The conjunction fallacy

11 01 2015

Screenshot 2015-01-11 17.47.12At long last, after several dalliances into things that didn’t quite work out (still pathetically part of my vast, unreported ‘backblog’), we found a book tough enough to hold our attention, but not so full of maths or pedantry as to be annoying: “Cognitive illusions”, a guide to what makes us so prone to fallacies and biases.

The first chapter we covered, which we spread over two weeks, was by John Fisk on the “conjunction fallacy”. This is often epitomized by the so-called ‘Linda Problem’, as follows: Linda is as an outspoken left wing philosophy student in her youth. Please rank these descriptions of what she might be like now, from most to least likely: Linda works for a bank; Linda is an active feminist; Linda works for a bank and is an active feminist.

Most people say that it’s more likely that she works in a bank and is a feminist than that she just works in a bank… but of course this is wrong, because  the probability of two events co-occurring (being ‘in conjunction’) is typically smaller than either of them happening on their own.  If there’s a 9/10 likelihood that Linda’s now a feminist, for example, and a 1/10 probability that she works in a bank, then the probability of both being true is 9/100. The question Fisk tried to tackle was, what is it that makes the conjunction fallacy so seductive?

Some clues come from seeing how many people get it right when the question is posed in different ways. For example, if asked to imagine 100 women like the young Linda, and then asked to allocate how many do what in adulthood (“how many go and work in a bank?” “how many are feminists” “how many are both?”), most people now get it right. It’s as if when imagining real groups of discrete individuals, they can see that the number of women spanning both of the two categories can’t be bigger than the number in either one.

Fisk then presented nine possible explanations, each of which has attracted empirical investigation: linguistic misunderstanding (people assume that ‘working in a bank’ means ‘working in a bank and not being a feminist’); signed summation (I didn’t really understand this one); frequentist interpretations (which just seemed like a redescription of how some ways of asking this question don’t yield fallacious answers); mental models (which was about yellow and brown cards in a box… don’t ask me more); applying the wrong probablistic rule (people really answer the question ‘if someone is a bank teller, OR both a bank teller and feminist, which one’s most likely to be Linda?’); averaging, where people average two probabilities instead of multiplying them; surprise theory (we under-estimate the likelihood of things we think are surprising, such as radical Linda selling out and working for Barclay’s); cognitive experiential self theory (similar, in that we’re swayed by links we think are natural); and fast and frugal heuristics (I think similar again).

I didn’t allow enough time to really understand these (as will be obvious), and they were dense, alien, and not compared in the nice explicit way I would have liked (I wanted a table with the predictions made by each idea compared and contrasted). However, there is nothing like reading the same fallacy multiple times to make it really hit home, and the combination of fallacy with empirical psychological investigation was pretty satisfying. We will be doing more!