Aggregation theory and the relevance of some issues to others

Dietrich, Franz (2006): Aggregation theory and the relevance of some issues to others.

Abstract

I propose a new axiom on the aggregation of individual yes/no judgments on propositions into collective judgments: each collective judgment depends only on people's judgments on 'relevant' propositions. This contrasts with classical independence: each collective judgment depends only on people's judgments on the 'current' proposition. I generalize the premise-based and sequential-priority rules to an arbitrary priority structure over propositions, instead of a dichotomous premise/conclusion structure or a linear order of priority. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow's Theorem (in its general and indifference-free versions) and the Arrow-type theorem in judgment aggregation.

• Item Type: MPRA Paper
• Language: English
• Keywords: judgment aggregation, relevance connections vs. logical connections between issues, generalized Arrow theorem, premise-based rule, sequential priority rule, general priority rule, priority graph, aggregation of non-binary evaluations
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations

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