Template-Type: ReDIF-Paper 1.0
Author-Name: Mulder, H.M.
Author-Name-Last: Mulder
Author-Name-First: Martyn
Author-Name: Novick, B.
Author-Name-Last: Novick
Author-Name-First: Beth
Title: A simple axiomatization of the median procedure on median graphs
Abstract: A profile = (x1, ..., xk), of length k, in a finite connected graph G is a sequence of vertices of G, with repetitions allowed. A median x of is a vertex for which the sum of the distances from x to the vertices in the profile is minimum. The median function finds the set of all medians of a profile. Medians are important in location theory and consensus theory. A median graph is a graph for which every profile of length 3 has a unique median. Median graphs are well studied. They arise in many arenas, and have many applications. We establish a succinct axiomatic characterization of the median procedure on median graphs. This is a simplification of the characterization given by McMorris, Mulder and Roberts [17] in 1998. We show that the median procedure can be characterized on the class of all median graphs with only three simple and intuitively appealing axioms: anonymity, betweenness and consistency. We also extend a key result of the same paper, characterizing the median function for profiles of even length on median graphs.
Creation-Date: 2011-08-01
File-URL: https://repub.eur.nl/pub/25628/EI2011-25.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI2011-25
Keywords: consensus axiom, consensus function, location function, median, median function, median graph
Handle: RePEc:ems:eureir:25628