This paper proposes a new framework for the measurement of population health and the ranking of the health of different geographies. Since population health is a latent variable, studies which measure and rank the health of different geographies must aggregate observable health attributes into one summary measure. We show that the methods used in nearly all the literature to date implicitly assume that all attributes are infinitely substitutable. Our method, based on the measurement of multidimensional welfare and inequality, minimizes the entropic distance between the summary measure of population health and the distribution of the underlying attributes. This summary function coincides with the constant elasticity of substitution and Cobb-Douglas production functions and naturally allows different assumptions regarding attribute substitutability or complementarity. To compare methodologies, we examine a well-known ranking of the population health of U.S. states, America's Health Rankings. We find that states' rankings are somewhat sensitive to changes in the weight given to each attribute, but very sensitive to changes in aggregation methodology. Our results have broad implications for well-known health rankings such as the 2000 World Health Report, as well as other measurements of population and individual health levels and the measurement and decomposition of health inequality.