A characterization of strategy-proof voting rules for separable weak orderings

Abstract

We consider the problem of choosing a subset of a finite set of indivisible objects (public projects, facilities, laws, etc.) studied by Barberà, Sonnenschein, and Zhou (1991). Here we assume that agents' preferences are separable weak orderings. Given such a preference, objects are partitioned into three types, "goods", "bads", and "nulls". We focus on "voting rules", which rely only on this partition rather than the full information of preferences. We characterize voting rules satisfying strategy-proofness (no one can ever be better off by lying about his preference) and null-independence (the decision on each object should not be dependent on the preference of an agent for whom the object is a null). We also show that serially dictatorial rules are the only voting rules satisfying efficiency as well as the above two axioms. We show that the "separable domain" is the unique maximal domain over which each rule in the first characterization, satisfying a certain fairness property, is strategy-proof.

Candidate Stable Voting Rules for Separable Orderings

“…4 Ju (2003) extends Barberà et al's (1991) model to allow indifferences of voters' preferences. This proposition holds even in Ju's (2003) model. The proof is the same.…”

On the operation of multiple matching markets

“…The separability is assumed for the many-side agents in a many-to-one two-sided matching market, agents in multiple-type markets, and those in multiple assignment problems. Moreover, the studies of social choice functions on product spaces work on the separable preference domain (e.g., Barberà, Sonnenschein, and Zhou 1991;Le Breton and Sen 1999;Ju 2003;Barberà, Massó, and Neme 2005). On the other hand, the study under interdependence or nonseparability of preferences has just started in matching models.…”

An efficiency characterization of plurality social choice on simple preference domains

“…In the linear separable preference domain, power structures with some additional properties reduce to the "committee structures" ofBarberà, Sonnenschein, and Zhou (1991). Power structures were introduced in the domain with separable preferences (not necessarily linear) byJu (2003a).10 In stating an axiom, we only state the condition on the generic rule ϕ required by the axiom.…”