Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation

Pigozzi, Gabriella

doi:10.1007/s11229-006-9063-7

Cited by 129 publications

(99 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Another procedure in the literature is the distance-based aggregation( [40]) which is a well known for preference aggregation (E.g., Kemeny voting rule [26], Dodgson voting rule [3], and lately a more systematic analysis in [19]). Our work contribute to this discussion by pointing out where one should search for solutions while not leaving the consistency and independence constraints entirely.…”

Section: Motivation and Known Resultsmentioning

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

Section: Motivation and Known Resultsmentioning

confidence: 99%

Approximate Judgement Aggregation

Nehama

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…See Duddy and Piggins (2009). 6 Pigozzi (2006) and Miller and Osherson (2009) discuss the distance-based approach to judgment aggregation. 7 Konieczny and Pino Pérez (2002).…”

Section: Majority Judgment T T T Fmentioning

confidence: 99%

A measure of distance between judgment sets

Duddy

Piggins

2011

Soc Choice Welf

View full text Add to dashboard Cite

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming's metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in A ∩ B jointly imply that the propositions in A−B share the same truth value, then the disagreement between A and B over those propositions in A−B should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings.

show abstract

“…Now, we investigate two different approaches to judgment aggregation. From the preceding analysis of the discursive dilemma in Bovens and Rabinowicz (2006), List (2005), List (2006) and Pigozzi (2006), two procedures are known: the premise-based procedure f P and the conclusion-based procedure f C . Recall that the agenda of the version of the discursive dilemma discussed in this paper is A = {A 1 , A 2 , D}, with the constraint rule L = (A 1 ∧ A 2 ) ↔ D. f P determines the aggregate vote on A 1 and A 2 by simple majority voting, and fixes the collective judgment on A according to the constraint (A 1 ∧ A 2 ) ↔ D. In conclusion-based reasoning, however, the members decide privately on A 1 and A 2 and only express their opinions on D publicly.…”

Section: Truth-tracking (Tt): For Any Admissible Situation Valuation mentioning

confidence: 99%

Judgment aggregation and the problem of tracking the truth

Hartmann

Sprenger

2011

Synthese

View full text Add to dashboard Cite

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on those propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. In this paper, we motivate that quite often, we do not only want to make a factually right decision, but also to correctly evaluate the reasons for that decision. In other words, we address the problem of tracking the truth. We set up a probabilistic model that generalizes the analysis of Bovens and Rabinowicz (Synthese 150: 131-153, 2006) and use it to compare several aggregation procedures. Demanding some reasonable adequacy constraints, we demonstrate that a reasons-or premise-based aggregation procedure tracks the truth better than any other procedure. However, we also illuminate that such a procedure is not in all circumstances easy to implement, leaving actual decision-makers with a tradeoff problem.

show abstract

Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation

Cited by 129 publications

References 26 publications

Approximate Judgement Aggregation

Approximate Judgement Aggregation

A measure of distance between judgment sets

Judgment aggregation and the problem of tracking the truth

Contact Info

Product

Resources

About