Judgement aggregators and boolean algebra homomorphism

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 414

Classification and Topics

• Classification: Wirtschaft
• Subject: Judgment aggregation ; Systematicity ; Impossibility theorems ; Filter ; Ultrafilter ; Boolean algebra homomorphism ; Präferenztheorie ; Aggregation ; Soziale Wohlfahrtsfunktion ; Unmöglichkeitstheorem ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Herzberg, Frederik
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/43814
• URN: urn:nbn:de:hbz:361-14507
• Last update: 10.03.2025, 11:41 AM CET