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

Frederik Herzberg
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Frederik Herzberg: Center for Mathematical Economics, Bielefeld University

No 445, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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.

Keywords: propositional attitude aggregation; judgment aggregation; linear opinion pooling; Arrow's impossibility theorem; many-valued logic; MV-algebra; homomorphism; Arrow's impossibility theorem; functional equation (search for similar items in EconPapers)
Pages: 13
Date: 2015-12-11
New Economics Papers: this item is included in nep-cdm and nep-hpe
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https://pub.uni-bielefeld.de/download/2900049/2900050 First Version, 2011 (application/x-download)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:445

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