| Title | A simple axiomatization of the median procedure on median graphs |
|---|---|
| Author | Mulder, H.M. (Henry); Novick, B. B. (Beth) |
| Date | 2011-08-01 |
| Language | English |
| Type | working paper |
| Publisher | Econometric Institute |
| 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. |
| Publication | http://hdl.handle.net/1765/25628 |
| Persistent Identifier | urn:NBN:nl:ui:15-1765/25628 |
| Metadata | XML |
| Repository | Erasmus University Rotterdam |
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