Given a set of propositions with unknown truth values, a ‘judgement aggregation function’ is a way to aggregate the personal truth-valuations of a group of voters into some ‘collective’ truth valuation. We introduce the class of ‘quasimajoritarian’ judgement aggregation functions, which includes majority vote, but also includes some functions which use different voting schemes to decide the truth of different propositions. We show that if the profile of individual beliefs satisfies a condition called ‘value restriction’, then the output of any quasimajoritarian function is logically consistent; this directly generalizes the recent work of Dietrich and List (Majority voting on restricted domains. Presented at SCW08; see http://personal.lse.ac.uk/LIST/PDF-files/MajorityPaper22November.pdf, 2007b). We then provide two sufficient conditions for value-restriction, defined geometrically in terms of a lattice ordering or a metric structure on the set of individuals 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.
Aggregation Function Vote Rule Winning Coalition Ultrametric Space Judgement Aggregation
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