Abstract
A median partition P* of a finite set X is a minimizer of a remoteness function φ(P)=∑i=1mD(P,Pi) defined from a profile of partitions E={P1,P2,…,Pm} and a function D that quantifies the distance between two partitions. This paper focuses in the location of median partitions within the lattice of partitions when the symmetric function D is such that, for every partition P, D(P,.) is a submodular function that decreases along any chain (either ascending or descending) starting at P. Especially, refinement relationships among median partitions and quota rules are investigated. Most of the results presented here remain valid in an arbitrary semimodular lattice.
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