The Median Procedure in a Formal Theory of Consensus
Fred R. McMorris, Robert Powers · SIAM Journal on Discrete Mathematics · 1995
A consensus rule on a finite set X is a function c from the set of k-tuples for all $K > 0$ into the set of nonempty subsets of X. Elements in the image of c represent a consensus, or agreement, of the input. Axioms for consensus rules are presented, and when X is partially ordered, some consequences of these axioms are determined. A generalization of the median consensus rule is given when X is a distributive semilattice and is based on a weighting of the least move metric on the covering graph of X. It is characterized under the assumption that every join irreducible of X is an atom.