UTILITY AND MEANS IN THE 1930S

This paper reviews the early axiomatic treatments of quasilinear means developed in the late 1920s and the 1930s. These years mark the begin ning of both axiomatic and subjectivist probability theory as we know them today. At the same time, Kolmogorov, de Finetti and, in a sense, Ramsey took part in a perhaps lesser known debate concerning the notio ns of mean and certainty equivalent. The results they developed offer interesting perspectives on computing data summaries. They also antici pate key ideas in current normative theories of rational decision maki ng. This paper includes an extended and self-contained introduction di scussing the main concepts in an informal way. The remainder focusses primarily on two early characterizations of quasi-linear means: the Na gumo-Kolmogorov theorem and de Finetti's extension of it. These result s are then related to Ramsey's expected utility theory, to von Neumann and Morgenstern's and to results on weighted means.