DROPS

Document

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

Authors: Daniel Eckert and Frederik Herzberg

Published in: Dagstuhl Seminar Proceedings, Volume 9351, Information processing, rational belief change and social interaction (2009)

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.

Cite as

Daniel Eckert and Frederik Herzberg. Systematic judgment aggregators: An algebraic connection between social and logical structure. In Information processing, rational belief change and social interaction. Dagstuhl Seminar Proceedings, Volume 9351, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@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/entities/document/10.4230/DagSemProc.09351.9},
  URN =		{urn:nbn:de:0030-drops-22302},
  doi =		{10.4230/DagSemProc.09351.9},
  annote =	{Keywords: Judgment aggregation; social structure; Boolean homorphism; ultraproduct}
}

Search Results

Documents authored by Herzberg, Frederik

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

Abstract

Cite as

Thanks for your feedback!

Could not send message