Drunkard's Walk - Leonard Mlodinow [12]
Statement
Average Probability Rank
Linda is active in the feminist movement.
2.1
Linda is a psychiatric social worker.
3.1
Linda works in a bookstore and takes yoga classes.
3.3
Linda is a bank teller and is active in the feminist movement.
4.1
Linda is a teacher in an elementary school.
5.2
Linda is a member of the League of Women Voters.
5.4
Linda is a bank teller.
6.2
Linda is an insurance salesperson.
6.4
At first glance there may appear to be nothing unusual in these results: the description was in fact designed to be representative of an active feminist and unrepresentative of a bank teller or an insurance salesperson. But now let’s focus on just three of the possibilities and their average ranks, listed below in order from most to least probable. This is the order in which 85 percent of the respondents ranked the three possibilities:
Statement
Average Probability Rank
Linda is active in the feminist movement.
2.1
Linda is a bank teller and is active in the feminist movement.
4.1
Linda is a bank teller.
6.2
If nothing about this looks strange, then Kahneman and Tversky have fooled you, for if the chance that Linda is a bank teller and is active in the feminist movement were greater than the chance that Linda is a bank teller, there would be a violation of our first law of probability, which is one of the most basic of all: The probability that two events will both occur can never be greater than the probability that each will occur individually. Why not? Simple arithmetic: the chances that event A will occur = the chances that events A and B will occur + the chance that event A will occur and event B will not occur.
Kahneman and Tversky were not surprised by the result because they had given their subjects a large number of possibilities, and the connections among the three scenarios could easily have gotten lost in the shuffle. And so they presented the description of Linda to another group, but this time they presented only these possibilities:
Linda is active in the feminist movement.
Linda is a bank teller and is active in the feminist movement.
Linda is a bank teller.
To their surprise, 87 percent of the subjects in this trial also ranked the probability that Linda is a bank teller and is active in the feminist movement higher than the probability that Linda is a bank teller. And so the researchers pushed further: they explicitly asked a group of thirty-six fairly sophisticated graduate students to consider their answers in light of our first law of probability. Even after the prompting, two of the subjects clung to the illogical response.
The interesting thing that Kahneman and Tversky noticed about this stubborn misperception is that people will not make the same mistake if you ask questions that are unrelated to what they know about Linda. For example, suppose Kahneman and Tversky had asked which of these statements seems most probable:
Linda owns an International House of Pancakes franchise.
Linda had a sex-change operation and is now known as Larry.
Linda had a sex-change operation, is now known as Larry, and owns an International House of Pancakes franchise.
In this case few people would choose the last option as more likely than either of the other two.
Kahneman and Tversky concluded that because the detail “Linda is active in the feminist movement” rang true based on the initial description of her character, when they added that detail to the bank-teller speculation, it increased the scenario’s credibility. But a lot could have happened between Linda’s hippie days and her fourth decade on the planet. She might have undergone a conversion to a fundamentalist religious cult, married a skinhead and had a swastika tattooed on her left buttock, or become too busy with other aspects of her life to remain politically active. In each of these cases and many others she would probably not be active in the feminist movement. So adding that detail