Pivato, Marcus (2008): The geometry of consistent majoritarian judgement aggregation.
Download (119Kb) | Preview
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.
|Item Type:||MPRA Paper|
|Commentary on:||Eprints 0 not found.|
|Original Title:||The geometry of consistent majoritarian judgement aggregation|
|Keywords:||judgement aggregation; discursive dilemma; doctrinal paradox; epistemic democracy; value restriction|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General|
|Depositing User:||Marcus Pivato|
|Date Deposited:||17. Jul 2008 01:06|
|Last Modified:||17. Feb 2013 09:28|
Dietrich, F., List, C., November 2007. Majority voting on restricted domains. Presented at SCW08; see http://personal.lse.ac.uk/LIST/PDF-files/MajorityPaper22November.pdf
Eckert, D., Klamler, C., 2008. A geometric approach to judgement aggregation. Presented at SCW08; see http://www.accessecon.com/pubs/SCW2008/SCW2008-08-00214S.pdf
Kornhauser, L., Sager, L., 1986. Unpacking the court. Yale Law Journal.
Kornhauser, L., Sager, L., 1993. The one and the many: adjudication in collegial courts. California Law Review 91, 1-51.
List, C., 2003. A possibility theorem on aggregation over multiple interconnected propositions. Math. Social Sci. 45 (1), 1-13.
List, C., 2006. Corrigendum to: ``A possibility theorem on aggregation over multiple interconnected propositions''. Math. Social Sci. 52 (1), 109-110.
List, C., Pettit, P., 2002. Aggregating sets of judgements: an impossibility result. Economics and Philosophy 18, 89-110.
List, C., Puppe, C., September 2007. Judgment aggregation: a survey. (preprint).
- Pivato, Marcus The geometry of consistent majoritarian judgement aggregation. (deposited 17. Jul 2008 01:06) [Currently Displayed]