An Objection to Decision Theory?
This section introduces the Ellsberg Paradox (Ellsberg, 1961) and considers how it might be used as an objection to decision theory.
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Is explained in this section.
Step by step.
You can hardly pick up a recent work on decision theory without
finding an objection to its axioms.
This section introduces on objection linked to the Ellsberg Paradox
(Ellsberg, 1961; see Hargreaves-Heap & Varoufakis, 2004 for an concise and easy to read
presentation if you prefer not to watch the recording).
This is just one of many potential objections. I chose it
arbitrarily. It gives me an excuse for sharing
a fun fact about Ellsberg
himself, which illustrates how research in decision making has had
It would be useful to
become familiar with other potential objections if you have time. See, for example,
Steele & Stefánsson (2020, p. §2.3) who present the Allais Paradox;
or the various objections in Hargreaves-Heap & Varoufakis (2004, p. Chapter 1);
or almost any recent text on decision theory.
It is perhaps tempting, initially, to think that the objections are simple.
They show that decision theory is wrong, misguided or at least too limited
to characterise the full richness of human behaviour.
But, as we will eventually see, things are much more interesting than that.
For it turns out that whether something is
an objection depends on
what you are using decision theory for.
A preference relation is _independent of irrelevant alternatives_
exactly if ‘no change in the set of candidates (addition to or subtraction from)
[can] change the rankings of the unaffected candidates.’
(Dixit, Skeath, & Reiley, 2014, p. 600)
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: I use ‘decision theory’ for the theory elaborated by Jeffrey (1983). Variants are variously called ‘expected utility theory’ (Hargreaves-Heap & Varoufakis, 2004), ‘revealed preference theory’ (Sen, 1973) and ‘the theory of rational choice’ (Sugden, 1991). As the differences between variants are not important for our purposes, the term can be used for any of core formal parts of the standard approaches based on Ramsey (1931) and Savage (1972).
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Dixit, A., Skeath, S., & Reiley, D. (2014). Games of strategy
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Ellsberg, D. (1961). Risk, Ambiguity, and the Savage Axioms. The Quarterly Journal of Economics
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Jia, R., Furlong, E., Gao, S., Santos, L. R., & Levy, I. (2020). Learning about the Ellsberg Paradox reduces, but does not abolish, ambiguity aversion. PLOS ONE
(3), e0228782. https://doi.org/10.1371/journal.pone.0228782
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(First edition). Oxford: Oxford University Press. Retrieved from http://webcat.warwick.ac.uk/record=b3405858~S1
Ramsey, F. (1931). Truth and probability. In R. Braithwaite (Ed.), The foundations of mathematics and other logical essays
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