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Strong maximals: Elements with maximal score in partial orders


  • Begoña Subiza
  • Josep Peris



It is usually assumed that maximal elements are the best option for an agent. But there are situations in which we can observe that maximal elements are “different” one from another. This is the case of partial orders, in which one maximal element can be strictly preferred to almost every other element, whereas another maximal is not strictly preferred to any element. As partial orders are an important tool for modelling human behavior, it is interesting to find, for this kind of binary relation, those maximal elements that could be considered the best ones. In so doing, we define a selection inside the maximal set, which we call strong maximals (elements with maximal score), which is proved to be appropriate for choosing among maximals in a partial order. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Begoña Subiza & Josep Peris, 2005. "Strong maximals: Elements with maximal score in partial orders," Spanish Economic Review, Springer;Spanish Economic Association, vol. 7(2), pages 157-166, June.
  • Handle: RePEc:spr:specre:v:7:y:2005:i:2:p:157-166 DOI: 10.1007/s10108-004-0092-4

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    References listed on IDEAS

    1. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    2. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    3. Dierker, Hildegard, 1975. "Equilibria and core of large economies," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 155-169.
    4. Bonnisseau, J.M. & Joffre, A., 1994. "Equilibrium Manifold for Linear Exchange Economies," Papiers d'Economie Mathématique et Applications 94.87, Université Panthéon-Sorbonne (Paris 1).
    5. Cheng, Hsueh-Cheng, 1979. "Linear economies are "gross substitute" systems," Journal of Economic Theory, Elsevier, vol. 20(1), pages 110-117, February.
    6. Eaves, B. Curtis, 1976. "A finite algorithm for the linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 197-203, July.
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    Cited by:

    1. Peris, Josep E. & Subiza, Begoña, 2012. "M-stability: A reformulation of Von Neumann-Morgenstern stability," QM&ET Working Papers 12-4, University of Alicante, D. Quantitative Methods and Economic Theory.
    2. García-Bermejo, Juan Carlos, 2012. "A Note on Selecting Maximals in Finite Spaces," Working Papers in Economic Theory 2012/06, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    3. Joseph, Rémy-Robert, 2010. "Making choices with a binary relation: Relative choice axioms and transitive closures," European Journal of Operational Research, Elsevier, vol. 207(2), pages 865-877, December.

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    Partial order; maximal element; score;


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