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Stochastic dominance relations for integer variables

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  • Chakravarty, Satya R.
  • Zoli, Claudio

Abstract

The objective of this paper is to derive some integer-majorization results for variable-sum comparisons. We use an axiomatic framework to establish equivalence between several intuitively reasonable conditions.

Suggested Citation

  • Chakravarty, Satya R. & Zoli, Claudio, 2012. "Stochastic dominance relations for integer variables," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1331-1341.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1331-1341
    DOI: 10.1016/j.jet.2011.05.018
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    1. Satya R. Chakravarty & Conchita D’Ambrosio, 2019. "The Measurement of Social Exclusion," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 167-189, Springer.
    2. Rothschild, Michael & Stiglitz, Joseph E., 1973. "Some further results on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 188-204, April.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Frank Milne & Edwin H. Neave, 1994. "Dominance Relations Among Standardized Variables," Management Science, INFORMS, vol. 40(10), pages 1343-1352, October.
    5. Deineko, Vladimir G. & Klinz, Bettina & Woeginger, Gerhard J., 2009. "The complexity of computing the Muirhead-Dalton distance," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 282-284, March.
    6. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    7. Marc Fleurbaey & Walter Bossert, 2002. "Equitable insurance premium schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 113-125.
    8. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    9. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    10. John Weymark, 2003. "Generalized Gini Indices of Equality of Opportunity," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 5-24, April.
    11. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
    12. Savaglio, Ernesto & Vannucci, Stefano, 2007. "Filtral preorders and opportunity inequality," Journal of Economic Theory, Elsevier, vol. 132(1), pages 474-492, January.
    13. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    14. Peter C. Fishburn & Irving H. Lavalle, 1995. "Stochastic Dominance on Unidimensional Grids," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 513-525, August.
    15. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    16. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    17. 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.
    18. Aboudi, Ronny & Thon, Dominique, 2006. "Refinements of Muirhead's Lemma and income inequality," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 201-216, March.
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    1. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2021. "Ranking distributions of an ordinal variable," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 33-80, February.
    2. 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.
    3. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    4. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    5. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    6. José V. Gallegos & Gaston Yalonetzky, 2015. "Robust ``pro-poorest'' poverty reduction with counting measures: The anonymous case," Working Papers 361, ECINEQ, Society for the Study of Economic Inequality.
    7. Gao, Jianwei & Zhao, Feng & Gu, Yundong, 2018. "Sufficient conditions of stochastic dominance for general transformations and its application in option strategy," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-15.
    8. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2019. "Inequality measurement with an ordinal and continuous variable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 453-475, March.
    9. Nicoleta Anca Matei & Claudio Zoli, 2012. "Restricted Finite Time Dominance," Working Papers 30/2012, University of Verona, Department of Economics.
    10. Valérie Bérenger, 2017. "Using ordinal variables to measure multidimensional poverty in Egypt and Jordan," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 143-173, June.
    11. Sabina Alkire & Mauricio Apablaza & Satya R. Chakravarty & Gaston Yalonetzky, 2014. "Measuring Chronic Multidimensional Poverty: A Counting Approach," OPHI Working Papers 75, Queen Elizabeth House, University of Oxford.
    12. Valérie Bérenger, 2017. "Using ordinal variables to measure multidimensional poverty in Egypt and Jordan," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 143-173, June.
    13. Sandip Sarkar & Sattwik Santra, 2020. "Extending the approaches to polarization ordering of ordinal variables," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(3), pages 421-440, September.
    14. Gao, Jianwei & Zhao, Feng, 2017. "Sufficient conditions of stochastic dominance for general transformations and its application in option strategy," Economics Discussion Papers 2017-40, Kiel Institute for the World Economy (IfW Kiel).
    15. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.
    16. Ramses H. Abul Naga, 2018. "Measurement of inequality with a finite number of pay states: the majorization set and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 99-123, January.
    17. Alejandro Corvalan, 2018. "How to rank rankings? Group performance in multiple-prize contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 361-380, August.

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    More about this item

    Keywords

    Stochastic dominance; Generalized Lorenz curve; Grids; Integers; Measures; Majorization;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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