Arrow’s theorem in judgment aggregation

Dietrich, Franz; List, Christian

doi:10.1007/s00355-006-0196-x

Cited by 210 publications

(214 citation statements)

References 13 publications

Supporting

Mentioning

209

Contrasting

Order By: Relevance

“…A binary evaluation is thus formally equivalent to an approval voting ballot. 5 While there is no technical reason to distinguish among these various equivalent formalisms, they do suggest different perspectives on the aggregation problem. Approval voting, for example, differs fundamentally from the mean rule discussed here, while the dichotomous weak order formalism invites comparison with other methods of aggregating orders.…”

Section: H H Hmentioning

confidence: 99%

“…The agenda for this problem is {ab, bc, ac} ± . This is an example of a "preference agenda" (Dietrich and List, 2007). Every complete judgment set is rational except for two: {ab, bc, ca} and {ba, cb, ac}.…”

Section: Preference Agenda With Three Alternativesmentioning

confidence: 99%

“…A binary evaluation can also be identified with a dichotomous weak order relation, and we take this approach in Section 6. 5 Once each member of faculty has submitted his or her partition we face the problem of aggregating them into a collective partition. One natural approach to this problem is to use the majority method, under which the faculty collectively assigns a student to S H (or S L ) if a majority of its members do.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Aggregation of binary evaluations: a Borda-like approach

2015

View full text Add to dashboard Cite

We characterize a rule for aggregating binary evaluations -equivalently, dichotomous weak orders -similar in spirit to the Borda rule from the preference aggregation literature. The binary evaluation framework was introduced as a general approach to aggregation by Wilson (J. Econ. Theory 10 (1975) 63-77). In this setting we characterize the "mean rule," which we derive from properties similar to those Young (J. Econ. Theory 9 (1974) 43-52) used in his characterization of the Borda rule. Complementing our axiomatic approach is a *

show abstract

Section: H H Hmentioning

confidence: 99%

Section: Preference Agenda With Three Alternativesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Aggregation of binary evaluations: a Borda-like approach

2015

View full text Add to dashboard Cite

show abstract

“…This means that F satisfies independence if one can find m binary functions 12 . An independent aggregation mechanism satisfies systematicity if F (X) = f (X 1 ), .…”

Section: The Modelmentioning

confidence: 99%

“…We are interested in Social Welfare Functions which are functions that aggregate n such orders to an aggregated order. As seen in [36] and [12], this problem can be stated naturally in our framework by defining s 2 issues 20 .…”

Section: Preference Aggregationmentioning

confidence: 99%

Approximate Judgement Aggregation

Nehama

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them (e.g., transitivity when describing preferences). We generalize the previous results by studying approximate judgement aggregation. We relax the main two constraints assumed in the current literature, Consistency and Independence and consider mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small portion of the inputs. The main question we raise is whether the relaxation of these notions significantly alters the class of satisfying aggregation mechanisms. The recent works for preference aggregation of Kalai, Mossel, and Keller fit into this framework. The main result of this paper is that, as in the case of preference aggregation, in the case of a subclass of a natural class of aggregation problems termed 'truth-functional agendas', the set of satisfying aggregation mechanisms does not extend non-trivially when relaxing the constraints. Our proof techniques involve boolean Fourier transform and analysis of voter influences for voting protocols.The question we raise for Approximate Aggregation can be stated using terms of Property Testing. For instance, as a corollary from our result we get a generalization of the classic result for property testing of linearity of boolean functions.

show abstract

Collective Choice

Wong

2014

The Encyclopedia of Political Thought

View full text Add to dashboard Cite

Collective choice is the aggregation of choices of more than one individual over a set of alternatives. It is relevant to politics whenever collective decisions are based on more than one individual choice or decision. The outcome of collective choice depends on the aggregation procedure used. Presumably, a desirable procedure should at least reflect the given individual choices as much as possible.

show abstract

Arrow’s theorem in judgment aggregation

Cited by 210 publications

References 13 publications

Aggregation of binary evaluations: a Borda-like approach

Aggregation of binary evaluations: a Borda-like approach

Approximate Judgement Aggregation

Collective Choice

Contact Info

Product

Resources

About