Somewhere Between Utopia and Dystopia: Choosing From Multiple Incomparable Prospects

In many fields of decision making, choices have to be made from multiple alternatives, but stochastic dominance rules do not yield a complete ordering due to incomparability of some or all of the prospects. For ranking incomparable prospects, a “Utopia Index” measuring the proximity to a lower envelope of integrated distribution functions is proposed. Economic interpretations in terms of Expected Utility are provided for the envelope and deviations from it. The analysis generalizes the existing Almost Stochastic Dominance concept from pairwise comparison to a joint analysis of an arbitrary number of prospects. The limit distribution for the empirical counterpart of the index for a general class of dynamic processes is derived together with a consistent and feasible inference procedure based on subsampling techniques. Empirical applications to Chinese household income data and historical investment returns data show that, in every choice set, a single prospect is ranked above all alternatives at conventional significance levels, despite the incomparability problem.