Somewhere between Utopia and Dystopia : Choosing from Incomparable Prospects

For ranking incomparable prospects, a ‘Utopia Index' measuring the proximity to a lower envelope of integrated distribution functions is proposed. The analysis generalizes the existing Almost Stochastic Dominance concept from pairwise comparison to a joint analysis of an arbitrary number of prospects. The exact limit distribution for the empirical counterpart of the index for a general class of dynamic processes is derived together with a feasible test procedure based on subsampling techniques, allowing for consistent statistical inference. To illustrate, empirical applications to Chinese household income data and historical investment returns data shows that, in every choice set, a single prospect is ranked above all alternatives at conventional significance levels