Numeracy Watch: 5 is Less than 10
Andrew Oxlade writes:
He [Ian Spreadbury] declined to predict the exact trigger but said it was more likely to happen in the next five years rather than 10.
There’s some pretty serious innumeracy going on here. I’m not sure if it’s Spreadbury or Oxlade who’s innumerate. Oxlade might be misreporting what Spreadbury said.
It reminds me of one of my favorite examples that Richard Thaler and Cass Sunstein use in their book Nudge. I use it when I teach numeracy in class. They write:
Again, biases can creep in when similarity and frequency diverge. The most famous demonstration of such biases involves the case of a hypothetical woman named Linda. In this experiment, subjects were told the following: “Linda is thirty-one 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 aIso participated in antinuclear demonstrations.” Then people were asked to rank, in order of the probability of their occurrence, eight possible futures for Linda. The two crucial answers were “bank teller” and “bank teller and active in the feminist movement.” Most people said that Linda was less likely to be a bank teller than to be a bank teller and active in the feminist movement.
This is an obvious logical mistake. It is, of course, not logically possible for any two events to be more likely than one of them alone. It just has to be the case that Linda is more likely to be a bank teller than a feminist bank teller, because all feminist bank tellers are bank tellers. The error stems from the use of the representativeness heuristic: Linda’s description seems. to match “bank teller and active in the feminist movement” far better than “bank teller.”
Just as all feminist bank tellers are bank tellers, the next ten years includes the next five years.