 3 chance of winning if you stick with your original choice.

While this may not make intuitive sense, and indeed a number of professional mathematicians don’t accept this outcome, you can prove it to yourself by doing a simulation with a friend a number of times with three cards (an Ace as the prize).  Ask a friend to pick a card, then show them a second card which is not the Ace and ask if they would like to switch their choice to the remaining card. If you do this 10 or 20 times, you will begin to see that by switching to the remaining card, your friend would win the prize 2 times out of 3, whereas by sticking, they only win 1 time out of 3.

This is a metaphor for cognitive inertia, and illustrates something interesting about our intuitive approach to risk.  And it’s a double whammy – it does this in two ways.

Firstly, the idea that we have already picked a door (ie, made a decision) makes it more difficult for us to consider changing that decision.  This is the first level of inertia.  But to switch doors increases our chances of winning, ie, it reduces our risk of losing.  So the change option is actually the low-risk option.

Secondly, there is a much more pervasive form of inertia where we justify our decision based on our own assessment of probability.  Most people think that they have a 50:50 chance whether they stick or switch, so why switch.  But what happens when I explain that actually the odds are twice as good if you switch.  Normally, the initial reaction to that piece of news is “You’re wrong!”, rather than “So how can you show me that that is the case”

It is fascinating that there is, or at least was, an internet site with this problem and solution set out, and a blog of commentary from supposedly leading mathematicians arguing quite vociferously that this is not true, that the odds do not improve or that this is bad mathematics.   And yet, as I suggest, you only need to run it as a simulation enough times to convince you of the pattern, to see that you do indeed double your odds.  So it’s an illustration of how hard it is to stand back from decisions and hard-fought beliefs, and to look at something from a different perspective.

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