This chapter presents the intuition and psychological background of rank-dependent utility. There will be no formal definitions, and the chapter can be skipped if you are only interested in formal theory. After Preston & Baratta (1948) it took 30 years before Quiggin discovered a proper way to transform probabilities, being through rank dependence. After Keynes (1921) and Knight (1921), it even took over 60 years before David Schmeidler discovered a proper way to model uncertainty (the topic of later chapters), through rank dependence. This history shows the depth of the rank-dependent idea, which is why we dedicate this chapter to developing the underlying intuition.

§5.1 presents the important intuition of probabilistic sensitivity, which is an essential component, in addition to utility curvature, to obtain empirically realistic models of risk attitudes. Probabilistic sensitivity underlies all nonexpected utility (nonEU) theories. The question is how to develop a sound decision model that incorporates this component. The rest of the chapter argues that rank-dependent utility can serve as a natural model to obtain such a sound theory. The arguments are based on psychological interpretations and heuristic graphs. These suggest, first, that the rank-dependent formula is natural from a mathematical perspective. They also suggest that the rank-dependent formula matches psychological processes of decision making, in agreement with the homeomorphic approach taken in this book. Heuristic ideas as presented in this chapter may have led John Quiggin and David Schmeidler to invent the rank-dependent model.