Linda is 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.
Which is more probable?
- Linda is a bank teller.
- Linda is a bank teller and is active in the feminist movement.
If you are like me and 85% of the people confronted with this question, then you were probably struck with a sure instinct to select the second option. Conversely, the context of this little pop-quiz may have aroused enough of your suspicion to second guess yourself and choose the former answer. Touché, reader, touché. The above is an example of a phenomenon called the conjunction fallacy. Mathematically speaking the correct answer is the first one. The likelihood of two events co-occurring will always be less than or equal to the likelihood of either one occurring exclusively.
At first, I thought this fallacy exemplified how the pattern seeking nature of our brains can misguide us. You see the description, you building a picture of Linda in your mind and immediately think the second answer fits best. Yet even with the knowledge of what is mathematically the correct option, I inevitably experience a lingering visceral compulsion towards the second answer. What confused me about this problem on reflection was why so many of us get it wrong, when we clearly do have the capacity to calculate basic probability even from a young age. So I went hunting for more answers, internet-Indiana Jones style.
Further exploration of this common blunder reveals where the real error occurs. Further studies on the topic have revealed that when the question is phrased in more mathematical language most people do select the correct answer (See Hertwig and Gigerenzer, 1999). It is thus clear that we are well equipped to handle the maths when the question is phrased with more semantic clarity. So where is our cognitive downfall taking place? I feel that the illusion is in the language. It appears, as demonstrated by the common response to the question above, that our brains are far more primed to deal with what is ‘plausible’ rather than ‘probable’. So rather than a fallacy of logic, failure to select the right answer about Linda’s most likely practices comes down to a pragmatic inference, misguided by ambiguous language. Hence, the most ‘probable’ answer can easily be taken to mean the most ‘credible’, ‘feasible’, ‘conceivable’, or ‘apparent’ answer. We can all be excused then for not jumping into a mathematical approach to the question. Ultimately, the lesson I reap from this intellectual conundrum and its results is that natural language is more sophisticated than logic. This may mean that the common ‘the glass is half full/empty’ perspectives may have greater implications given these observations of just how powerful a tool language is.
For my interests, it most certainly provides us with a better insight into the workings of our own minds… but I still have no idea what the hell Linda does.