In this paper we present a formal framework to define and study the properties of utility-oriented measurements of retrieval effectiveness, like AP, RBP, ERR and many other popular IR evaluation measures. The proposed framework is laid in the wake of the representational theory of measurement, which provides the foundations of the modern theory of measurement in both physical and social sciences, thus contributing to explicitly link IR evaluation to a broader context. The proposed framework is minimal, in the sense that it relies on just one axiom, from which other properties are derived. Finally, it contributes to a better understanding and a clear separation of what issues are due to the inherent problems in comparing systems in terms of retrieval effectiveness and what others are due to the expected numerical properties of a measurement.