Somewhere Between Utopia and Dystopia

Choosing From Multiple Incomparable Prospects

Gordon Anderson, Gerrit Tjeerd (Thierry) Post, Yoon Jae Whang

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
JournalJournal of Business and Economic Statistics
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Stochastic Dominance
utopia
Lower Envelopes
Subsampling
Significance level
Pairwise Comparisons
Alternatives
Expected Utility
Limit Distribution
Dynamic Process
household income
Envelope
Proximity
ranking
Ranking
Distribution Function
Deviation
Decision Making
Economics
decision making

Keywords

  • Almost stochastic dominance
  • Convex stochastic dominance
  • Portfolio choice
  • Subsampling
  • Well-being analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

Somewhere Between Utopia and Dystopia : Choosing From Multiple Incomparable Prospects. / Anderson, Gordon; Post, Gerrit Tjeerd (Thierry); Whang, Yoon Jae.

In: Journal of Business and Economic Statistics, 01.01.2019.

Research output: Contribution to journalArticle

@article{9d2bd4f0052f4518a06c1e17349066f0,
title = "Somewhere Between Utopia and Dystopia: Choosing From Multiple Incomparable Prospects",
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.",
keywords = "Almost stochastic dominance, Convex stochastic dominance, Portfolio choice, Subsampling, Well-being analysis",
author = "Gordon Anderson and Post, {Gerrit Tjeerd (Thierry)} and Whang, {Yoon Jae}",
year = "2019",
month = "1",
day = "1",
doi = "10.1080/07350015.2018.1515765",
language = "English",
journal = "Journal of Business and Economic Statistics",
issn = "0735-0015",
publisher = "American Statistical Association",

}

TY - JOUR

T1 - Somewhere Between Utopia and Dystopia

T2 - Choosing From Multiple Incomparable Prospects

AU - Anderson, Gordon

AU - Post, Gerrit Tjeerd (Thierry)

AU - Whang, Yoon Jae

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Almost stochastic dominance

KW - Convex stochastic dominance

KW - Portfolio choice

KW - Subsampling

KW - Well-being analysis

UR - http://www.scopus.com/inward/record.url?scp=85061274426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061274426&partnerID=8YFLogxK

U2 - 10.1080/07350015.2018.1515765

DO - 10.1080/07350015.2018.1515765

M3 - Article

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

SN - 0735-0015

ER -