Somewhere Between Utopia and Dystopia: Choosing From Incomparable Prospects

For ranking incomparable prospects, a ‘Utopia Index’ measuring the proximity to a lower envelope of the integrated distribution functions is proposed which can be interpreted as a locus of optimal satisfaction levels for a range of permitted preferences. 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 procedures based on bootstrapping techniques. There are a wide variety of potential applications wherein classical dominance techniques fail to yield definitive conclusions. To illustrate, an empirical application to Chinese household income data shows how the well-being of cohorts impacted by the vagaries of Era’s before, during and after the Cultural Revolution can be ranked in the absence of a dominance relationship and an application to historical investment returns data shows that, depending on the investment universe, investing in small value stocks or small winner stocks is ranked above all alternative strategies.