For Thursday, read Wedgwood. A standard reading response (about Wedgewood’s chapter) is due on Thursday, in class. For the remainder of the term, I plan to cover chapters 7, 9, 10, 13, 14, 15, 17, and 19.
Widespread Irrationality? Kahneman and Tversky and the conjunction fallacy: 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 likely? 1. Linda is a bank teller 2. Linda is a bank teller and is active in the feminist movement
In the original experiment, 86% of the subjects chose (2). This answer is clearly irrational: the range of possibilities in which Linda is a bank teller AND a feminist is a subset of the range of possibilities in which she’s a bank teller. So, it’s impossible for (2) to be more likely than (1).
K&T and the Base-Rate Fallacy In Beantown, there are two kinds of cabs, blue and green. Blue Cab is much more successful. 80% of the cabs in town are blue, and 20% are green. A witness in a trial testifies that he saw a green cab at the scene of a crime. The defense lawyer decides to test the witness’s ability to identify the cab colors, exposing the witness to one hundred green cabs and one hundred blue cabs.
In the test, the witness was 80% reliable, in the sense that he correctly identified 80 of the 100 green cabs as green (misidentifying the others as blue) and correctly identified 80 of the 100 blue cabs as blue (misidentifying the others as green). Question: How likely is the witness’s testimony (that the cab at the scene of the crime was green) to be right?
Answer: 50%. Out of a given 100 cabs, 16 of the green ones and 16 of the blue ones will be identified as green. So, the witness’s testimony is no better than a coin toss! We’re inclined to think otherwise, because we tend to ignore base-rates, i.e., relative prevalence of the two kinds of cabs, and thus (un)likelihood that a green cab would have been at the scene.
The math: Consider running a 100 trials representative of life in Beantown. Of these 100 cabs, 80 will be blue and 20, green. Of the blue cabs, our witness will identify 80% (64) correctly, as blue, 20% (16) incorrectly, as green. Of the 20 green cabs, 80% (16) will be correctly identified as green. So the chance that a cab identified as green is actually green (16/100ths) is the same as the chance (16/100ths) that it is blue.
Rey’s Points -The subjects are thinking about probability, even if they violate the rational norms. So, normativism about content is wrong (particularly with respect to the norm of rationality). -This kind of empirical work also pressures the normativists to say exactly what the “mandatory” norms are.