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Judgment aggregators and Boolean algebra homomorphisms

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  • Herzberg, Frederik

    (Center for Mathematical Economics, Bielefeld University)

Abstract

The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent complete judgment aggregators and (ii) 2-valued Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Since the shell of such a homomorphism equals the set of winning coalitions and since (ultra)filters are shells of (2-valued) Boolean algebra homomorphisms, we suggest an explanation for the effectiveness of the (ultra)filter method in social choice theory.

Suggested Citation

  • Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Center for Mathematical Economics Working Papers 414, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:414
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    References listed on IDEAS

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    1. Philippe Mongin, 2011. "Judgment aggregation," Working Papers hal-00579346, HAL.
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    6. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
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    Cited by:

    1. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    2. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.

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    More about this item

    Keywords

    Systematicity; Judgment aggregation; Impossibility theorems; Filter; Boolean algebra homomorphism; Ultrafilter;
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