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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.

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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)

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@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}
}

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DOI: 10.4230/DagSemProc.05321.8

Belief merging, judgment aggregation and some links with social choice theory

Authors: Daniel Eckert and Gabriella Pigozzi

Published in: Dagstuhl Seminar Proceedings, Volume 5321, Belief Change in Rational Agents: Perspectives from Artificial Intelligence, Philosophy, and Economics (2005)

Abstract

In this paper we explore the relation between three areas: judgment aggregation, belief merging and social choice theory. Judgment aggregation studies how to aggregate individual judgments on logically interconnected propositions into a collective decision on the same propositions. When majority voting is applied to some propositions (the premises) it may however give a different outcome than majority voting applied to another set of propositions (the conclusion). Starting from this so-called doctrinal paradox, the paper surveys the literature on judgment aggregation (and its relation to preference aggregation), and shows that the application of a well known belief merging operator can dissolve the paradox. Finally, the use of distances is shown to establish a link between belief merging and preference aggregation in social choice theory.

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Daniel Eckert and Gabriella Pigozzi. Belief merging, judgment aggregation and some links with social choice theory. In Belief Change in Rational Agents: Perspectives from Artificial Intelligence, Philosophy, and Economics. Dagstuhl Seminar Proceedings, Volume 5321, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{eckert_et_al:DagSemProc.05321.8,
  author =	{Eckert, Daniel and Pigozzi, Gabriella},
  title =	{{Belief merging, judgment aggregation and some links with social choice theory}},
  booktitle =	{Belief Change in Rational Agents: Perspectives from Artificial Intelligence, Philosophy, and Economics},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5321},
  editor =	{James Delgrande and Jerome Lang and Hans Rott and Jean-Marc Tallon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05321.8},
  URN =		{urn:nbn:de:0030-drops-3330},
  doi =		{10.4230/DagSemProc.05321.8},
  annote =	{Keywords: Judgment aggregation, belief merging, preference aggregation, social choice theory}
}

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Documents authored by Eckert, Daniel

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

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Belief merging, judgment aggregation and some links with social choice theory

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