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Axiomatic Characterization of the Median and Antimedian Function on a Complete Graph minus a Matching

Author

Listed:
  • Changat, M.
  • Lekha, D.S.
  • Mohandas, S.
  • Mulder, H.M.
  • Subhamathi, A.R.

Abstract

__Abstract__ A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the sum of the distances to the elements in the profile. The median (antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (obnoxious) facility in a network. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper an axiomatic characterization is obtained for the median and antimedian function on complete graphs minus a matching.

Suggested Citation

  • Changat, M. & Lekha, D.S. & Mohandas, S. & Mulder, H.M. & Subhamathi, A.R., 2015. "Axiomatic Characterization of the Median and Antimedian Function on a Complete Graph minus a Matching," Econometric Institute Research Papers EI2015-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:78348
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    References listed on IDEAS

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    1. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
    2. Roberts, Fred S., 1991. "Characterizations of the plurality function," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 101-127, April.
    3. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    4. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    median; antimedian; consensus function; consistency; cocktail-party graph; complete graph; consensus axiom;
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