The geometry of consistent majoritarian judgement aggregation

Marcus Pivato

MPRA Paper from University Library of Munich, Germany

Abstract: Given a set of propositions with unknown truth values, a `judgement aggregation rule' is a way to aggregate the personal truth-valuations of a set of jurors into some `collective' truth valuation. We introduce the class of `quasimajoritarian' judgement aggregation rules, which includes majority vote, but also includes some rules which use different weighted voting schemes to decide the truth of different propositions. We show that if the profile of jurors' beliefs satisfies a condition called `value restriction', then the output of any quasimajoritarian rule is logically consistent; this directly generalizes the recent work of Dietrich and List (2007). We then provide two sufficient conditions for value-restriction, defined geometrically in terms of a lattice ordering or an ultrametric structure on the set of jurors and propositions. Finally, we introduce another sufficient condition for consistent majoritarian judgement aggregation, called `convexity'. We show that convexity is not logically related to value-restriction.

Keywords: judgement aggregation; discursive dilemma; doctrinal paradox; epistemic democracy; value restriction (search for similar items in EconPapers)
JEL-codes: D70 (search for similar items in EconPapers)
Date: 2008-07-16
New Economics Papers: this item is included in nep-cdm and nep-pol
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Citations: View citations in EconPapers (1)

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