Multidimensional welfare rankings under weight imprecision: a social choice perspective

Ranking alternatives based on multidimensional welfare indices 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. With this voting construct in mind, the well-known Kemeny rule from social choice theory is introduced as a means of aggregating the preferences of many plausible choices of weights, suitably weighted by the importance attached to them. The axiomatic characterization of Kemeny's rule due to Young and Levenglick (1978) and Young (1988) extends to the present context. An analytic solution is derived for an interesting special case of the model corresponding to generalized weighted means and the -contamination framework of Bayesian statistics. The model is applied to the ARWU index of Shanghai University. Graph-theoretic insights are shown to facilitate computation significantly.