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Aggregation theory and the relevance of some issues to others

Abstract : I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people's judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people's judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a dichotomous premise/conclusion order resp. a linear priority order. 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 well-known Arrow-like theorem in judgment aggregation.
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Contributor : Franz Dietrich <>
Submitted on : Friday, January 1, 2016 - 10:56:08 PM
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Franz Dietrich. Aggregation theory and the relevance of some issues to others. Journal of Economic Theory, Elsevier, 2015, 160, pp.463-493. ⟨halshs-01249513⟩

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