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The geometry of consistent majoritarian judgement aggregation

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  • Pivato, Marcus

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9608.

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Date of creation: 16 Jul 2008
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Handle: RePEc:pra:mprapa:9608

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Keywords: judgement aggregation; discursive dilemma; doctrinal paradox; epistemic democracy; value restriction;

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  1. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  2. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
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