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The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications

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  • Østerdal, Lars Peter

Abstract

A fundamental result in the theory of stochastic dominance tells that first order dominance between two finite multivariate distributions is equivalent to the property that the one can be obtained from the other by shifting probability mass from one outcome to another that is worse a finite number of times. This paper provides a new and elementary proof of that result by showing that starting with an arbitrary system of mass transfers, whenever the resulting distribution is first order dominated one can gradually rearrange transfers, according to a certain decentralized procedure, and obtain a system of transfers all shifting mass to outcomes that are worse.

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  • Østerdal, Lars Peter, 2010. "The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1222-1228, November.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:1222-1228
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    Cited by:

    1. Malokele Nanivazo, 2014. "First Order Dominance Analysis: Child Wellbeing in the Democratic Republic of Congo," WIDER Working Paper Series wp-2014-025, World Institute for Development Economic Research (UNU-WIDER).
    2. Olu Ajakaiye & Afeikhena T. Jerome & Olanrewaju Olaniyan & Kristi Mahrt & Olufunke A. Alaba, 2014. "Multidimensional Poverty in Nigeria: First Order Dominance Approach," WIDER Working Paper Series wp-2014-143, World Institute for Development Economic Research (UNU-WIDER).
    3. Channing Arndt & Azhar M. Hussain & Vincenzo Salvucci & Finn Tarp & Lars Peter Østerdal, 2016. "Poverty Mapping Based on First‐Order Dominance with an Example from Mozambique," Journal of International Development, John Wiley & Sons, Ltd., vol. 28(1), pages 3-21, January.
    4. Julien Combe & Vladyslav Nora & Olivier Tercieux, 2021. "Dynamic assignment without money: Optimality of spot mechanisms," Working Papers 2021-11, Center for Research in Economics and Statistics.
    5. Nanivazo, Malokele, 2014. "First order dominance analysis: Child wellbeing in the Democratic Republic of Congo," WIDER Working Paper Series 025, World Institute for Development Economic Research (UNU-WIDER).
    6. 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.
    7. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.
    8. Ajakaiye, Olu & Jerome, Afeikhena T. & Olaniyan, Olanrewaju & Mahrt, Kristi & Alaba, Olufunke A., 2014. "Multidimensional poverty in Nigeria: First order dominance approach," WIDER Working Paper Series 143, World Institute for Development Economic Research (UNU-WIDER).
    9. Frank A Cowell & Martyna Kobus & Radoslaw Kurek, 2017. "Welfare and Inequality Comparisons for Uni- and Multi-dimensional Distributions of Ordinal Data," STICERD - Public Economics Programme Discussion Papers 31, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Combe, Julien & Nora, Vladyslav & Tercieux, Olivier, 0. "Dynamic assignment without money: optimality of spot mechanisms," Theoretical Economics, Econometric Society.
    11. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 2020. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 645-686, December.
    12. Sonne-Schmidt, Christoffer & Tarp, Finn & Østerdal, Lars Peter, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series 097, World Institute for Development Economic Research (UNU-WIDER).
    13. Channing Arndt & Nikolaj Siersbæk, & Lars Peter Østerdal, 2015. "Multidimensional first-order dominance comparisons of population wellbeing," WIDER Working Paper Series 122, World Institute for Development Economic Research (UNU-WIDER).
    14. Channing Arndt & Azhar M. Hussain & Vincenzo Salvucci & Finn Tarp & Lars Peter Østerdal, 2016. "Poverty Mapping Based on First‐Order Dominance with an Example from Mozambique," Journal of International Development, John Wiley & Sons, Ltd., vol. 28(1), pages 3-21, January.
    15. 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.
    16. 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.
    17. M. Hussain, 2016. "EU Country Rankings’ Sensitivity to the Choice of Welfare Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 125(1), pages 1-17, January.
    18. Marling, Tina Gottschalk & Range, Troels Martin & Sudhölter, Peter & Østerdal, Lars Peter, 2018. "Decomposing bivariate dominance for social welfare comparisons," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 1-8.
    19. Malokele Nanivazo, 2015. "First Order Dominance Analysis: Child Wellbeing in the Democratic Republic of Congo," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 122(1), pages 235-255, May.
    20. Channing Arndt & Azhar Hussain & Vincenzo Salvucci & Finn Tarp & Lars Peter Østerdal, 2013. "Advancing Small Area Estimation," WIDER Working Paper Series wp-2013-053, World Institute for Development Economic Research (UNU-WIDER).
    21. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series wp-2013-097, World Institute for Development Economic Research (UNU-WIDER).
    22. Sonne-Schmidt, Christoffer & Tarp, Finn & Peter, Lars, 2011. "Ordinal multidimensional inequality: theory and application to the 2x2 case," MPRA Paper 72838, University Library of Munich, Germany.
    23. 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).
    24. repec:unu:wpaper:wp2012-36 is not listed on IDEAS
    25. Arndt, Channing & Mahrt, Kristi & Hussain, M. Azhar & Tarp, Finn, 2018. "A human rights-consistent approach to multidimensional welfare measurement applied to sub-Saharan Africa," World Development, Elsevier, vol. 108(C), pages 181-196.

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