An axiomatic characterization of some locations in trees

Abstract

We describe axioms that uniquely characterize the absolute median and the squared median (the point that minimizes the sum of squared distances) of a tree. A common feature of these characterizations is a Consistency axiom of the type first used by H.P. Young to characterize a voting procedure called Borda's rule. These results make it possible to argue in favor of, or against, a particular location in terms of principles satisfied or violated.