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

Working Paper n.867 Dicembre 2021

Ernesto Savaglio

DEC, University of Pescara

Stefano Vannucci

DEPS, USiena

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 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.

Keywords

Strategy-proofness, single peakedness, median join-semilattice, social welfare function

Jel Codes

D71