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Axiomatic Characterization of the Mean Function on Trees

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  • McMorris, F.R.
  • Mulder, H.M.
  • Ortega, O.

Abstract

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this paper the mean function on finite trees is characterized axiomatically.

Suggested Citation

  • McMorris, F.R. & Mulder, H.M. & Ortega, O., 2010. "Axiomatic Characterization of the Mean Function on Trees," Econometric Institute Research Papers EI 2010-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:18261
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    References listed on IDEAS

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    1. Vohra, Rakesh, 1996. "An axiomatic characterization of some locations in trees," European Journal of Operational Research, Elsevier, vol. 90(1), pages 78-84, April.
    2. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    3. 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.
    4. Ron Holzman, 1990. "An Axiomatic Approach to Location on Networks," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 553-563, August.
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    Cited by:

    1. Correa-Morris, Jyrko, 2021. "The median partition and submodularity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Changat, M. & Lekha, D.S. & Mulder, H.M. & Subhamathi, A.R., 2014. "Axiomatic Characterization of the Median and Antimedian Functions on Cocktail-Party Graphs and Complete Graphs," Econometric Institute Research Papers EI 2014-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Balakrishnan, K. & Changat, M. & Mulder, H.M. & Subhamathi, A.R., 2011. "Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes," Econometric Institute Research Papers EI 2011-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Mulder, H.M. & Novick, B., 2011. "A simple axiomatization of the median procedure on median graphs," Econometric Institute Research Papers EI2011-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. McMorris, F.R. & Novick, B. & Mulder, H.M. & Powers, R.C., 2015. "An ABC-Problem for Location and Consensus Functions on Graphs," Econometric Institute Research Papers EI 2015-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. McMorris, F.R. & Mulder, H.M. & Novick, B. & Powers, R.C., 2014. "Five axioms for location functions on median graphs," Econometric Institute Research Papers EI 2014-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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