This book has presented a number of theories for decision under uncertainty and risk, primarily classical expected utility, rank-dependent utility, and prospect theory. Throughout we have treated risk with given probabilities as a special limiting case of uncertainty. We have strived for homeomorphic models, where the algebraic operations in models resemble psychological processes. To achieve this goal, we developed nonparametric deterministic measurement methods, where model parameters can directly be linked to observable choice, the empirical primitive. Behavioral foundations were derived from consistency requirements for the measurements of the model parameters.

In Part I, on expected utility, there were relatively many exercises and applications because this model is classic and has existed for a long time. The first new concept beyond the classical model was rank dependence, introduced informally in Chapter 5 and developed in the following chapters. Using rank dependence we could define pessimism and optimism which, while formally new, were closely related to the classical risk aversion and risk seeking. We also found a new phenomenon, likelihood insensitivity, the second new concept beyond the classical model. It reflects a lack of understanding of risk and uncertainty rather than an aversion or a preference. No similar phenomenon can be modeled with expected utility. The third new concept was reference dependence, leading to a different treatment of gains than losses, in prospect theory. The fourth new concept was source dependence, with ambiguity referring to differences between sources with unknown probabilities versus chance (known probabilities).