License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.09351.9
URN: urn:nbn:de:0030-drops-22302
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/2230/
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Eckert, Daniel ; Herzberg, Frederik

Systematic judgment aggregators: An algebraic connection between social and logical structure

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09351.EckertDaniel.Paper.2230.pdf (0.2 MB)

Abstract

We present several results that show that systematic (complete) judgment
aggregators can be viewed as both (2-valued) Boolean homomorphisms and as syntatic versions of reduced (ultra)products. Thereby, Arrovian judgment aggregators link the Boolean algebraic structures of (i) the set of coalitions (ii) the agenda, and (iii) the set of truth values of collective judgments. Since filters arise naturally in the context of Boolean algebras, these findings provide an explanation for the extraordinary effectiveness of the filter method in abstract aggregation theory.


BibTeX - Entry

@InProceedings{eckert_et_al:DagSemProc.09351.9,
  author =	{Eckert, Daniel and Herzberg, Frederik},
  title =	{{Systematic judgment aggregators: An algebraic connection between social and logical structure}},
  booktitle =	{Information processing, rational belief change and social interaction},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9351},
  editor =	{Giacomo Bonanno and James Delgrande and Hans Rott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2009/2230},
  URN =		{urn:nbn:de:0030-drops-22302},
  doi =		{10.4230/DagSemProc.09351.9},
  annote =	{Keywords: Judgment aggregation; social structure; Boolean homorphism; ultraproduct}
}

Keywords: Judgment aggregation; social structure; Boolean homorphism; ultraproduct
Collection: 09351 - Information processing, rational belief change and social interaction
Issue Date: 2009
Date of publication: 04.11.2009

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