Strategy-proof aggregation rules in median semilattices with applications to preference aggregation

TL;DR

This paper characterizes strategy-proof aggregation rules in median semilattices, showing they are generalized weak sponsorship rules, and explores their applications to preference aggregation and social welfare functions.

Contribution

It provides a complete characterization of strategy-proof aggregation rules in median join-semilattices, including their relation to co-majority and Condorcet-Kemeny rules.

Findings

Co-majority rule is characterized and shown equivalent to Condorcet-Kemeny median.

Strategy-proof rules are precisely generalized weak sponsorship rules.

Existence of strategy-proof social welfare functions with relaxed conditions is established.

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.