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


  • Herzberg, Frederik

    (Center for Mathematical Economics, Bielefeld University)


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.

Suggested Citation

  • Herzberg, Frederik, 2015. "An algebraic approach to general aggregation theory: Propositional-attitude aggregators as MV-homomorphisms," Center for Mathematical Economics Working Papers 445, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:445

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    propositional attitude aggregation; judgment aggregation; linear opinion pooling; Arrow's impossibility theorem; many-valued logic; MV-algebra; homomorphism; Arrow's impossibility theorem; functional equation;

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