Axiomatic Characterization of the Median and Antimedian Function on a Complete Graph minus a Matching

Manoj Changat, Divya Lekha, Shilpa Mohandas, Martyn Mulder and Ajitha Subhamathi

No EI2015-17, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: __Abstract__ A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the sum of the distances to the elements in the profile. The median (antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (obnoxious) facility in a network. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper an axiomatic characterization is obtained for the median and antimedian function on complete graphs minus a matching.

Keywords: median; antimedian; consensus function; consistency; cocktail-party graph; complete graph; consensus axiom (search for similar items in EconPapers)
Pages: 15
Date: 2015-06-18
New Economics Papers: this item is included in nep-gth
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