The t-median function on graphs

F.R. McMorris, Martyn Mulder and Robert Powers

No EI 2005-31, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: A median of a sequence pi = x1, x2, … , xk of elements of a finite metric space (X, d ) is an element x for which ∑ k, i=1 d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(pi) = {x: x is a median of pi} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(pi), a generalization of the median function is introduced and studied on various graphs and ordered sets. In addition, new results are presented for median graphs.

Keywords: consensus; median function; median graph; median semilattice (search for similar items in EconPapers)
Date: 2005-08-23
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