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Preserving dominance relations through disaggregation: the evil and the saint

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  • Eugenio Peluso
  • Alain Trannoy

Abstract

Disaggregation arises when broad categories like households budget units are divided into elementary units as individual income recipients. We study the preservation of stochastic dominance for every order beyond two after disaggregation: If we observe a dominance relation among household income distributions, it is also true at the individual level. We find necessary and sufficient conditions satisfied by the common sharing rule adopted by households to divide the cake among individuals. The sharing function, which maps the household income into the outcome of the disadvantaged individual, must have derivatives of the same sign as the utility function characterizing the stochastic order of interest. In addition, the household has to follow a compensating rule, meaning that at the margin the distribution should be in favor of the disadvantaged individual.
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  • Eugenio Peluso & Alain Trannoy, 2012. "Preserving dominance relations through disaggregation: the evil and the saint," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 633-647, July.
    • Handle: RePEc:spr:sochwe:v:39:y:2012:i:2:p:633-647
    DOI: 10.1007/s00355-011-0612-8
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    References listed on IDEAS

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    1. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
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    5. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 249-268, September.
    6. Markus Haas, 2007. "Do investors dislike kurtosis?," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-9.
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    8. Foster, James E & Shorrocks, Anthony F, 1988. "Poverty Orderings," Econometrica, Econometric Society, vol. 56(1), pages 173-177, January.
    9. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December.
    10. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
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    Cited by:

    1. M Denuit & L Eeckhoudt & O Jokung, 2013. "Non-differentiable transformations preserving stochastic dominance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(9), pages 1441-1446, September.
    2. 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).

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    More about this item

    JEL classification:

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