Axioms for Consensus Functions on then-Cube

Abstract

Apvalue of a sequenceπ=(x1,x2,…,xk)of elements of a finite metric space(X,d)is an elementxfor which∑i=1kdp(x,xi)is minimum. Thelp–function with domain the set of all finite sequences onXand defined bylp(π)={x:  xis apvalue ofπ}is called thelp–function on(X,d). Thel1andl2functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of thelp–functions on then-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.