Judgment aggregators and Boolean algebra homomorphisms
The theory of Boolean algebras can be fruitfully applied to judgment aggregation: assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent complete judgment aggregators and (ii) 2-valued Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Since the shell of such a homomorphism equals the set of winning coalitions and since (ultra)filters are shells of (2-valued) Boolean algebra homomorphisms, we suggest an explanation for the effectiveness of the (ultra)filter method in social choice theory. From the (ultra)filter property of the set of winning coalitions, one obtains two general impossibility theorems for judgment aggregation on finite electorates, even without assuming the Pareto principle.
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- Franz Dietrich & Christian List, 2008.
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- Dietrich Franz & List Christian, 2007. "Judgment aggregation without full rationality," Research Memorandum 023, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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LSE Research Online Documents on Economics
27896, London School of Economics and Political Science, LSE Library.
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- Dietrich Franz & Mongin Philippe, 2008. "The Premiss-Based Approach to Judgment Aggregation," Research Memorandum 013, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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