Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/81123
Authors: 
Herzberg, Frederik
Year of Publication: 
2011
Series/Report no.: 
Working Papers, Institute of Mathematical Economics 445
Abstract: 
This paper continues Dietrich and List's [2010] work on propositional-attitude aggregation theory, which is a generalised unification of the judgment-aggregation and probabilistic opinion-pooling literatures. We first propose an algebraic framework for an analysis of (many-valued) propositional-attitude aggregation problems. Then we shall show that systematic propositional-attitude aggregators can be viewed as homomorphisms in the category of C.C. Chang's [1958] MV-algebras. Since the 2-element Boolean algebra as well as the real unit interval can be endowed with an MV-algebra structure, we obtain as natural corollaries two famous theorems: Arrow's theorem for judgment aggregation as well as McConway's [1981] characterisation of linear opinion pools.
Subjects: 
propositional attitude aggregation
judgment aggregation
linear opinion pooling
Arrow's impossibility theorem
many-valued logic
MV-algebra
homomorphism
Arrow's impossibility theorem
functional equation
JEL: 
D71
Document Type: 
Working Paper

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