Aggregation theory and the relevance of some issues to others

Franz Dietrich

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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.

Keywords: judgment aggregation; generalized Arrow theorem; generalized premise-based and sequential-priority rules; priority graph; aggregation of non-binary evalua-tions (search for similar items in EconPapers)
Date: 2015
New Economics Papers: this item is included in nep-mic
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01249513v1
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Citations: View citations in EconPapers (10)

Published in Journal of Economic Theory, 2015, 160, pp.463-493

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Journal Article: Aggregation theory and the relevance of some issues to others (2015)
Working Paper: Aggregation theory and the relevance of some issues to others (2015)
Working Paper: Aggregation theory and the relevance of some issues to others (2015)
Working Paper: Aggregation theory and the relevance of some issues to others (2014)
Working Paper: Aggregation theory and the relevance of some issues to others (2007)
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