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Simplifying and Solving Decision Problems by Stochastic Dominance Relations

  1. Louis Eeckhoudt1,2,
  2. Harris Schlesinger3,
  3. Ilia Tsetlin4,5

Published Online: 15 JUN 2010

DOI: 10.1002/9780470400531.eorms0776

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Eeckhoudt, L., Schlesinger, H. and Tsetlin, I. 2010. Simplifying and Solving Decision Problems by Stochastic Dominance Relations. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. 1

    LEM, Université Catholique de Lille, IESEG School of Management, Lille, France

  2. 2

    Université Catholique de Louvain, CORE, Louvain-la-Neuve, Belgium

  3. 3

    University of Alabama, Department of Finance, Tuscaloosa, Alabama

  4. 4

    INSEAD, Fontainebleau, France

  5. 5

    INSEAD, Singapore

Publication History

  1. Published Online: 15 JUN 2010

Abstract

Stochastic dominance is a formal statistical property that partially orders probability distributions. If two alternatives can be ordered by the stochastic dominance criterion, then all individuals whose utility functions satisfy a few easy-to-verify criteria will unanimously prefer the dominant alternative. We review several extant characterizations of stochastic dominance, including a recent result that shows how stochastic dominance can be linked to a preference for combining “good” and “bad” outcomes. In particular, if a decision context is about allocating pairs of alternatives in two different states, then lotteries between two “good-bad” pairs dominate lotteries that yield both “bad” alternatives in one state versus both “good” alternatives in the other state. We explain this dominance relationship and show how it can be used in solving several decision problems involving choice under risk. We also show how individual preference for always pairing such good with bad alternatives implies utility that is a weighted average of exponential functions, which can each be characterized as exhibiting constant absolute risk aversion (CARA). Thus, if preference for one alternative over the others holds under CARA with a wide range of risk aversion coefficients, the decision can be determined with only a limited amount of information about the decision maker's particular utility function.

Keywords:

  • downside risk;
  • precautionary effects;
  • prudence;
  • risk apportionment;
  • risk aversion;
  • stochastic dominance;
  • temperance;
  • completely monotone utility