Since Keynes (1921), Knight (1921), and Ellsberg (1961) it had been understood that we need a theory for decision under uncertainty when no probabilities are given. A first proposal came from de Finetti (1931a) and Ramsey (1931), and was later perfected by Savage (1954). These authors showed that, if no objective probabilities are given, then we have to provide subjective probabilities as well as we can, assuming some conditions. This led to expected utility for uncertainty, the topic of Chapter 4. Because we still had probabilities available, we could use many techniques from risk. No very new techniques had to be developed.

The results of de Finetti, Ramsey, and Savage were first challenged by Allais (1953a), who showed that people often do not maximize expected utility. Allais did not challenge the role of probabilities (the concern of Keynes and Knight), and assumed those given. A more serious challenge came from Ellsberg (1961). He provided a paradox where, again, the conditions of de Finetti et al. were violated. These violations were, however, more fundamental. They showed that under plausible circumstances no subjective probabilities can be provided in any manner. Thus Ellsberg put the question of Keynes and Knight back on the table: We need a new theory for decision under uncertainty, one that essentially extends beyond probabilistic reasoning. Yet, despite the importance of such a theory, for more than 60 years after Keynes (1921) and Knight (1921) no one had been able to invent it due to the subtle nature of uncertainty in the absence of probabilities.