Strategy-proof aggregation rules in median semilattices with applications to preference aggregation
Abstract
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.
Cite
@article{arxiv.2208.12732,
title = {Strategy-proof aggregation rules in median semilattices with applications to preference aggregation},
author = {Ernesto Savaglio and Stefano Vannucci},
journal= {arXiv preprint arXiv:2208.12732},
year = {2022}
}