7 research outputs found
Acyclic domains of linear orders: a survey
Among the many significant contributions that Fishburn made to social choice theory some have focused on what he has called "acyclic sets", i.e. the sets of linear orders where majority rule applies without the "Condorcet effect" (majority relation never has cycles). The search for large domains of this type is a fascinating topic. I review the works in this field and in particular consider a recent one that allows to show the connections between some of them that have been unrelated up to now.acyclic set;alternating scheme;distributive lattice;effet Condorcet;linear order,maximal chain,permutoèdre lattice, single-peaked domain,weak Bruhat order,value restriction.
Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules
It is shown that simple and coalitional strategy-proofness of an aggregation rule on any rich weakly unimodal domain of an idempotent interval space are equivalent properties if that space satisfies interval anti-exchange, a basic property also shared by a large class of convex geometries including -but not reducing to- trees and Euclidean convex spaces
Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem
This paper provides a general framework to explore the possibility of agenda
manipulation-proof and proper consensus-based preference aggregation rules, so
powerfully called in doubt by a disputable if widely shared understanding of
Arrow's `general possibility theorem'. We consider two alternative versions of
agenda manipulation-proofness for social welfare functions, that are
distinguished by `parallel' vs. `sequential' execution of agenda formation and
preference elicitation, respectively. Under the `parallel' version, it is shown
that a large class of anonymous and idempotent social welfare functions that
satisfy both agenda manipulation-proofness and strategy-proofness on a natural
domain of single-peaked `meta-preferences' induced by arbitrary total
preference preorders are indeed available. It is only under the second,
`sequential' version that agenda manipulation-proofness on the same natural
domain of single-peaked `meta-preferences' is in fact shown to be tightly
related to the classic Arrowian `independence of irrelevant alternatives' (IIA)
for social welfare functions. In particular, it is shown that using IIA to
secure such `sequential' version of agenda manipulation-proofness and combining
it with a very minimal requirement of distributed responsiveness results in a
characterization of the `global stalemate' social welfare function, the
constant function which invariably selects universal social indifference. It is
also argued that, altogether, the foregoing results provide new significant
insights concerning the actual content and the constructive implications of
Arrow's `general possibility theorem' from a mechanism-design perspective
On strategy-proofness and the salience of sIngle-peakedness
Chatterji would like to acknowledge research support from SMU grant number C244/MSS13E001 and thank KIER, Kyoto University for its hospitality. Massó would like to acknowledge finnancial support from the Spanish Ministry of Economy and Competitiveness, through Grant ECO2014-53051 and the Severo Ochoa Programme for Centers of Excellence in R&D (SEV-2015-0563), and from the Generalitat de Catalunya, through the research Grant SGR2014-515.We consider strategy-proof rules operating on a rich domain of preference profiles. We show that if the rule satisfies in addition tops-onlyness, anonymity and unanimity, then the preferences in the domain have to satisfy a variant of single-peakedness (referred to as semilattice single-peakedness). We do so by deriving from the rule an endogenous partial order (a semilattice) from which the concept of a semilattice single-peaked preference can be defined. We also provide a converse of this main finding. Finally, we show how well-known restricted domains under which nontrivial strategy-proof rules are admissible are semilattice single-peaked domains
Strategy-proof aggregation rules and single peakedness in bounded distributive lattices
It is shown that, under a very comprehensive notion of single peakedness, an aggregation rule on a bounded distributive lattice is strategy-proof if and only if it admits one of three distinct and mutually equivalent representations by lattice-polynomials, namely whenever it can be represented as a generalized weak consensus rule, a generalized weak sponsorship rule, or an iterated median rule. The equivalence of individual and coalitional strategy-proofness that is known to hold for single peaked domains in bounded linearly ordered sets and in finite trees typically fails in such an extended setting. A related impossibility result concerning non-trivial anonymous and coalitionally strategy-proof aggregation rules is also obtained