One of the books I’m currently reading is Priceless: The Myth of Fair Value (and How to Take Advantage of It) by William Poundstone. It’s an interesting look as some of the psychology behind how we think about prices and perceive value. Poundstone recounts one experiment done by Kahneman and Tversky called “Linda the Bank Teller” that I’d like you to think about.
“Linda is 31 years old, 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 of the following is more likely to be true?
Linda is a bank teller.
Linda is a bank teller and is active in the feminist movement.
Astonishingly, 85% of the college students tested responded that the second statement is more likely to be true than the first, which is absolutely ridiculous. The point that Kahneman and Tversky were making is that we rely on heuristics or “rules of thumb” more often than is logically sound. The point I’d like to make is about drawing diagrams.
The information you’re given in this situation, although different in format from what you’re going to see on a standardized test is nonetheless similar. You’re given a few different pieces of information that fit together in some way that may not be intuitively obvious. One of the best ways to deal with that situation is to draw a graphical representation of what you’ve been told. When given two overlapping sets, you should draw a Venn diagram.
Now, let’s consider the two situations. First, the chance that Linda is a bank teller is represented by the region in red.
The chance that Linda is a bank teller and is active in the feminist movement is represented by the region in blue.
As you can see, the second set is a subset of the first. A drawing with only the two regions we’re concerned with would look something like this:
Linda can’t be a feminist and bank teller without being a bank teller. In this graphic form it’s pretty obvious, and yet 85% of the students missed this fact the first time around. This is a great example of the benefits of converting words into graphical forms so that you can make sure you have a good understanding of what you’re doing before you go forward with a problem.