Stochastic Dominance in Nonlinear Utility Theory

Stochastic dominance has interested mathematicians for more than half a century (Karamata, 1932; Hardy, Littlewood and Polya, 1934; Sherman, 1951; Lehmann, 1955), and its integration into decision theory began nearly forty years ago (Masse and Morlat, 1953; Allais, 1953a, 1953b; Blackwell and Girshick, 1954; Quirk and Saposnik, 1962; Fishburn, 1964). However, it was not until a cluster of important papers on stochastic dominance appeared around 1969–71 (Hadar and Russell, 1969, 1971; Hanoch and Levy, 1969; Whitmore, 1970; Rothschild and Stiglitz, 1970, 1971) that it emerged as a central topic in economic decision theory. Hundreds of papers as well as a survey book (Whitmore and Findlay, 1978) and an extensive research bibliography (Bawa, 1982) testify to its popularity.