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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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The Objection

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 life-or-death consequences.

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.[1]

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.

Independence Axiom

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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decision theory : 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. New York: W. W. Norton; Company.
Ellsberg, D. (1961). Risk, Ambiguity, and the Savage Axioms. The Quarterly Journal of Economics, 75(4), 643–669.
Hargreaves-Heap, S., & Varoufakis, Y. (2004). Game theory: A critical introduction. London: Routledge. Retrieved from
Jeffrey, R. C. (1983). The logic of decision, second edition. Chicago: University of Chicago Press.
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, 15(3), e0228782.
Mandler, M. (2001). A difficult choice in preference theory: Rationality implies completeness or transitivity but not both. In E. Millgram (Ed.), Varieties of practical reasoning (pp. 373–402). Cambridge, Mass: MIT Press.
Mandler, M. (2005). Incomplete preferences and rational intransitivity of choice. Games and Economic Behavior, 50(2), 255–277.
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O’Connor, C. (2019). The origins of unfairness: Social categories and cultural evolution (First edition). Oxford: Oxford University Press. Retrieved from
Ramsey, F. (1931). Truth and probability. In R. Braithwaite (Ed.), The foundations of mathematics and other logical essays. London: Routledge.
Savage, L. J. (1972). The foundations of statistics (2nd rev. ed). New York: Dover Publications.
Sen, A. (1973). Behaviour and the Concept of Preference. Economica, 40(159), 241–259.
Steele, K., & Stefánsson, H. O. (2020). Decision Theory. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2020). Metaphysics Research Lab, Stanford University.
Sugden, R. (1991). Rational Choice: A Survey of Contributions from Economics and Philosophy. The Economic Journal, 101(407), 751–785.


  1. There are some interesting and influential considerations in Sugden (1991), but this is not the place to start so I recommend considering it only if you already have a good understanding of decision theory and comparatively straightforward objections. ↩︎