Risk or uncertainty?

In this textbook version of Raiffa and Schlaifer's statistical decision theory of experimentation combined with Savage's theory of statistics, the authors scratched the risk/uncertainty difference with a stroke:

...a number of economists have attempted to distinguish between risk and uncertainty, as originally proposed by Frank H. Knight. (1) Risk, Knight said, refers to situations where an individual is able to calculate probabilities on the basis of an objective classification of instances. For example, in tossing a fair die the chance of any single one of the six faces showing is exactly one-sixth. (2) Uncertainty, he contended, refers to situations where no objective classification is possible, for example, in estimating whether or not a cure for cancer will be discovered in the next decade...

...in this book, we disregard Knight's distinction. For our purpose, risk and uncertainty mean the same thing. It does not matter, we contend, whether an 'objective' classification is or is not possible. For we will be dealing throughout with a 'subjective' probability concept (as developed especially by Savage, 1954): probability is simply degree of belief. In fact, even in cases like the toss of a die where assigning 'objective' probabilities appears possible, such an appearance is really illusory. That the chance of any single face turning up is one-sixth is a valid inference only if the die is a fair one - a condition about which no one could ever be 'objectively' certain. Decision makers are therefore never in Knight's world of risk but instead always in his world of uncertainty. That this approach, assigning probabilities on the basis of subjective degree of belief, is a workable and fruitful procedure will be shown constructively throughout the book...

In a similarly direct manner, the authors defended analytic decision theory:

...the approach here does not allow for the psychological sensations of vagueness or confusion that people often suffer in facing situations with uncertain (risky) outcomes. In our model, the individual is neither vague nor confused. While recognizing that his knowledge is imperfect, so that he cannot be sure which state of the world will occur, he nevertheless can assign exact numerical probabilities representing his degree of belief as to the likelihood of each possible state. Our excuse for not picturing vagueness or confusion is that we are trying to model economics (/rational behavior), not psychology...The ultimate justification, for indifference-curve diagrams or for theories of decision under uncertainty, is the ability of such models to help us understand and predict behavior.