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

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