The reasons for and against composite indicators are briefly reviewed, as well as the available theories for their construction. After noting the strong normative dimension of these measures—which ultimately aim to ‘tell a story’, e.g. to promote the social discovery of a particular phenomenon, we inquire whether a less partisan use of a composite indicator can be proposed by allowing more latitude in the framing of its construction. We thus explore whether a composite indicator can be built to tell ‘more than one story’ and test this in practical contexts. These include measures used in convergence analysis in the field of cohesion policies and a recent case involving the World Bank’s Doing Business Index. Our experiments are built to imagine different constituencies and stakeholders who agree on the use of evidence and of statistical information while differing on the interpretation of what is relevant and vital
