Strategy-Proof Aggregation Rules in Median Semilattices with Applications to Preference Aggregation

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 rule. Applications to preference aggregation rules including Arrowian social welfare functions are also considered. The existence of strategy-proof anonymous 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.