Abstract
Let (X,d) be a metric space The functionM:X k → 2x defined by\(M(x_1 ,,x_k ) = \{ x \in X:\sum\limits_{i = 1}^k {d(x,x_i )}\) is the minimum } is called themedian procedure and has been found useful in various applications involving the notion of consensus Here we present axioms that characterizeM whenX is a certain class of trees (hierarchical classifications), andd is the symmetric difference metric
Résumé
Soit (X, d) un espace métrique On appelleprocédure médiane la fonctionM deX k dans 2X définie par:
Cette procédure médiane s'est avèrée fort utile, en particulier pour des problèmes de consensus Dans cet article, nous proposons une caractèrisation axiomatique deM, dans le cas oúX est l'ensemble des classifications hierarchies d'un ensemble d'objets et oùd est la distance de la différence symétrique (cette distance dénombre les classes dont deux hierarchies différent)
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References
BANDELT, H J, and BARTHELEMY, J P (1984), “Medians in Median Graphs,”Discrete Applied Mathematics, 8, 131–142
BARTHELEMY, J P, and MONJARDET, B (1981), “The Median Procedure in CLuster Analysis and Social Choice Theory,”Mathematical Social Sciences, 1, 235–267
BOBISUD, H M, and BOBISUD, L E (1972), “A Metric for Classifications,”Taxon, 21, 607–613
MARGUSH, T, and MCMORRIS, F R (1981), “Consensus n-Trees,”Bulletin of Mathematical Biology, 43, 239–244
PENNY, D, FOULDS, L R, and HENDY, M D (1982), “Testing the Theory of Evolution by Comparing Phylogenetic Trees Constructed from Five Different Protein Sequences,”Nature, 297, 197–200
YOUNG, H P, and LEVENGLICK, A (1978), “A Consistent Extension of Condorcet's Election Principle,”SIAM Journal of Applied Mathematics, 35, 285–300
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Barthélemy, JP., McMorris, F.R. The median procedure for n-trees. Journal of Classification 3, 329–334 (1986). https://doi.org/10.1007/BF01894194
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DOI: https://doi.org/10.1007/BF01894194