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

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

1. 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])

2. State the axiom it contradicts.

3. Explain how the finding contradicts the axiom.

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

5. 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 objections 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.

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