Logical, psychological, and normative theories of choice under uncertainty
When looking at a formal theory of choice under uncertainty, there are (at least) three questions one might ask about it:
1) Is it mathematically sound?
2) Should people be applying it in some or all situations? If some, which ones?
3) Do people actually reason that way?
The authors of G. L. S. Shackle sometimes seem to be mixing these three questions together, to the detriment of their analysis. For instance, they contend, "Whether probability is relevant [to single cases, rather than to a sequence of repeated trials,] is testable even by simple thought experiments" (p. 71). Well, first of all, what the authors next describe are not thought experiments à la Einstein, but experiments they have thought about someone performing. (The difference being they are asking "Think about this: how will people really respond in this situation?" rather than claiming the thought experiment itself proves anything.)
And what they claim (I think correctly) is that, in the situations they describe, many people would indeed apply probabilistic reasoning. But this hardly addresses Shackle's point: he was arguing against applying probabilistic reasoning to single cases precisely because he knew people do so. So showing that people do so merely shows he was not tilting at windmills, and not that he was wrong.
A little later, they write: "Specialists indeed later found serious faults in Bayesian reasoning (e.g. the Ellsberg paradox)" (p. 81). Let me admit that when I first read that sentence, I chuckled to myself and thought, "Named after Daniel Ellsberg of Pentagon Papers fame, no doubt, ha ha!" Well, I looked it up, and it is named after Daniel Ellsberg!
In any case, having now studied the paradox, I cannot see that it shows any fault in Bayesian reasoning at all. Instead, it shows that people often don't use Bayesian reasoning. But this is something most Bayesians readily acknowledge, as I often see them criticizing people's reasoning by saying something like, "Well, if they had been good Bayesian reasoners, they would have reached conclusion X."
1) Is it mathematically sound?
2) Should people be applying it in some or all situations? If some, which ones?
3) Do people actually reason that way?
The authors of G. L. S. Shackle sometimes seem to be mixing these three questions together, to the detriment of their analysis. For instance, they contend, "Whether probability is relevant [to single cases, rather than to a sequence of repeated trials,] is testable even by simple thought experiments" (p. 71). Well, first of all, what the authors next describe are not thought experiments à la Einstein, but experiments they have thought about someone performing. (The difference being they are asking "Think about this: how will people really respond in this situation?" rather than claiming the thought experiment itself proves anything.)
And what they claim (I think correctly) is that, in the situations they describe, many people would indeed apply probabilistic reasoning. But this hardly addresses Shackle's point: he was arguing against applying probabilistic reasoning to single cases precisely because he knew people do so. So showing that people do so merely shows he was not tilting at windmills, and not that he was wrong.
A little later, they write: "Specialists indeed later found serious faults in Bayesian reasoning (e.g. the Ellsberg paradox)" (p. 81). Let me admit that when I first read that sentence, I chuckled to myself and thought, "Named after Daniel Ellsberg of Pentagon Papers fame, no doubt, ha ha!" Well, I looked it up, and it is named after Daniel Ellsberg!
In any case, having now studied the paradox, I cannot see that it shows any fault in Bayesian reasoning at all. Instead, it shows that people often don't use Bayesian reasoning. But this is something most Bayesians readily acknowledge, as I often see them criticizing people's reasoning by saying something like, "Well, if they had been good Bayesian reasoners, they would have reached conclusion X."
In fairness to the authors, I have seen a prominent Bayesian assert that the Bayesian decision making approach does mean freely using your utility function and your subjective probabilities in just such a way where this would be a problem, in that you could be "Dutch booked". But that's not a paradox, it's an argument for changing your preference in gambles.
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