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
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.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
Which is more probable?
(i) Linda is a bank teller.
(ii) Linda is a bank teller and is active in the feminist movement.
Police know, from existing evidence, that one of two suspects committed a crime.Common sense and Bayes rule agree that, whatever the prior probabilities from other evidence, this extra evidence shifts the probability toward suspect 1.
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?
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.