Value-driven multidimensional welfare analysis: a dominance approach with application to comparisons of European populations

We consider the problem of comparing multidimensional probability distributions and its use in comparing the social welfare of different populations. We introduce theoretical results on two multidimensional stochastic orders, termed multidimensional first- and second-order dominance, that characterise the dominance relations and permit the practical comparison of discrete multi-dimensional probability distributions. Our results form the basis for a new framework for social welfare evaluation, which accommodates multiple dimensions of individual welfare, permits incorporating value judgements and enables robust social welfare comparisons. Our framework utilises non-decreasing and potentially concave multi-attribute functions to model individual welfare. We describe how this enables capturing a variety of trade-offs between welfare attributes as well as incorporating concerns about inequality in social welfare evaluation. Our framework also incorporates a welfare measurement scale. This facilitates a richer form of analysis, compared to other dominance-based methods, from which we can gauge the overall level of social welfare in different populations relative to some meaningful benchmarks, as opposed to deriving only partial rankings. We illustrate the application of our framework with a case study investigating social welfare across 31 European countries based on the EU-SILC dataset.