Multidimensional welfare rankings

Social well-being is intrinsically multidimensional. Welfare indices attempting to reduce this complexity to a unique measure abound in many areas of economics and public policy. Ranking alternatives based on such measures depends, sometimes critically, on how the different dimensions of welfare are weighted. In this paper, a theoretical framework is presented that yields a set of consensus rankings in the presence of such weight imprecision. The main idea is to consider a vector of weights as an imaginary voter submitting preferences over alternatives in the form of an ordered list. With this voting construct in mind, a rule for aggregating the preferences of many plausible choices of weights, suitably weighted by the importance attached to them, is proposed. An axiomatic characterization of the rule is provided, and its computational implementation is developed. An analytic solution is derived for an interesting special case of the model corresponding to generalized weighted means and the $\epsilon$-contamination framework of Bayesian statistics. The model is applied to the Academic Ranking of World Universities index of Shanghai University, a popular composite index measuring academic excellence.