Value-driven multidimensional welfare analysis: A dominance approach with application to comparisons of European populations
研究多维概率分布比较问题，提出多维一阶和二阶随机支配理论，构建社会福利评估新框架，允许纳入价值判断和福利权衡，并用欧盟数据比较31国社会福利。
<p dir="ltr">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.</p>