The Allais paradox: what it became, what it really was, what it now suggests to us

Abstract

Whereas many others have scrutinized the Allais paradox from a theoretical angle, we study the paradox from an historical perspective and link our findings to a suggestion as to how decision theory could make use of it today. We emphasize that Allais proposed the paradox as a normative argument, concerned with ‘the rational man’ and not the ‘real man’, to use his words. Moreover, and more subtly, we argue that Allais had an unusual sense of the normative, being concerned not so much with the rationality of choices as with the rationality of the agent as a person. These two claims are buttressed by a detailed investigation – the first of its kind – of the 1952 Paris conference on risk, which set the context for the invention of the paradox, and a detailed reconstruction – also the first of its kind – of Allais’s specific normative argument from his numerous but allusive writings. The paper contrasts these interpretations of what the paradox historically represented, with how it generally came to function within decision theory from the late 1970s onwards: that is, as an empirical refutation of the expected utility hypothesis, and more specifically of the condition of von Neumann–Morgenstern independence that underlies that hypothesis. While not denying that this use of the paradox was fruitful in many ways, we propose another use that turns out also to be compatible with an experimental perspective. Following Allais’s hints on ‘the experimental definition of rationality’, this new use consists in letting the experiment itself speak of the rationality or otherwise of the subjects. In the 1970s, a short sequence of papers inspired by Allais implemented original ways of eliciting the reasons guiding the subjects’ choices, and claimed to be able to draw relevant normative consequences from this information. We end by reviewing this forgotten experimental avenue not simply historically, but with a view to recommending it for possible use by decision theorists today.

Ellsberg 1961: text, context, influence

“…However, this pair of preferences violates EU because no utility function is capable of rationalizing them by using the EU utility formula. 11 On the normative goals of Allais's paradox, see Mongin (2019).…”

Fitness-Maximizers Employ Pessimistic Probability Weighting for Decisions Under Risk

“…The independence axiom asserts that adding a common outcome to two prospects should not change the preference ordering of the prospects. Perhaps the most notable behavioural anomaly is the Allais paradox (Mongin, 2019 , for a recent review), or common consequence effect, which uncovers a violation of the independence assumption. Quiggin ( 1993 , p. 30) writes: ‘The Allais problem is the pons asinorum of theories of choice under uncertainty.…”

Who accepts Savage’s axiom now?

“…Firstly, the Allais paradox has played a central role in the evolution of risky choice theory (van de Kuilen & Wakker, 2006;Mongin, 2019). By speaking to both the descriptive and normative performance of the sure-thing principle, Slovic and Tversky's result has occupied a significant position in that programme of research.…”