Aggregation of binary evaluations for truth-functional agendas

Dokow, Elad; Holzman, Ron

doi:10.1007/s00355-008-0320-1

Cited by 37 publications

(48 citation statements)

References 9 publications

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“…(This characterization is a direct corollary from a series of works in the more general framework of aggregation, E.g., [37], [16]. We include a proof of it in the appendix)…”

Section: Proof Sketchmentioning

confidence: 85%

“…Since our work can be stated as impossibility results, we prefer using the more general model. In [16] Dokow and Holzman prove that the two models are equivalent in the sense that each set of consistent opinions can be described using a proposition set (although not uniquely).…”

Section: Abstract Judgement Aggregationmentioning

confidence: 99%

“…We define the model similarly to [16] (which is Rubinstein and Fishburn's model [43] for the binary case)…”

Section: The Modelmentioning

confidence: 99%

“…In [15] Dietrich and List define the notion of manipulability of an aggregation mechanism 16 and proved that any aggregation mechanism that does not satisfy independence is manipulable. In this paper they further prove that this manipulability property is equivalent to a more game-theoretic property of strategy-proofness under some assumptions on players' preferences.…”

Section: The Independence Propertymentioning

confidence: 99%

“…According to this criterion the aggregation of 'complex' issues is done without regarding the reasons of the voters for their opinions and hence lacks the information for good aggregation. 16 An aggregation mechanism F is manipulable at the profile X by individual i(the manipulator) on issue j if X i j = (F (X)) j (The manipulator disagrees with the aggregated opinion on issue j), but X i j = (F (X ′ )) j for some profile X ′ that differs form X in i's vote only.(I.e. the manipulator can get his will on j by voting differently) set of issues the relevant one (For instance, the definition of Social Welfare Functions as returning a choice function so only at a later stage the society is faced with the menu of alternatives).…”

Section: The Independence Propertymentioning

confidence: 99%

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Approximate Judgement Aggregation

Nehama

2011

Lecture Notes in Computer Science

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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.

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“…(This characterization is a direct corollary from a series of works in the more general framework of aggregation, E.g., [37], [16]. We include a proof of it in the appendix)…”

Section: Proof Sketchmentioning

confidence: 85%

Section: Abstract Judgement Aggregationmentioning

confidence: 99%

“…We define the model similarly to [16] (which is Rubinstein and Fishburn's model [43] for the binary case)…”

Section: The Modelmentioning

confidence: 99%

Section: The Independence Propertymentioning

confidence: 99%

Section: The Independence Propertymentioning

confidence: 99%

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Approximate Judgement Aggregation

Nehama

2011

Lecture Notes in Computer Science

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The Present and Future of Judgement Aggregation Theory. A Law and Economics Perspective

Mongin

2019

The Future of Economic Design

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This chapter brie ‡y reviews the present state of judgment aggregation theory and tentatively suggests a future direction for that theory. In the review, we start by emphasizing the di¤erence between the doctrinal paradox and the discursive dilemma, two idealized examples which classically serve to motivate the theory, and then proceed to reconstruct it as a brand of logical theory, unlike in some other interpretations, using a single impossibility theorem as a key to its technical development. In the prospective part, having mentioned existing applications to social choice theory and computer science, which we do not discuss here, we consider a potential application to law and economics. This would be based on a deeper exploration of the doctrinal paradox and its relevance to the functioning of collegiate courts. On this topic, legal theorists have provided empirical observations and theoretical hints that judgment aggregation theorists would be in a position to clarify and further elaborate. As a general message, the chapter means to suggest that the future of judgment aggregation theory lies with its applications rather than its internal theoretical development.

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Aggregation of Votes with Multiple Positions on Each Issue

Kirousis¹,

Kolaitis

Livieratos³

2017

Relational and Algebraic Methods in Computer Science

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We consider the problem of aggregating votes cast by a society on a fixed set of issues, where each member of the society may vote for one of several positions on each issue, but the combination of votes on the various issues is restricted to a set of feasible voting patterns. We require the aggregation to be supportive, i.e. for every issue j the corresponding component fj of every aggregator on every issue should satisfy fj (x1, , . . . , xn) ∈ {x1, , . . . , xn}. We prove that, in such a set-up, non-dictatorial aggregation of votes in a society of some size is possible if and only if either non-dictatorial aggregation is possible in a society of only two members or a ternary aggregator exists that either on every issue j is a majority operation, i.e. the corresponding component

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Aggregation of binary evaluations for truth-functional agendas

Cited by 37 publications

References 9 publications

Approximate Judgement Aggregation

Approximate Judgement Aggregation

The Present and Future of Judgement Aggregation Theory. A Law and Economics Perspective

Aggregation of Votes with Multiple Positions on Each Issue

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