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Somewhere Between Utopia and Dystopia: Choosing From Incomparable Prospects


  • Gordon Anderson
  • Thierry Post
  • Yoon-Jae Whang


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.

Suggested Citation

  • Gordon Anderson & Thierry Post & Yoon-Jae Whang, 2016. "Somewhere Between Utopia and Dystopia: Choosing From Incomparable Prospects," Working Papers tecipa-568, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-568

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    More about this item


    Choice Under Uncertainty; Stochastic Dominance; Complete Orderings;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • D6 - Microeconomics - - Welfare Economics
    • G0 - Financial Economics - - General
    • H0 - Public Economics - - General
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty


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