One of the main boons of me getting involved in statistics is that it taught me a lot about how irrational people’s thinking can end up being sometimes. It gave me the idea to create a series of posts to elaborate more on some topics I found useful in my education. My hope is for someone who doesn’t have a strong math background to read these posts and start thinking statistically in their everyday lives, even if only a little bit.
A good example to start off these series of posts is known as the conjunction fallacy, which causes people to assume that specific conditions are more probable than a general condition.
The Main Example
The following example found by Amos Tversky and Daniel Kahneman best encapsulates the issue:
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.
Many people will default to answering the latter, because the context clues indicate that she’s more likely to be a feminist than a banker. However, the second statement has more conditions on it than the former. At absolute best, the probability of both statements being true is equivalent, if you assume that Linda has a 100% chance of being a feminist. Otherwise, the first option is more probable.
Why Do So Many People Choose Incorrectly?
There are a few theories as to why people make this mistake. One is that the wording of the question is poor and encourages representative thinking rather than mathematical thinking. Consider this restructuring of the question:
There are 100 persons who fit the description above (that is, Linda’s). How many of them are:
Bank tellers? __ of 100
Bank tellers and active in the feminist movement? __ of 100
When the question is reformatted to ask people what they think in terms of frequencies, almost nobody falls into the trap and makes the mistake, according to this study. Previously, up to 85% of participants had gotten the wrong answer! That’s a pretty drastic turnaround.
Conclusion
Given that a more mathematical phrasing allowed people to see the error in their ways, I’m tempted to lean more on the poor wording of the question as the main cause of this particular fallacy. However, I think that it’s important to recognize how easily the brain can slip into default thinking patterns, especially if one is not mathematically minded naturally. The framing of an event can directly influence the way a person looks at it, and everyone is susceptible to it.