Representativeness Heuristic, Base Rates, and Bayes

23 Apr

From the Introduction of their edited volume:
Tversky and Kahneman used the following experiment for testing ‘representativeness heuristic’ –

Subjects are shown a brief personality description of several individuals, sampled at random from 100 professionals – engineers and lawyers.
Subjects are asked to assess whether the description is of an engineer or a lawyer.
In one condition, subjects are told group = 70 engineers/30 lawyers. Another the reverse = 70 lawyers/30 engineers.

Results –
Both conditions produced same mean probability judgments.

Tversky and Kahneman call this result a ‘sharp violation’ of Bayes Rule.

I am not sure the experiment shows any such thing. Mathematical formulation of the objection is simple and boring so an example. Imagine, there are red and black balls in an urn. Subjects are asked if the ball is black or red under two alternate descriptions of the urn composition. When people are completely sure of the color, the urn composition obviously should have no effect. Just because there is one black ball in the urn (out of say a 100), it doesn’t mean that the person will start thinking that the black ball in her hand is actually red. So on and so forth. One wants to apply Bayes by accounting for uncertainty. People are typically more certain (lots of evidence it seems – even in their edited volume) so that automatically discounts urn composition. People may not be violating Bayes Rule. They may just be feeding the formula incorrect data.