Imprecise sampling and direct decision making

In decision theory, uncertainty is generally modeled through probabilities or probability intervals. Data however, when collected by sampling, do not provide probabilities (resp., lower/upper probabilities) but frequencies (resp., lower/upper frequencies). Discrepancies between the former and the latter are taken into account by the model presented: axiomatic requirements are shown to imply that the ordering of the decision must only depend on a quadruple (GEU, u, U, N), where GEU is the generalized expected utility evaluation of the decision that would result from the assimilation of frequencies to lower/upper probabilities; u and U are the utility levels of, respectively, the worst and the best reachable outcomes; and N is the size of the sample. Additional axioms are given that ensure the existence of an additive utility representing the ordering.