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Multivariate Discrete First Order Stochastic Dominance


  • Finn Tarp

    (Department of Economics, University of Copenhagen)

  • Lars Peter Østerdal

    (Department of Economics, University of Copenhagen)


This paper characterizes the principle of first order stochastic dominance in a multivariate discrete setting. We show that a distribution f first order stochastic dominates distribution g if and only if f can be obtained from g by iteratively shifting density from one outcome to another that is better. For the bivariate case, we develop the theoretical basis for an algorithmic dominance test that is easy to implement.

Suggested Citation

  • Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0723

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    References listed on IDEAS

    1. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
    2. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
    3. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    4. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
    5. Gleb Koshevoy, 1997. "The Lorenz zonotope and multivariate majorizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 1-14.
    6. David Levhari & Jacob Paroush & Bezalel Peleg, 1975. "Efficiency Analysis for Multivariate Distributions," Review of Economic Studies, Oxford University Press, vol. 42(1), pages 87-91.
    7. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
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    More about this item


    multidimensional first degree distributional dominance; robust poverty gap dominance; majorization; generalized equivalence result;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration

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