id: 00894190
dt: j
an: 00894190
au: Crown, G.D.; Janowitz, M.-F.; Powers, R.C.
ti: Further results on neutral consensus functions.
so: Math. Inf. Sci. Hum. 132, 5-11 (1995).
py: 1995
pu: 
la: EN
cc: 
ut: set theoretic approach; consensus function; brick; lattice filter;
    ultrafilter
ci: 
li: numdam:MSH_1995__132__5_0
ab: Summary: We use a set theoretic approach to consensus by viewing an object
    as a set of smaller pieces called “bricks”. A consensus function is
    neutral if there exists a family ${\cal D}$ of sets such that a brick
    $s$ is in the output of a profile if and only if the set of positions
    with objects that contain $s$ belongs to ${\cal D}$. We give sufficient
    set theoretic conditions for ${\cal D}$ to be a lattice filter and, in
    the case of a finite lattice, these conditions turn out to be
    necessary. Our final result, which involves a finite distributive join
    semilattice, provides necessary and sufficient conditions for ${\cal
    D}$ to be an ultrafilter.
rv: