Axioms for Consensus Functions on the n-Cube

Abstract

A p value of a sequence π=(x1,x2,…,xk) of elements of a finite metric space (X,d) is an element x for which ∑i=1kdp(x,xi) is minimum. The lp–function with domain the set of all finite sequences on X and defined by lp(π)={x: x is a p value of π} is called the lp–function on (X,d). The l1 and l2 functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the lp–functions on the n-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.