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The median procedure for n-trees

Authors:	Jean-Pierre Barthélemy F R McMorris

Institution:	(1) Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris, Cedex 13, France;(2) Division of Mathematical Sciences, Office of Naval Research, 22217-5000 Arlington, VA, USA

Abstract:	Let (X,d) be a metric space The functionM:X ^k 2^x 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 metricWe would like to thank the referees and Editor for helpful comments

Keywords:	n-Trees Consensus Median procedure Majority rule
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