Thinking, Fast and Slow (2011)
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Kahneman and Tversky's critique of Bayesian analysis is basically: If more data should override a prior belief, then why is it as more data comes in people have increasingly divergent opinions? For example we have 24 hour news media throwing information at us and people only seem to be more divided politically. If we reasoned in a Bayesian manner then our opinions should converge, which they clearly do not.
Jaynes' answer is really fascinating and is covered in the chapter "Queer uses for probability theory" from 'Probability theory: The Logic of Science'. Basically Jaynes' argues that we are never really testing just one hypothesis. He gives an example of an experiment designed to prove ESP, and points out that no matter how low of a p-value the experiment reports, if you have a strong prior belief that ESP does not exist the evidence won't convince you. He argues this is because you actually have other hypotheses with other priors: The subject is tricking the experimenters, there is an error in experiment design, the people running the experiment are intentionally being deceptive etc.
He then shows that if your prior belief in ESP is sufficiently lower than your prior belief in these alternative hypothesis, not only will further evidence fail to convince you of ESP, but will actually increase your belief that you are being lied to in some way. So while Jaynes agrees that these priors may be irrational, our reasoning given new information is completely rational.
And just to be clear Jaynes is not explicitly arguing for or against the idea of ESP, though he himself does not believe he points out that there are many prior beliefs widely held in science that change dramatically over time. What he is saying if that if your prior belief in ESP is dramatically lower than your belief that people trying to prove ESP to you would deceive you in some way, the ESP is real hypothesis will never gain enough evidence to overcome the "I'm being tricked" hypothesis.
If you have any interest in how people make decisions then "Thinking, Fast and Slow" is worth reading.
The conventional definition of utility is pretty strict, for example, it must be a function of the final outcome only, and there is no model uncertainty, which would go under the title of ambiguity aversion instead. So maybe it's not that surprising that a really specific narrow concept doesn't describe all of human behaviour and needs to be extended. But since you can extend it sufficiently to describe some interesting behaviours, is it really necessary to focus specifically on the utility function, and not the other things that people might be maximizing?
So if rational maximization means that people have a utility function that they maximize, then yes, rational maximization is not what people do. But that is partly the fault of how the definition of utility was chosen.
What Kahneman and Tversky observed is that people don't even choose consistently. It depends on how the choices are presented. For instance, whether the subject frames an outcome as a loss or a smaller-than-expected gain. No matter how you define a utility function, it will not always be maximized. So, it's not a question of defining the function less narrowly. You can present two games with mathematically identical sets of outcomes and people consistently rank the outcomes differently.
Anyway, it's a very good and important book, and doesn't have much to do with Bayesian statistics.
[Ninja-edited since HN doesn't let me respond further below...if you can show the outcomes K & T observed are in fact consistent with a more broadly defined utility function, then you too can win a Nobel prize!]
I disagree, I think you are assuming that people accept questions at face value and unfailingly trust the experimenter. Then equivalent but differently-stated problems would be equivalent, and you would reach that conclusion.
But when people use heuristics, those heuristics are grounded in their experience, and are like a prior on the meaning of the question. Stating the same question in two different ways and getting different answers means either that there is no utility function, or that the "utility function" depends (through model uncertainty, for example) on the exact phrasing of the question.
My point is that these discussions are very closely tied to the kinds of assumptions you make about how people reason, what is rational, and what inputs the utility function has. Kahneman and Tversky got around this problem, I think, by doing something eminently reasonable: postulating a clear and unambiguous definition of a utility function. But the concept of "rationality" is richer than that, so the conversation should not stop there.
The word "rationality" may be ambiguous, as most words describing anything complex are, but the authors attempted to provide a clear model and work within those bounds. When we begin discussing the ideas informally, and using terms in a broader and more colloquial sense, then we're at fault if the results have become muddied.
The authors demonstrated a reasonable utility function, one which most people upon reflection would agree is logical, and demonstrated that people do not consistently act in a way that maximizes that function.
We can always move the goal post, and claim that if people appear to be acting irrationally it's because we simply don't understand their concept of rationality (or the more complex function they're maximizing). But that seems rather circular; it would be nice hear examples of a richer concept of rationality, in the context of the author's experiments, that might explain seemingly inconsistent behavior.
think fast and slow is also an amazing book - and i recommend it to almost everyone that i talk to about books. it is not a quick read (it's almost 500 pages i believe), but you will never think about advertising or your brain the same way after you reading about anchoring , substitution, and framing
Does that example really fit their critique? We sometimes pretend we can compress a person's beliefs down to a single bit -- red vs blue -- and when you consider how many bits you'd expect your own political views to require it's unbelievable that anyone could offer a single bit a meaningful summary of them. The idea that anyone could even dream that a single bit could be a meaningful lossy compression of my views indicates there is not much meaningful diversity in the population.
That's bold? Didn't Kahneman and Tversky demolished the idea of humans being rational, empirically, in the 70s? Is there any solid evidence of humans being rational, or even an evolutionary explanation of why that'd happen?
Do we expect other animals to have accurate probability processing psychology, too?
As for the book itself, I agree with some others' postings here -- it's absolutely fantastic. It changed the way I think about human cognition and education... not to mention machine learning, politics, and marketing.
For the record, I think the blank is "butter."