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arXiv · 2208.12732

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

Ernesto Savaglio·Stefano Vannucci
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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.

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Ernesto Savaglio, Stefano Vannucci. 2022-08-26. Strategy-proof aggregation rules in median semilattices with applications to preference aggregation. https://arxiv.org/abs/2208.12732

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