  Two characterizations of the whole class of strategy-proof aggregation rules
on rich domains of locally unimodal preorders in finite median
join-semilattices are provided. In particular, it is shown that such a class
consists precisely of generalized weak sponsorship rules induced by certain
families of order filters of the coalition poset. It follows that the
co-majority rule and many other inclusive aggregation rules belong to that
class. The co-majority rule for an odd number of agents is characterized and
shown to be equivalent to a Condorcet-Kemeny median rule. Applications to
preference aggregation rules including Arrowian social welfare functions are
also considered. The existence of strategy-proof anonymous, weakly neutral and
unanimity-respecting social welfare functions which are defined on arbitrary
profiles of total preorders and satisfy a suitably relaxed independence
condition is shown to follow from our characterizations.
