Abstract
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.
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