TY  - GEN
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.
DA  - 2009
KW  - Systematicity
KW  - Judgment aggregation
KW  - Impossibility theorems
KW  - Filter
KW  - Boolean algebra homomorphism
KW  - Ultrafilter
LA  - eng
PY  - 2009
SN  - 0931-6558
TI  - Judgment aggregators and Boolean algebra homomorphisms
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:361-14507
Y2  - 2024-11-22T03:18:38
ER  -