Consider the following question:
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.
What do you think the correct answer is?
If you chose option #2, then you’re wrong!
In fact, 85% of the people, when asked this question in an experiment, chose option 2. The reason why that is the wrong answer is that the probability of two events occurring together (in “conjunction”) is always less than or equal to the probability of either one occurring alone.
Why do most people make this mistake? Innumeracy? Impatient intelligence? No, this is actually a logical fallacy called the conjunction fallacy. It occurs when someone assume that a specific event X is more likely to occur than a general event Y (where X is a subset of Y). And it’s related to the “representativeness heuristic”:
Most people get this problem wrong because they use the representativeness heuristic to make this kind of judgment: Option 2 seems more “representative” of Linda based on the description of her, even though it is clearly mathematically less likely.
I thought this was really interesting — adding more (specific) details makes us feel that the event (or condition) becomes more likely, even though it becomes less probable.
[Example and quotes from the Wikipedia article on conjunction fallacy. If you found this little teaser interesting, you might also want to check out the Wikipedia page on the representativeness heuristic.]