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The Actuary The magazine of the Institute & Faculty of Actuaries
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Food for thought

We student actuaries often begin our careers as calculation ‘doers’ before graduating to be calculation checkers. Accuracy is obviously critical to this, and with our rigorous training we make few mistakes. But as time goes on I’ve come across a few pitfalls that I like to keep in mind when doing and when checking — because we too are human, and are therefore prone to logical errors.

A puzzle
You’re good at maths, right? Have a think about this question before moving on. There’s a rule that applies to this triple of numbers: 2, 4, 6. What triples of numbers would you ask to see in order to figure out the rule?

Chances are you may have picked, for example, 8, 10, 12 if you thought the rule is ‘increase by two each time’; or you may have picked 5, 10, 15 if you thought the rule is ‘the middle number is the average of the other two’. But actually the rule is ‘any ascending sequence’, and the triples you chose probably satisfied this rule even if they satisfied your conjectured rule. This example from Peter Wason 1 shows we prefer confirmation to falsification, which can lead to basic errors in checking.

It’s easy to forget but it may be worth asking yourself now and again, ‘am I falling for the confirmation bias?’ (I’ll give a brief, related example: when I came to check over this article a week after first drafting it, I saw that I’d written Peter Watson here, as that is what I expected — and may well be what you thought you read just a moment ago!)

Transfer of learning
In his book How Children Fail 2, John Holt describes this anecdote. A teacher had a class made up of the “dumbest kids” in the school. Among these children, one was “clearly the dumbest, utterly hopeless at any kind of schoolwork”. But the teacher went ten-pin bowling one day and was amazed to see the boy had a paid job keeping official score in league games, and was scoring two lanes at once (before the advent of automated scoring, no doubt). No one would stand for mistakes there; anyone who has ever played ten-pin bowling knows this would be no mean feat.

The teacher thought to give the boy questions about bowling scores in school, no doubt to foster a sense of achievement. But the boy couldn’t do them — in fact, he frequently gave absurd answers. This extreme example shows how what you learn in one place or time is often hard to transfer elsewhere. Do you transfer exam knowledge to work easily? Or do you think of exams as being in a separate domain from work? I know that when I use Excel at home, I am often much clunkier than I would be at work, purely because I am not at the place where I learnt most of my Excel skills.

Expert opinion
One subconscious rule we often follow is to assume: Because someone has been doing something longer than me, their view is more likely to be correct; or She was right last time, so she must be right this time.

These rules save time, and time is at a premium. But relying on the reputation of the giver of the information, rather than their arguments, can lead to reassessing your work incorrectly. It can give a sense of self-fulfilling prophecy: so and so says this is wrong, so I will look to see if I can confirm that belief. Clearly, there is a tradeoff here, because we don’t go to the doctor and doubt everything he says — there isn’t time to do that and we put faith in his training. If someone contradicts you, be willing to question them and expect them to convince you at the same level of detail as you would hope to convince them.

None of these things is easy to avoid, and in some sense owes to the evolution of the brain. But an awareness of these fallacies can do us no harm and give us greater cause to trust the work we produce.

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1 Oswald, Margit E.; Grosjean, Stefan (2004), ‘Confirmation Bias’, in Pohl, Rüdiger F., Cognitive Illusions: A Handbook on Fallacies and Biases in Thinking, Judgement and Memory, Hove, UK

2 Holt, J (1970) How Children Fail Harmondsworth: Penguin