Axioms for Consensus Functions on the $n$-Cube

A value of a sequence of elements of a finite metric space is an element for which is minimum. The –function with domain the set of all finite sequences on and defined by is a value of is called the –function on . The and functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the –functions on the -cube are given. In addition, the center function (using the minimax criterion) is characterized as well as new results proved for the median and antimedian functions.