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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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This is an optional section that was not covered in all versions of the lecture this year.

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.

How to Object

  1. State the construal of decision theory you are considering.

  2. State the finding.

    • (In this case, the finding is Ellsberg’s discovery of cases where people prefer A over B but also prefer B or C over A or C.[2])
  3. State the axiom it contradicts.

  4. Explain how the finding contradicts the axiom.

  5. (If possible, explain why it is significant.)

  6. Consider responses.

Independence Axiom

The Independence Axiom states that if b⪰a then for any probability p, {pA,(1−p)C}⪯{pB,(1−p)C}. Put roughly, if you prefer a to b then you should prefer a and c to b and c.

‘Intuitively, this means that preferences between lotteries should be governed only by the features of the lotteries that differ; the commonalities between the lotteries should be effectively ignored.’ (Steele & Stefánsson, 2020)

The Paradox of Decision Theory

On the one hand, it has become a commonplace that there are plenty of objections to the idea that decision theory characterises how people choose.

On the other hand, there is a growing range of cases in which decision theory (or something based on it, like game theory) has been fruitfully applied. Motor control is a prominent example (see Trommershäuser, Maloney, & Landy, 2009; Wolpert & Landy, 2012).

If the objects are as decisive as usually assumed, why have applications of decision theory proved so fruitful?

Perhaps the answer is that decision theory is a model. Like any model, it can be given different construals. The objections are not objections to decision theory as such, which is simply a model. Instead each objection is an objection to one or more construals of decision theory.

If this is right, it will be important to be clear about which construals your objections concern.

Ask a Question

Your question will normally be answered in the question session of the next lecture.

More information about asking questions.


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).
game theory : This term is used for any version of the theory based on the ideas of Neumann et al. (1953) and presented in any of the standard textbooks including. Hargreaves-Heap & Varoufakis (2004); Osborne & Rubinstein (1994); Tadelis (2013); Rasmusen (2007).
model : A model is a way some part or aspect of the world could be.


Davidson, D. (1987). Problems in the explanation of action. In P. Pettit, R. Sylvan, & J. Norman (Eds.), Metaphysics and morality: Essays in honour of j. J. C. smart (pp. 35–49). Oxford: Blackwell.
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.
Neumann, J. von, Morgenstern, O., Rubinstein, A., & Kuhn, H. W. (1953). Theory of Games and Economic Behavior. Princeton, N.J. ; Woodstock: Princeton University Press.
O’Connor, C. (2019). The origins of unfairness: Social categories and cultural evolution (First edition). Oxford: Oxford University Press. Retrieved from
Osborne, M. J., & Rubinstein, A. (1994). A course in game theory. MIT press.
Ramsey, F. (1931). Truth and probability. In R. Braithwaite (Ed.), The foundations of mathematics and other logical essays. London: Routledge.
Rasmusen, E. (2007). Games and information: An introduction to game theory (4th ed). Malden, MA ; Oxford: Blackwell Pub.
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.
Tadelis, S. (2013). Game theory: An introduction. Princeton: Princeton University Press.
Trommershäuser, J., Maloney, L. T., & Landy, M. S. (2009). Chapter 8 - The Expected Utility of Movement. In P. W. Glimcher, C. F. Camerer, E. Fehr, & R. A. Poldrack (Eds.), Neuroeconomics (pp. 95–111). London: Academic Press.
Wolpert, D. M., & Landy, M. S. (2012). Motor control is decision-making. Current Opinion in Neurobiology, 22(6), 996–1003.


  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. ↩︎

  2. You can also mention Jia et al. (2020)’s findings if you are being especially thorough. ↩︎