An elementary general result is proved that allows for simple
characterizations of well-known location/consensus functions (median, mean and
center) on the n-cube. In addition, alternate new characterizations are given
for the median and anti-median functions on the n-cube.Comment: 12 page

Garcia-Martinez, C.

McMorris, F. R.

Ortega, O.

Powers, R. C.

Journal of Applied Mathematics

English

arXiv

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

Axioms for consensus functions on the n-cube

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