Cognitive Biases: Weakness at Computation

Computational weakness is one of the most common causes of irrational decisions, and it is exactly as it sounds – humans are terrible mathematicians, especially under pressure. Here, we will look at its causes, effects and examples of where it can impact decision-making.

Weakness at computation is one of the main contributors to irrational decision making that affects most humans. When large numbers, many variables and/or complex calculations are involved, people often fail to measure these accurately when deciding and rush into a decision with the wrong answer and thus an irrational outcome. It could be miscalculating a probability, which can cause someone to irrationally spend their money on lotteries and raffles as they believe they have a much higher chance than they actually do. In the context of the retirement savings schemes, this could be working out how much should be saved for retirement. This would involve multiple variables such as how much will be spent each year when retired, how many years you will continue working for, predicted earnings growth and much more. This involves a variety of calculations combining these different variables, and so it is very easy to understand how it would be prone to this human bias of computational weakness.

I wanted to test this idea of computational weakness myself to observe and analyse the process, and so the final question in the study I created attempted to create a scenario where the participant would demonstrate this weakness at computation. For this, the participants were asked the following question:

‘A kid has a bat and a ball. Combined, they cost £1.10, and the bat costs £1 more than the ball. What does the ball cost individually?’

This question is well-known for the number of people who answer it incorrectly. For many, upon first inspection of the question, they see the value of £1.10 and that the bat costs £1 more than the ball, and so they subtract the values to get an answer of 10p for the ball. However, by considering this answer, you find that 10p added to £1.10 is equal to £1.20, and so this answer is incorrect. 13 out of the 40 participants, or 32.5%, failed to see this due to computational weakness, with the other 27 coming to the correct answer of 5p for the ball. This is a clear example of the weakness at computation bias that can cause irrational decision making, as it was a problem of simple arithmetic, and yet just under one-third of the participants answered incorrectly.

One particular drawback of this question is that the sampling frame used consisted entirely of A-Level students, all of whom have completed GCSE Maths and may be doing A-Level Maths as well. This means they are less likely to fall prone to computational weakness, and so the results may have been different if a broader sample was used. Oppositely, this shows the power of weakness at computation and its influence over the decision-making process, as 32.5% of participants still got the wrong answer despite having this advantage.

Weakness at computation was also present in the question investigating availability. In addition to examples of people being struck by lightning or winning the lottery being more ‘available’ in a person’s mind, the irrational decisions could have been prevented through simple calculations, which the participants simply failed to do. For example, if the 23% of participants who guessed ‘winning the lottery’ as having the highest likelihood of occurring used merely the average number of lottery tickets bought, which for the Lotto is around 30 million[1], and assuming they only had one ticket, could have worked out that their probability of winning the lottery was roughly 1 in 30 million. This would make it by far the least likely option and allow them to choose a different option, preventing the irrational decision.

[1] Data obtained from (ranged between 15 million to 45 million tickets sold, so the midpoint of 30 million was used)


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