Aggregation theory and the relevance of some issues to others

Dietrich, Franz

doi:10.1016/j.jet.2015.03.012

Cited by 15 publications

(3 citation statements)

References 33 publications

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“…At the opposite extreme is the "conclusion-based" aggregation rule, which aggregates the voters' opinions on each conclusion by majority vote, and mostly ignores their opinions about the premises, except when these opinions can be aggregated in a manner which is logically consistent with the majority opinions about the conclusions (Pigozzi et al 2009). Between these extremes, there are rules which give greater or lesser weight to the voters' views on different premises and conclusions (Dietrich 2015).…”

Section: Extension To Weighted Judgement Contextsmentioning

confidence: 99%

The median rule in judgement aggregation

Nehring

Pivato

2021

Econ Theory

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A judgement aggregation rule takes the views of a collection of voters over a set of interconnected issues and yields a logically consistent collective view. The median rule is a judgement aggregation rule that selects the logically consistent view which minimizes the average distance to the views of the voters (where the “distance” between two views is the number of issues on which they disagree). In the special case of preference aggregation, this is called the Kemeny rule. We show that, under appropriate regularity conditions, the median rule is the unique judgement aggregation rule which satisfies three axioms: Ensemble Supermajority Efficiency, Reinforcement, and Continuity. Our analysis covers aggregation problems in which the consistency restrictions on input and output judgements may differ. We also allow for issues to be weighted, and provide numerous examples in which issue weights arise naturally.

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Section: Extension To Weighted Judgement Contextsmentioning

confidence: 99%

The median rule in judgement aggregation

Nehring

Pivato

2021

Econ Theory

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“…For subjunctive implications, Dietrich shows possibility results for quota rules. Moreover, the notion of relevant premises in a judgment aggregation problem has been discussed in Dietrich (2015) by tuning the axioms of aggregation procedures. Here, we have approached the problem of relevance by studying judgement aggregation within relevant and linear logics, that is, by introducing suitable logical operators.…”

Section: Related Workmentioning

confidence: 99%

Judgement aggregation in non-classical logics

Porello

2017

Journal of Applied Non-Classical Logics

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This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgment aggregation in non-classical logics is that they offer a number of modelling choices to represent agents' reasoning in aggregation problems. By studying judgment aggregation in logics that are weaker than classical logic, we investigate whether some well-known impossibility results, that were tailored for classical logic, still apply to those weak systems.

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“…It is actually the case in many legislative systems, like the German one, that simple laws can be changed by getting the approval of a simple majority in the parliament, while constitutional laws require, for instance, a 2/3 majority.3 We have previously outlined this idea in a preliminary version of this paper(Terzopoulou and Endriss 2019).4 In the judgment aggregation literature, binary relations between propositions have also been employed to capture priority(List 2004;Dietrich and List 2007b) or relevance(Dietrich 2015). Although our axioms formally rely on a binary relation as well, our intended interpretation of it-hinging on the propositions' standards of acceptance-is different.…”

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confidence: 99%

Neutrality and relative acceptability in judgment aggregation

Terzopoulou

Endriss

2019

Soc Choice Welf

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One of the fundamental normative principles in social choice theory is that of neutrality. In the context of judgment aggregation, neutrality is encoded in the form of an axiom expressing that, when two possible judgments enjoy the same support amongst the individuals, then either both or neither of them should be accepted. This is a reasonable requirement in many scenarios. However, we argue that for scenarios in which individuals are asked to pass judgment on very diverse kinds of propositions, a notion of relative acceptability is better suited. We capture this notion by a new axiom that hinges on a binary "acceptability" relation A between propositions: if a given coalition accepting a proposition p entails the collective acceptance of p, then the same should be true for every other proposition q related to p via A. Intuitively, p Aq means that p is at least as acceptable as q. Classical neutrality is then a special case where all propositions are equally acceptable. We show that our new axiom allows us to circumvent a classical impossibility theorem in judgment aggregation for certain scenarios of practical interest. Also, we offer a precise characterisation of all scenarios that are safe, in the sense that any aggregation rule respecting the relative acceptability between propositions will always return logically consistent outcomes.

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Aggregation theory and the relevance of some issues to others

Cited by 15 publications

References 33 publications

The median rule in judgement aggregation

The median rule in judgement aggregation

Judgement aggregation in non-classical logics

Neutrality and relative acceptability in judgment aggregation

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