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Ethically Robust Comparisons of Bidimensional Distributions with an Ordinal Attribute

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  • Patrick MOYES (GREThA, CNRS, UMR 5113)
  • Nicolas GRAVEL (Aix-Marseille University and AMSE (GREQAM))

Abstract

We provide foundations for robust normative evaluation of distributions of two attributes,\r\none of which is cardinally measurable and transferable between individuals and the other is\r\nordinal and non-transferable. The result that we establish takes the form of an analogue to the standard Hardy, Littlewood, and Pólya (1934) theorem for distributions of one cardinal\r\nattribute. More specifically, we identify the transformations of the distributions which\r\nguarantee that social welfare increases according to utilitarian unanimity provided that the utility function is concave in the cardinal attribute and that its marginal utility with respect to the same attribute is non-increasing in the ordinal attribute. We establish that this\r\nunanimity ranking of the distributions is equivalent to the Bourguignon (1989) ordered\r\npoverty gap quasi-ordering. Finally, we show that, if one distribution dominates another\r\naccording to the ordered poverty gap criterion, then the former can be derived from the latter by means of an appropriate and finite sequence of such transformations

Suggested Citation

  • Patrick MOYES (GREThA, CNRS, UMR 5113) & Nicolas GRAVEL (Aix-Marseille University and AMSE (GREQAM)), 2011. "Ethically Robust Comparisons of Bidimensional Distributions with an Ordinal Attribute," Cahiers du GREThA 2011-36, Groupe de Recherche en Economie Théorique et Appliquée.
  • Handle: RePEc:grt:wpegrt:2011-36
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    References listed on IDEAS

    as
    1. Georges Dionne & Christian Gourieroux & Charles Vanasse, 1998. "Evidence of Adverse Selection in Automobile Insurance Markets," Working Papers 98-24, Center for Research in Economics and Statistics.
    2. Blackorby,Charles & Bossert,Walter & Donaldson,David J., 2005. "Population Issues in Social Choice Theory, Welfare Economics, and Ethics," Cambridge Books, Cambridge University Press, number 9780521532587, December.
    3. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Economics Series Working Papers 655, University of Oxford, Department of Economics.
    4. Brice Magdalou & Patrick Moyes, 2009. "Deprivation, welfare and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, pages 253-273.
    5. Nicolas Gravel & Patrick Moyes, 2013. "Utilitarianism or welfarism: does it make a difference?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 529-551, February.
    6. Nicolas Gravel & Patrick Moyes & Benoît Tarroux, 2009. "Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods," Economica, London School of Economics and Political Science, vol. 76(303), pages 432-461, July.
    7. Ebert, Udo, 2000. "Sequential Generalized Lorenz Dominance and Transfer Principles," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 113-122, April.
    8. Jenkins, Stephen P & Lambert, Peter J, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, pages 337-356.
    9. 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.
    10. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    11. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    12. Patrick MOYES (GREThA, CNRS, UMR 5113), 2011. "Rearrangements and Sequential Rank Order Dominance. A Result with Economic Applications," Cahiers du GREThA 2011-35, Groupe de Recherche en Economie Théorique et Appliquée.
    13. Margaret Meyer & Bruno Strulovici, 2011. "Increasing Interdependence of Multivariate Distributions," Discussion Papers 1523, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, pages 1450-1459.
    15. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
    16. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    17. Duclos, Jean-Yves & Sahn, David E. & Younger, Stephen D., 2011. "Partial multidimensional inequality orderings," Journal of Public Economics, Elsevier, vol. 95(3), pages 225-238.
    18. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    19. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-1135, September.
    20. Anderson, Gordon & Crawford, Ian & Leicester, Andrew, 2011. "Welfare rankings from multivariate data, a nonparametric approach," Journal of Public Economics, Elsevier, pages 247-252.
    21. repec:cor:louvrp:-2425 is not listed on IDEAS
    22. Peter C. Fishburn, 1978. "Stochastic Dominance Without Transitive Preferences," Management Science, INFORMS, pages 1268-1277.
    23. Moyes, Patrick, 2012. "Comparisons of heterogeneous distributions and dominance criteria," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1351-1383.
    24. Patrick Moyes & Stephen Bazen, 2003. "International Comparisons of Income Distribution," LIS Working papers 341, LIS Cross-National Data Center in Luxembourg.
    25. Fleurbaey, Marc & Hagnere, Cyrille & Trannoy, Alain, 2003. "Welfare comparisons with bounded equivalence scales," Journal of Economic Theory, Elsevier, pages 309-336.
    26. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, pages 1435-1464.
    27. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, pages 67-80.
    28. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, pages 1849-1892.
    29. Massimo Marinacci & Luigi Montrucchio, 2005. "Ultramodular Functions," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 311-332, May.
    30. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    31. 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.
    32. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, Oxford University Press, pages 1-13.
    33. Ebert U., 1996. "Income inequality and differences in household size," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 57-58, February.
    34. Moyes Patrick, 1994. "Inequality Reducing and Inequality Preserving Transformations of Incomes: Symmetric and Individualistic Transformations," Journal of Economic Theory, Elsevier, vol. 63(2), pages 271-298, August.
    35. Müller, Alfred & Scarsini, Marco, 2012. "Fear of loss, inframodularity, and transfers," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1490-1500.
    36. 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.
    37. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
    38. Bishop, John A & Chakraborti, S & Thistle, Paul D, 1989. "Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves," The Review of Economics and Statistics, MIT Press, pages 725-727.
    39. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
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    Cited by:

    1. Patrick MOYES, 2013. "Rearrangements and Sequential Rank Order Dominance," Cahiers du GREThA 2013-10, Groupe de Recherche en Economie Théorique et Appliquée.
    2. 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.
    3. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART-LERECO.
    4. Benoît Tarroux, 2015. "Comparing two-dimensional distributions: a questionnaire-experimental approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, pages 87-108.
    5. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    6. Nicolas Gravel & Patrick Moyes, 2013. "Utilitarianism or welfarism: does it make a difference?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 529-551, February.
    7. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, pages 207-251.
    8. Moyes, Patrick, 2012. "Comparisons of heterogeneous distributions and dominance criteria," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1351-1383.
    9. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
    10. Rolf Aaberge & François Bourguignon & Andrea Brandolini & Francisco H. G. Ferreira & Janet C. Gornick & John Hills & Markus Jäntti & Stephen P. Jenkins & Eric Marlier & John Micklewright & Brian Nolan, 2017. "Tony Atkinson and his Legacy," Review of Income and Wealth, International Association for Research in Income and Wealth, pages 411-444.
    11. 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).
    12. 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).
    13. repec:spr:joecth:v:65:y:2018:i:1:d:10.1007_s00199-016-1011-2 is not listed on IDEAS
    14. Muller, Christophe & Trannoy, Alain, 2012. "Multidimensional inequality comparisons: A compensation perspective," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1427-1449.
    15. Udo Ebert & Patrick Moyes, 2017. "Inequality and isoelastic equivalence scales: restrictions and implications," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 295-326, February.

    More about this item

    Keywords

    Normative Analysis; Utilitarianism; Bidimensional Stochastic Dominance; Inequality Reducing Transformations;

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • 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

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