An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms

Herzberg F (2011) Working Papers. Institute of Mathematical Economics; 445.
Bielefeld: Center for Mathematical Economics.

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This paper continues Dietrich and List's [2010] work on propositionalattitude aggregation theory, which is a generalised unication of the judgment-aggregation and probabilistic opinion-pooling literatures. We rst 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.
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Herzberg F. An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms. Working Papers. Institute of Mathematical Economics. Vol 445. Bielefeld: Center for Mathematical Economics; 2011.
Herzberg, F. (2011). An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms (Working Papers. Institute of Mathematical Economics, 445). Bielefeld: Center for Mathematical Economics.
Herzberg, F. (2011). An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms. Working Papers. Institute of Mathematical Economics, 445, Bielefeld: Center for Mathematical Economics.
Herzberg, F., 2011. An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms, Working Papers. Institute of Mathematical Economics, no.445, Bielefeld: Center for Mathematical Economics.
F. Herzberg, An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms, Working Papers. Institute of Mathematical Economics, vol. 445, Bielefeld: Center for Mathematical Economics, 2011.
Herzberg, F.: An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms. Working Papers. Institute of Mathematical Economics, 445. Center for Mathematical Economics, Bielefeld (2011).
Herzberg, Frederik. An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms. Bielefeld: Center for Mathematical Economics, 2011. Working Papers. Institute of Mathematical Economics. 445.
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