Psychology of probability: predictable irrationality

Cognitive biases in how people think about Probability have been widely described, e.g. in Kahneman's bestseller Thinking, Fast and Slow. In the Berkeley course I give a lecture by shamelessly reciting a selection of my favorite topics from Kahneman and from Dan Ariely's Predictably Irrational and from the more detailed technical and wide-ranging overview Cognition and Chance. The psychology of probabilistic reasoning by Raymond S. Nickerson. So I will not repeat such topics, but instead add some personal commentary.

1. It's always fun to start a lecture with juxtaposing quotes, so

There is much evidence that people are not rational, in the economist's sense [maximization of expected utility (MEU)]. Some would argue we need descriptive economics; I would argue that all should be taught about probability, utility and MEU and act accordingly. [Dennis Lindley, Understanding Uncertainty].

You mentioned research which revealed that shoppers often prefer ``50% extra free" to a notionally more generous 33% reduction in price, and you cited this as evidence of irrationality or poor mathematical ability on the part of consumers. Since all value is subjective, if people value 50% extra free more highly than 33% off, then that is an end of the matter. Whether or not the resulting behaviour conforms to some autistic neoclassical idea of rationality is irrelevant. [Rory Sutherland, Ogilvy & Mather UK. Letter to The Economist July 21 2012.]

2. The psychology research in this field gets real data from real people, but the data mostly consists of subjects' answers to hypothetical limited explicit relevant data exam-style questions involving uncertainty. My personal view of this field is that we have a good understanding of how people think about such hypothetical questions, but it is less clear how closely this translates to their "real life" behavior, two obvious issues being
(i) real life does not present us with limited explicit relevant data
(ii) your answer to a "what you would do if ....." question may well not be what you would actually do in real life.

3. A famous example, copying Wikipedia conjunction fallacy, is

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 probable?
(i) Linda is a bank teller.
(ii) Linda is a bank teller and is active in the feminist movement.

Most people say (ii) is more likely. This is incorrect, and the error is usually explained as an instance of the representativeness heuristic. But to me, the example has a specific logical structure, comparing P(A) with P(A and B), which we never encounter in real life. A much more common structure is

Police know, from existing evidence, that one of two suspects committed a crime.
Suspect 1 is tall and was wearing dark jacket at the time
Suspect 2 is tall; not known if wearing a dark jacket at the time.
A new witness appears who is sure the criminal is tall and was wearing a dark jacket. What can we infer?

Common sense and Bayes rule agree that, whatever the prior probabilities from other evidence, this extra evidence shifts the probability toward suspect 1.

These two examples are superficially similar. Even when reading a written version, it is not so easy to see they have opposite answers. So to me it is unsurprising that people confuse the settings.