Biases and Heuristics: Beyond the Numbers

Actuaries deal with a conflation of academic fields including mathematics, statistics, and finance. However, we tend to ignore the more human, behavioural insights that psychology offers. This article will examine a variety of systematic errors that we are all susceptible to and explore how our field can benefit from a study of behavioural sciences.

When it comes to solving a problem, some actuaries are traditionally intrigued by the beauty of a singular, concrete, ‘right’ answer. However, the reality of problem-solving is that it is far from black and white. To navigate the irrational opacity that presents itself before us, we have various tools at our disposal. Statistical logic is certainly one way to brush aside our biases and partialities. Amos Tversky and Daniel Kahneman’s famous ‘Linda problem’ evinces the way in which statistical insight negates what they called ‘heuristics’, shortcuts that the human mind takes when faced with uncertainty.

The problem describes Linda – “31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations”. They proceed to ask “which is more probable:

1. Linda is a bank teller, or
2. Linda is a bank teller and is active in the feminist movement?”

85% of those surveyed answered ‘2’ due to what the eminent psychologists later coined as ‘representativeness’; a heuristic that leads people to overestimate their confidence when faced with vivid descriptions, leading to a neglection of Bayes’ Theorem.

However, the two psychologists found that even those statistically inclined are subject to the ineluctability of behavioural biases. Kahneman and Tversky devised a series of complex statistical questions that they posed to mathematical psychologists in an attempt to extend their previous findings. One such problem asked the respondent to imagine a situation in which “a certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. For a period of 1 year, each hospital recorded the days on which more than 60% of the babies born were boys. Which hospital do you think recorded more such days?

1. The larger hospital
2. the smaller hospital, or
3. about the same (that is, within 5% of each other)”

As we know, a smaller sample will have a higher variance, and thus we would expect the smaller hospital to record more of these days. However, 56% of subjects actually chose option 3. Whilst statisticians clearly possess a multitude of rigorous tests that make the correct solution evident, when they were surveyed away from their work, many were susceptible to the same biases that undergrads displayed.

How is this applicable to being an actuary? The following experiment illustrates the importance of behavioural science to fully understanding an actuarial problem. Insurance professionals were asked “What causes the most deaths in the UK amongst women aged 20 to 29?

1. Accidents
2. Cancer
3. Self-inflicted injuries”

Responses suggested that accidents accounted for around 50% of deaths in that age bracket, however, the actual percentage was closer to 30%. This disparity is perhaps quite hard to believe, how could those whose job deals with accidents provide such a large margin of error? Psychologists explain this systematic error as ‘availability’. Ironically, the fact that these insurers dealt with accidents so frequently was the reason why they tended to overestimate their significance, they could easily recall situations in which similar accidents resulted in death.

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