The median function on Boolean lattices

Abstract

A median of a sequence π = (x 1 , x 2 , . . . , x k ) of elements of a finite metric space (X, d)The function Median with domain the set of all finite sequences on X and defined by Med(π) = {x : x is a median of π} is called the median function on X. In this paper, the median function on finite Boolean lattices is axiomatically characterized via location functions.

Axioms for Consensus Functions on then-Cube

“…We mention that the following results can be framed in the more abstract context of finite Boolean algebras, as it is done in [7,21,22]. We prefer to work in the more specific situation of n-cube since properties become quite easy to visualize, and yet we are working without loss of generality since every finite Boolean algebra is isomorphic to an n-cube.…”