  Alternative novel measures of the distance between any two partitions of a
n-set are proposed and compared, together with a main existing one, namely
'partition-distance' D(.,.). The comparison achieves by checking their
restriction to modular elements of the partition lattice, as well as in terms
of suitable classifiers. Two of the new measures obtain through the size, a
function mapping every partition into the number of atoms finer than that
partition. One of these size-based distances extends to geometric lattices the
traditional Hamming distance between subsets, when these latter are regarded as
hypercube vertexes or binary n-vectors. After carefully framing the
environment, a main comparison finally results from the following bounding
problem: for every value k, with 0<k<n, of partition-distance D(.,.), determine
the minimum and maximum of the 'indicator-Hamming' distance d(P,Q) proposed
here over all pairs of partitions P,Q such that D(P,Q)=k.
