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Poverty orderings: A graphical illustration


  • Buhong Zheng

    () (Department of Economics, University of Colorado at Denver, Denver, CO, USA)


This note graphically illustrates the power of various poverty ordering conditions. Using the Kolm three-person simplex, we are able to show that (1) for a fixed poverty line the power may be increased as higher degrees of stochastic dominance are considered, (2) for a single but variable poverty line the power is reduced as the line increases, and (3) for a range of poverty lines the power of the third degree ordering condition may be reduced to that of the second degree if the lower bound poverty line is arbitrarily close to zero.

Suggested Citation

  • Buhong Zheng, 2001. "Poverty orderings: A graphical illustration," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 165-178.
  • Handle: RePEc:spr:sochwe:v:18:y:2001:i:1:p:165-178
    Note: Received: 9 September 1998/Accepted: 11 January 2000

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    References listed on IDEAS

    1. Hervé Moulin, 2007. "On Scheduling Fees to Prevent Merging, Splitting, and Transferring of Jobs," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 266-283, May.
    2. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    3. Hamers, Herbert & Suijs, Jeroen & Tijs, Stef & Borm, Peter, 1996. "The Split Core for Sequencing Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 165-176, August.
    4. Debasis Mishra & Bharath Rangarajan, 2007. "Cost sharing in a job scheduling problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 369-382, October.
    5. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, Tilburg University, School of Economics and Management.
    6. Moulin, Herve, 1992. "An Application of the Shapley Value to Fair Division with Money," Econometrica, Econometric Society, vol. 60(6), pages 1331-1349, November.
    7. Manipushpak Mitra, 2002. "Achieving the first best in sequencing problems," Review of Economic Design, Springer;Society for Economic Design, vol. 7(1), pages 75-91.
    8. Flip Klijn & Estela Sánchez, 2006. "Sequencing games without initial order," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 53-62, February.
    9. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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    Cited by:

    1. Duclos, Jean-Yves & Makdissi, Paul, 2001. "Restricted Inequality and Relative Poverty," Cahiers de recherche 0113, Université Laval - Département d'économique.
    2. Vivien Kana Zeumo & Blaise Some & Alexis Tsoukiàs, 2011. "A survey on Multidimensional Poverty Measurement: a Decision Aiding Perspective," Working Papers hal-00875525, HAL.

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