Domain Conditions in Social Choice Theory

Gaertner, Wulf

doi:10.1017/cbo9780511492303

Cited by 80 publications

(54 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In still a different framework, Nehring (2003) derives a version of Arrow's theorem for weak preferences that involves a monotonic addition to independence of irrelevant alternatives. 35 Such as those described by Gaertner (2006) and Le Breton and Weymark (2011). In classical propositional logic, there are at least two agendas that could give rise to this, i.e. X = {a, a ∨ b} ± and X = {a ∧ b, a → b} ± , and it would be a conceptual abuse to treat them as they were the same.…”

Section: And Non-dictatorship Being Replaced By Non-oligarchymentioning

confidence: 99%

The doctrinal paradox, the discursive dilemma, and logical aggregation theory

Mongin

2012

Theory Decis

View full text Add to dashboard Cite

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager's doctrinal paradox and List and Pettit's discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the 'general logic' built in this framework.The present English paper has evolved from an earlier French paper co-authored with Franz Dietrich ("Un bilan interprétatif de la théorie de l'agrégation logique", Revue d 'économie politique, vol. 120, 2010, pp. 929-972). Many thanks to him for allowing this author to present this new version. Thanks also for their comments to

show abstract

Section: And Non-dictatorship Being Replaced By Non-oligarchymentioning

confidence: 99%

The doctrinal paradox, the discursive dilemma, and logical aggregation theory

Mongin

2012

Theory Decis

View full text Add to dashboard Cite

show abstract

“…In the case of unidimensional alignment, the extreme positions on the given dimension correspond to either clear acceptance or clear rejection of each proposition, and, for each proposition, there is a threshold between these extremes (which may vary across propositions) that divides the 'acceptance-region'from the 'rejection-region'. 16 On unidimensionally ordered pro…les, majority voting preserves consistency, and we can say something about the nature of its outcome: it is a subset of the middle individual's judgment set (or, for even n, a subset of the intersection of the two middle individuals' judgment sets). If the pro…le is unidimensionally aligned, the majority outcome is not just included in that set but coincides with it.…”

Section: Conditions Based On Orders Of Individualsmentioning

confidence: 99%

“…The following result answers this question. 17 Proposition 7 (a) Restricted to pro…les of consistent judgment sets, 16 In List [21], unidimensional alignment is interpreted in terms of 'meta-agreement'. 17 The non-implication claims in (a) do not refer to a …xed agenda X and group size n. Rather, for some (in fact, most) X and n, there are pro…les satisfying one condition but not the other.…”

Section: The Logical Relationships Between the Four Conditionsmentioning

confidence: 99%

“…Here one individual prefers x to y to z, a second y to z to x, and a third z to x to y, and thus there are majorities for x against y, for y against z, and for z against x, a 'cycle'. But it is equally well known that if individual preferences fall into a suitably restricted domain, majority cycles can be avoided (for an excellent overview, see Gaertner [16]). The most famous domain restriction with this e¤ect is Black's single-peakedness [1].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Majority voting on restricted domains

Dietrich

List

2010

Journal of Economic Theory

View full text Add to dashboard Cite

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments su¢ -cient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results provide new support for the robustness of majority rule.

show abstract

“…First it allows one to provide some endogenous domain restrictions on the space of admissible preferences or on the set of utilities functions considered in aggregation procedures. Restrictions of domains have been thought as one way to escape the gloom of Arrow's or Sen's [64] theorems and have been at the origin of a large literature whose a thorough account can be found in Gaertner [36]. For instance, it is often assumed that the individual utility function are concave.…”

Section: Introductionmentioning

confidence: 99%

Consistency between tastes and values: A universalization approach

Gravel

Laslier

Trannoy

2000

Social Choice and Welfare

View full text Add to dashboard Cite

Abstract. The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals`tastes' ± which re¯ect the self-interested view point of the individuals ± into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called`ethics of responsibility' and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of`laundering' individual preferences is also provided.The principle of right, and so of justice, puts limit on which satisfactions have value; they impose restrictions on what are reasonable conceptions of one's * We thank Nick Baigent, John Broome, David Donaldson, Marc Fleurbaey, Emmanuel Picavet and an anonymous referee for very helpful discussions and/or comments. The usual disclaimer applies fully. Earlier versions of this paper have circulated under various titles including, notably, Self-Laundering of Preferences and Universalization and A Theory of Individual Moral Consistency.good. In drawing up plans and in deciding on aspirations, men are to take these constraints into account.

show abstract

Domain Conditions in Social Choice Theory

Cited by 80 publications

References 0 publications

The doctrinal paradox, the discursive dilemma, and logical aggregation theory

The doctrinal paradox, the discursive dilemma, and logical aggregation theory

Majority voting on restricted domains

Consistency between tastes and values: A universalization approach

Contact Info

Product

Resources

About