License
When quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-22302
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2230/
Go to the corresponding Portal


Eckert, Daniel ; Herzberg, Frederik

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

pdf-format:
Document 1.pdf (200 KB)


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:DSP:2009:2230,
  author =	{Daniel Eckert and Frederik Herzberg},
  title =	{Systematic judgment aggregators: An algebraic connection between social and logical structure},
  booktitle =	{Information processing, rational belief change and social interaction},
  year =	{2009},
  editor =	{Giacomo Bonanno and James Delgrande and Hans Rott},
  number =	{09351},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2230},
  annote =	{Keywords: Judgment aggregation; social structure; Boolean homorphism; ultraproduct}
}

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


DROPS-Home | Fulltext Search | Imprint Published by LZI