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Checking bivariate first order dominance

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Abstract

We consider the problem of checking first order dominance for finite bivariate distributions. We observe that this can be formulated as a special bipartite network problem related to the classical transportation problem. We exploit this observation to develop a new characterization of first order dominance and fast dominance-checking algorithms.

Suggested Citation

  • Range, Troels Martin & Østerdal, Lars Peter, 2013. "Checking bivariate first order dominance," Discussion Papers of Business and Economics 9/2013, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2013_009
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    File URL: https://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2013/dpbe9_2013.pdf
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    References listed on IDEAS

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    1. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    2. Vijay S. Bawa, 1982. "Research Bibliography---Stochastic Dominance: A Research Bibliography," Management Science, INFORMS, vol. 28(6), pages 698-712, June.
    3. Arndt, Channing & Distante, Roberta & Hussain, M. Azhar & Østerdal, Lars Peter & Huong, Pham Lan & Ibraimo, Maimuna, 2012. "Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty," World Development, Elsevier, vol. 40(11), pages 2290-2301.
    4. K. C. Mosler, 1984. "Stochastic Dominance Decision Rules when the Attributes are Utility Independent," Management Science, INFORMS, vol. 30(11), pages 1311-1322, November.
    5. William R. Russell & Tae Kun Seo, 1978. "Ordering Uncertain Prospects: The Multivariate Utility Functions Case," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 605-610.
    6. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Management Science, INFORMS, vol. 34(4), pages 454-460, April.
    7. 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.
    8. Arndt, Channing & Salvucci, Vincenzo & Tarp, Finn & Østerdal, Lars Peter & Hussain, M. Azhar, 2013. "Advancing Small Area Estimation," WIDER Working Paper Series 053, World Institute for Development Economic Research (UNU-WIDER).
    9. 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.
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    Cited by:

    1. Gottschalk, Tina & Range, Troels Martin & Sudhölter, Peter & Østerdal, Lars Peter, 2015. "Decomposing bivariate dominance for social welfare comparisons," Discussion Papers of Business and Economics 12/2015, University of Southern Denmark, Department of Business and Economics.
    2. M. Azhar Hussain & Mette Møller Jørgensen & Lars Peter Østerdal, 2016. "Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 739-759, November.

    More about this item

    Keywords

    Multidimensional first order dominance; usual stochastic order; characterization; network problem; checking algorithm;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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