Preference foundations of expected utility, supporting the rationality of this theory, became widely known in the 1960s. They gave a big boost to the popularity of expected utility in many fields. Clarifying illustrations of early applications include Keeney & Raiffa (1976 Chs. 7 and 8), McNeil et al. (1978, 1981), Weinstein et al. (1980 Ch. 9), and Winkler (1972 §5.10). After a first, optimistic, period it gradually became understood that there are systematic empirical deviations, and that applications will have to be more complex than first meets the eye. Kahneman & Tversky's (1979) prospect theory was the major paper to disseminate this insight, and to initiate new and more refined nonexpected utility models. In the same way as Bernoulli's (1738) expected utility entailed a departure from objectivity, prospect theory entailed a departure from rationality. Another influential paper to initiate new models was Machina (1982) who, however, argued for a rational status of those new models. Parts II and III of this book are dedicated to descriptive nonexpected utility theories that may depart from rationality.