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Somewhere Between Utopia and Dystopia: Choosing From Multiple Incomparable Prospects

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  • Gordon Anderson
  • Thierry Post
  • Yoon-Jae Whang

Abstract

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.

Suggested Citation

  • Gordon Anderson & Thierry Post & Yoon-Jae Whang, 2020. "Somewhere Between Utopia and Dystopia: Choosing From Multiple Incomparable Prospects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 502-515, July.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:3:p:502-515
    DOI: 10.1080/07350015.2018.1515765
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    Cited by:

    1. Gordon Anderson & Oliver Linton & Maria Grazia Pittau & Yoon-Jae Whang & Roberto Zelli, 2021. "On unit free assessment of the extent of multilateral distributional variation," The Econometrics Journal, Royal Economic Society, vol. 24(3), pages 502-518.
    2. Mehmet Pinar & Thanasis Stengos & Nikolas Topaloglou, 2022. "Stochastic dominance spanning and augmenting the human development index with institutional quality," Annals of Operations Research, Springer, vol. 315(1), pages 341-369, August.
    3. Anderson, Gordon & Fu, Rui & Leo, Teng Wah, 2022. "Health, loneliness and the ageing process in the absence of cardinal measure: Rendering intangibles tangible," The Journal of the Economics of Ageing, Elsevier, vol. 22(C).
    4. Gordon Anderson, 2024. "Human Resource Investment and Early-Stage Career Choice: Evaluating Work–Life Income Paths in 21st-Century Canada," JRFM, MDPI, vol. 17(1), pages 1-19, January.

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