TY  - JOUR
AB  - 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. (C) 2009 Elsevier B.V. All rights reserved.
DA  - 2010
DO  - 10.1016/j.jmateco.2009.06.002
KW  - Impossibility theorems
KW  - Filter
KW  - Ultrafilter
KW  - Boolean algebra homomorphism
KW  - Judgment aggregation
KW  - Systematicity
LA  - eng
IS  - 1
M2  - 132
PY  - 2010
SN  - 0304-4068
SP  - 132-140
T2  - JOURNAL OF MATHEMATICAL ECONOMICS
TI  - Judgment aggregators and Boolean algebra homomorphisms
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-15890561
Y2  - 2024-11-22T03:07:21
ER  -