Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/43814
Authors: 
Herzberg, Frederik
Year of Publication: 
2009
Series/Report no.: 
Working papers // Institute of Mathematical Economics 414
Abstract: 
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 the Pareto principle.
Subjects: 
Judgment aggregation
Systematicity
Impossibility theorems
Filter
Ultrafilter
Boolean algebra homomorphism
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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