On the rationality of some decision roles in a stochastic environment

A classical decision rule consists of finding the decision which minimizes the expected cost. Liberty and Hartwig [1] proposed another decision rule which consists of minimizing a combination of the expectation and the variance of the cost in order to reduce the probability of bad realizations. We show that this decision rule does not meet a "minimal rationality requirement" in general. We relate it to another one and exhibit special cases when it does so.