The median procedure for n-trees (Q1822174)

One approach to produce a consensus of several classifications constructed for a set of objects is to produce a reasonable-looking method and then seek to discover those properties that characterize it. In the present paper this is made by giving an axiomatic characterization of the median procedure for n-trees. Let (X,d) be a metric space. The function \(M: X^ k\to 2^ X\) defined by \[ M(x_ 1,...,x_ k)=\{x\in X:\sum^{k}_{j>1}d(x,x_ j)\quad is\quad \min imum\} \] is called the median procedure. Axioms are presented that characterize M when X is a certain class of trees (hierarchical classification), and d is the symmetric difference metric. The median complete multiconsensus function (CMF) is shown to be the unique CMF that is efficient, stable on clusters, consistent, symmetric, and quasi-Condorcet.