Abstract

In 1738 Daniel Bernoulli published an influential paper and discussed the St. Petersburg paradox, to show that the expected value theory must be wrong. In the 20th century Abraham Wald was interested in pointing out that the two central procedures of sampling distribution based statistical theory, namely hypotheses testing and parameter estimation, are special cases of the general decision problem. Wald renowned and synthesized many concepts of statistical theory. In a subsequent work Wald discussed about loss function, risk function, admissible decision rules, Bayesian procedures and the minimax procedures. The revival of subjective probability theory extended the scope of expected utility theory to situations where sub probability can be used. For this reason the works of F. Ramsey, B. de Finetti e L.J. Savage became very useful. In the same time, John von Neumann e Oskar Morgenstern introduced the utility theory arguing that expected utility maximization follows the basic probabilities about rational behavior. The works of M. Allais and D. Ellesberg suggested that human behavior has systematic and some basic departures from expected utility maximization. The prospect theory of D. Kahneman e A. Tversky renowned the empirical study of economic behavior with less emphasis on rationality presuppositions. In our paper we discuss the role of means related to decisions. In the 1920 and 1930 many authors discussed the axiomatic and subjective probability theory. At the same time, A.N. Kolmogorov, B. de Finetti, F. Ramsey discussed the notions of the mean and certainty equivalent and anticipate the theories of rational decision. Finally, we present the role of the means in decision-making and the Bayesian approach to decision theory