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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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File URL: http://hdl.handle.net/10.1007/s00355-011-0612-8
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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 39 (2012)
Issue (Month): 2 (July)
Pages: 633-647

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Handle: RePEc:spr:sochwe:v:39:y:2012:i:2:p:633-647

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Web page: http://link.springer.de/link/service/journals/00355/index.htm

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  1. Foster, James E & Shorrocks, Anthony F, 1988. "Poverty Orderings," Econometrica, Econometric Society, vol. 56(1), pages 173-77, January.
  2. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  3. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  4. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December.
  5. Markus Haas, 2007. "Do investors dislike kurtosis?," Economics Bulletin, AccessEcon, vol. 7(2), pages 1-9.
  6. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," Journal of Economic Inequality, Springer, vol. 7(3), pages 249-268, September.
  7. Zheng, Buhong, 2000. " Poverty Orderings," Journal of Economic Surveys, Wiley Blackwell, vol. 14(4), pages 427-66, September.
  8. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
  9. Peluso, Eugenio & Trannoy, Alain, 2007. "Does less inequality among households mean less inequality among individuals?," Journal of Economic Theory, Elsevier, vol. 133(1), pages 568-578, March.
  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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