An sxiomatization of the median procedure on the n-cube
AbstractThe general problem in location theory deals with functions that find sites on a graph (discrete case) or network (continuous case) in such a way as to minimize some cost (or maximize some benefit) to a given set of clients represented by vertices on the graph or points on the network. The axiomatic approach seeks to uniquely distinguish, by using a list of intuitively pleasing axioms, certain specific location functions among all the arbitrary functions that address this problem. For the median function, which minimizes the sum of the distances to the client locations, three simple and natural axioms, anonymity, betweenness, and consistency suffice on tree networks (continuous case) as shown by Vohra, and on cube-free median graphs (discretecase) as shown by McMorris et.al.. In the latter paper, in the case of arbitrary median graphs, a fourth axiom was added to characterize the median function. In this note we show that, at least for the hypercubes, a special instance of arbitrary median graphs, the above three natural axioms still suffice.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2010-32.
Date of creation: 28 Jul 2010
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consensus axiom; hypercube; location function; median function; median;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-03 (All new papers)
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