The structure of strategy-proof social choice — Part I: General characterization and possibility results on median spaces

Nehring, Klaus; Puppe, Clemens

doi:10.1016/j.jet.2006.04.008

Cited by 158 publications

(132 citation statements)

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“…For instance, the existence of non-dictatorial Arrovian aggregators and/or strategy-proof social choice functions can be demonstrated under much weaker domain restrictions (Kalai and Muller [1977]). Also in this context, richness and/or connectedness assumptions have frequently been imposed, and variants of the single-peakedness condition have been found to play an important role in the derivation of possibility results (Nehring and Puppe [2007], Chatterji et al [2013], Chatterji and Massó [2015]). In a recent paper, Chatterji et al [2016] have characterized a weaker notion of single-peakedness ('single-peakedness with respect to a tree') using strategy-proofness and other conditions imposed on random social choice functions.…”

Section: Resultsmentioning

confidence: 99%

The single-peaked domain revisited: A simple global characterization

Puppe

2018

Journal of Economic Theory

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for particularly helpful comments.Abstract It is proved that, among all restricted preference domains that guarantee consistency (i.e. transitivity) of pairwise majority voting, the single-peaked domain is the only minimally rich and connected domain that contains two completely reversed strict preference orders. It is argued that this result explains the predominant role of single-peakedness as a domain restriction in models of political economy and elsewhere. The main result has a number of corollaries, among them a dual characterization of the single-dipped domain; it also implies that a single-crossing ('order-restricted') domain can be minimally rich only if it is a subdomain of a single-peaked domain. The conclusions are robust as the results apply both to domains of strict and of weak preference orders, respectively. JEL Classification D71, C72

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Section: Resultsmentioning

confidence: 99%

The single-peaked domain revisited: A simple global characterization

Puppe

2018

Journal of Economic Theory

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“…The problem is very general: Remark 1. Inconsistent majority judgments can arise as soon as the set of propositions and their negations on which judgments are to be made exhibits a simple combinatorial property List 2007b, Nehring andPuppe 2007): it has a minimally inconsistent subset of three or more propositions, where a set of propositions is called minimally inconsistent if it is inconsistent and every proper subset of it is consistent.…”

Section: The Problem Of Inconsistent Majority Judgmentsmentioning

confidence: 99%

“…However, if judge 3 were su¢ ciently strongly opposed to this outcome, he or she could strategically manipulate the outcome by pretending to believe that q is false, contrary to his or her sincere judgment; the result would be the majority rejection of q, and consequently a 'not liable'verdict. It can be shown that an aggregation rule is non-manipulable if and only if it satis…es the conditions of independence and monotonicity (Dietrich and List 2007e; for closely related results in a more classic social-choice-theoretic framework, see Nehring and Puppe 2007). Assuming that, other things being equal, the relaxation of independence is the most promising way to make non-degenerate judgment aggregation possible, the impossibility theorems reviewed above can therefore be seen as pointing to a trade-o¤ between degeneracy of judgment aggregation on the one hand (most notably, in the form of dictatorship) and its potential manipulability on the other.…”

Section: Relaxing the Responsiveness Conditionsmentioning

confidence: 99%

The theory of judgment aggregation: an introductory review

List

2011

Synthese

134

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This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the …eld, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers new to the …eld of judgment aggregation a sense of this rapidly growing research area.

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“…It now encompasses aggregation problems of very general form, including even the aggregation of general logical propositions. This area, known as judgment aggregation theory or abstract aggregation theory, has seen seminal contributions by List and Pettit (2002), Dietrich and Mongin (2007), Nehring and Puppe (2007), Dokow and Holzman (2010), Dietrich and List (2007, 2010; for a survey, see List and Puppe (2009). A very recent development in this area is the investigation of the aggregation of more general propositional attitudes which allows for a unified treatment of both judgment aggregation and probabilistic opinion pooling (cf.…”

Section: Introductionmentioning

confidence: 99%

The (im)possibility of collective risk measurement: Arrovian aggregation of variational preferences

Herzberg

2013

Econ Theory Bull

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This paper studies collective decision making when individual preferences can be represented by convex risk measures. It addresses the question whether there exist non-dictatorial aggregation functions of convex risk measures satisfying the following Arrow-type rationality axioms: a weak form of universality, systematicity (a strong variant of independence), and the Pareto principle. Herein, convex risk measures are identified with variational preferences on account of the For finite electorates, we prove a variational analogue of Arrow's impossibility theorem. For infinite electorates, the possibility of rational aggregation depends on an equicontinuity condition for the variational preference profiles; we prove a variational analogue of Fishburn's possibility theorem and point to potential analogues of Campbell's impossibility theorem. The proof methodology is based on a model-theoretic approach to aggregation theory inspired by Lauwers and Van Liedekerke (J Math Econ 24(3): 1995). Diverse applications of these results are conceivable, in particular (a) the constitutional design of panels of risk managers and (b) microfoundations for (macroeconomic) multiplier preferences.

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The structure of strategy-proof social choice — Part I: General characterization and possibility results on median spaces

Cited by 158 publications

References 8 publications

The single-peaked domain revisited: A simple global characterization

The single-peaked domain revisited: A simple global characterization

The theory of judgment aggregation: an introductory review

The (im)possibility of collective risk measurement: Arrovian aggregation of variational preferences

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