The ℓp-function on finite Boolean lattices

Abstract

Let [Formula: see text] be an integer such that [Formula: see text]. A [Formula: see text]-value of a sequence [Formula: see text] of elements of a finite metric space [Formula: see text] is an element [Formula: see text] for which [Formula: see text] is minimum. The [Formula: see text] function whose domain is the set of all finite sequences on [Formula: see text], and defined by [Formula: see text] is a [Formula: see text]-value of [Formula: see text] is called the [Formula: see text] function on [Formula: see text]. In this note, an axiomatic characterization of the [Formula: see text] function on finite Boolean lattices is presented.

Axioms for Consensus Functions on then-Cube

“…Lemma 3.12 in [22] gives the following proposition. Here are three other examples of consensus functions that satisfy the Translation property.…”

“…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.…”