It is a commonplace that most people are bad at probability. It would be useful to know what sort of errors they make.
Errors which have been observed:
- People tend to be excessively averse to risks with very small probability – e.g. Mobile Phone Masts (and most other media “health scares”).
- People tend to be insufficiently averse to risks which are not likely but are quite significant – e.g. falls in house prices, road accidents.
- People tend to be overly attracted to tiny probabilities of benefits – e.g. one-in-ten-million chances of lottery wins.
These are all explained by the theory that folk probability is not quantitative, but consists of five categories:
- Practically Impossible
- Practically Certain
The risks that are being overestimated are those that are towards the far end of “Unlikely”, while the risks being underestimated are towards the near end: in Folk Probability they are equivalent. In the popular mind, being involved in a train crash or a car crash have the same probability “unlikely”, even if there is a factor of 100 between the real probabilities.
An argument about lottery tickets between two folk probabilitists would address not expected returns (in the mathematical sense), but whether the chance of a big win should be counted as “Practically Impossible” or as “Unlikely”. The advertising for the (UK) national lottery is aimed squarely at that question (it could be you).
The consequences of these probability errors are severe, both for their perpetrators and for the rest of us. I will visit one particular consequence in a later essay.
What can be done about it? One solution would be to teach mathematics effectively in schools. But since that lies itself somewhere near the boundary between the unlikely and the practically impossible, let’s put it aside for the moment. The best quick fix I can think of is to massively liberalise gambling law. Probability theory originated in a study of gambling games, after all. One of Epstein’s most telling points is that people who struggle to achieve the simplest qualifications are able to master complex skills that they need for what they want to do – such as driving a car. A population of poker players would have a much more realistic idea of quantitative probabilities than we see today.