Kahneman next introduces a puzzle that he created, which centers on a fictional graduate student named Tom W. Kahneman asks us to rank the likelihood of Tom studying in nine different fields (e.g., business, medicine, humanities, etc.). If people are given only this fact, they will rank the fields based on their relative frequencies. But if a description of Tom includes the facts that he likes sci-fi, is intelligent but not really creative, not very sympathetic, people will vastly alter their rankings. They will prioritize fields like computer science and engineering, even though statistically these groups are much smaller, because he is more “representative” of those categories.
The Tom W example becomes (like the Linda example in the next chapter) one of the prime ways in which Kahneman demonstrates how we value stories over statistics. Even though the first part of the problem requires people to calculate what they think the base rates of given graduate fields are, these base rates become largely irrelevant to people in the face of new information about Tom’s personality.
The study is meant to demonstrate that people will most of the time ignore base rates and instead prioritize the similarity of Tom W to the stereotype of a computer scientist. Instead of answering the question about probability, people answer a question about similarity. This is a large mistake, as judgments of similarity and probability have very different rules.
The relevant “rules” for the cases like Tom W are provided by Bayesian statistics—named after Reverend Thomas Bayes. Bayes’s rule specifies that prior beliefs (base rates) should be combined with representativeness. If 3% of graduate students are enrolled in computer science (the base rate) and you also believe that Tom W is 4 times more likely to be a computer scientist than a student in another field, the probability that Tom W is a computer scientist is still only 11%.
The actual mathematical calculations that Kahneman lays out prove just how misguided our intuitions are at calculating probability when we try to incorporate representativeness: we often vastly overweight similarity instead of taking into account the base rates.
Kahneman writes that the mathematical details are not relevant in the book, but there are two ideas to keep in mind: we should anchor probability on a plausible base rate, and question how much the evidence presented to us should affect our answer.
Kahneman returns to the thesis of his book: in a “cognitive minefield” like this one, we should slow down, question our intuitions, and rely on our System 2 processing.