A median of a sequence ï° = x1, x2, … , xk of elements of a finite metric space (X, d ) is an element x for which  1 ≤ I ≤ k d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(ï°) = {x: x is a median of ï°} is...

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on...

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this...

The majority decision function is extended to median semilattices and then characterized using three simple axioms.

__Abstract__ In previous work, two axiomatic characterizations were given for the median function on median graphs: one involving the three simple and natural axioms anonymity, betweenness and consistency; the other involving faithfulness, consistency and ½-Condorcet. To date, the independence...

The notion of a decisive family of voters has played an important role in the analysis of various consensus functions defined on preference profiles. This role remains when the domain shifts to profiles of hierarchical classifications. The main result of this paper is a characterization of...

A median of a sequence pi = x1, x2, … , xk of elements of a finite metric space (X, d ) is an element x for which ∑ k, i=1 d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(pi) = {x: x is a median of pi} is called the median function on X,...