IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v147y2012i4p1331-1341.html
   My bibliography  Save this article

Stochastic dominance relations for integer variables

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000846
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2011.05.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. 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.
    6. Peter C. Fishburn & Irving H. Lavalle, 1995. "Stochastic Dominance on Unidimensional Grids," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 513-525, August.
    7. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    8. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
    9. Frank Milne & Edwin H. Neave, 1994. "Dominance Relations Among Standardized Variables," Management Science, INFORMS, vol. 40(10), pages 1343-1352, October.
    10. Savaglio, Ernesto & Vannucci, Stefano, 2007. "Filtral preorders and opportunity inequality," Journal of Economic Theory, Elsevier, vol. 132(1), pages 474-492, January.
    11. 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.
    12. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    13. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    14. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    15. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    16. 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.
    17. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    2. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    3. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 77(1), pages 119-161, December.
    4. 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.
    5. Alain Chateauneuf & Patrick Moyes, 2002. "Measuring inequality without the Pigou-Dalton condition," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00156475, HAL.
    6. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    7. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    8. Rolf Aaberge & Eugenio Peluso & Henrik Sigstad, 2015. "The dual approach for measuring. Multidimesional deprivation and poverty," Discussion Papers 820, Statistics Norway, Research Department.
    9. 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.
    10. Aaberge, Rolf & Peluso, Eugenio & Sigstad, Henrik, 2019. "The dual approach for measuring multidimensional deprivation: Theory and empirical evidence," Journal of Public Economics, Elsevier, vol. 177(C), pages 1-1.
    11. Vincenzo Prete & Alessandro Sommacal & Claudio Zoli, 2016. "Optimal Non-Welfarist Income Taxation for Inequality and Polarization Reduction," Working Papers 23/2016, University of Verona, Department of Economics.
    12. Rolf Aaberge, 2003. "Mean-Spread-Preserving Transformations," Discussion Papers 360, Statistics Norway, Research Department.
    13. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2019. "A family of rules to share the revenues from broadcasting sport events," Working Papers 19.07, Universidad Pablo de Olavide, Department of Economics.
    14. Dubois, Marc, 2022. "Dominance criteria on grids for measuring competitive balance in sports leagues," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 1-10.
    15. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 279-303, December.
    16. Laurence Kranich, 2009. "Measuring opportunity inequality with monetary transfers," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(4), pages 371-385, December.
    17. Rolf Aaberge & Magne Mogstad, 2009. "On the Measurement of Long-Term Income Inequality and Income Mobility," ICER Working Papers 09-2009, ICER - International Centre for Economic Research.
    18. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
    19. Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
    20. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1331-1341. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.