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Good and bad objects: the symmetric difference rule

Author

Listed:
  • Dinko Dimitrov

    (Tilburg University)

  • Ruud Hendrickx

    (Tilburg University)

  • Peter Borm

    (Tilburg University)

Abstract

We consider the problem of ranking sets of objects, the members of which are mutually compatible. Assuming that each object is either good or bad, we axiomatically characterize a cardinality-based rule which arises naturally in this dichotomous setting.

Suggested Citation

  • Dinko Dimitrov & Ruud Hendrickx & Peter Borm, 2004. "Good and bad objects: the symmetric difference rule," Economics Bulletin, AccessEcon, vol. 4(11), pages 1-7.
    • Handle: RePEc:ebl:ecbull:eb-04d60002
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    References listed on IDEAS

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    1. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    2. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    3. Pattanaik, Prasanta K. & Xu, Yongsheng, 2000. "On diversity and freedom of choice," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 123-130, September.
    4. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    5. Dolors Berga & Gustavo Berganti?s & Jordi MassóAuthor-Email: jordi.masso@uab.es & Alejandro Neme, 2002. "Voting by Committees with Exit," UFAE and IAE Working Papers 511.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    6. Prasanta K. PATTANAIK & Yongsheng XU, 1990. "On Ranking Opportunity Sets in Terms of Freedom of Choice," Discussion Papers (REL - Recherches Economiques de Louvain) 1990036, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    7. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    8. Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
    9. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    10. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
    11. Fishburn, Peter C., 1992. "Signed orders and power set extensions," Journal of Economic Theory, Elsevier, vol. 56(1), pages 1-19, February.
    12. Biung-Ghi Ju, 2003. "A characterization of strategy-proof voting rules for separable weak orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(3), pages 469-499, December.
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    Cited by:

    1. Murat Çengelci & M. Sanver, 2010. "Simple Collective Identity Functions," Theory and Decision, Springer, vol. 68(4), pages 417-443, April.
    2. Arlegi, Ritxar & Dimitrov, Dinko, 2016. "Power set extensions of dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 20-29.
    3. Arlegi, Ritxar & Dimitrov, Dinko, 2011. "On freedom, lack of information and the preference for easy choices," Center for Mathematical Economics Working Papers 364, Center for Mathematical Economics, Bielefeld University.
    4. Dimitrov, Dinko & Haake, Claus-Jochen, 2011. "Regrouping of endowments in exchange markets with indivisible goods," Center for Mathematical Economics Working Papers 367, Center for Mathematical Economics, Bielefeld University.
    5. Ricardo Arlegi & Dinko Dimitrov, 2006. "On Freedom of Choice, Ambiguity, and the Preference for Easy Choices," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0607, Departamento de Economía - Universidad Pública de Navarra.

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    More about this item

    JEL classification:

    • D6 - Microeconomics - - Welfare Economics
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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