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A Geometric Approach to Paradoxes of Majority Voting in Abstract Aggregation Theory

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Algorithmic Decision Theory (ADT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5783))

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Abstract

In this paper we extend Saari’s geometric approach to paradoxes of preference aggregation to the analysis of paradoxes of majority voting in a more general setting like Anscombe’s paradox and paradoxes of judgment aggregation. In particular we use Saari’s representation cubes to provide a geometric representation of profiles and majority outcomes. Within this geometric framework, we show how profile decompositions can be used to derive restrictions on profiles that avoid the paradoxes of majority voting.

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Authors and Affiliations

  1. Institute of Public Economics, University of Graz, Universitaetsstr. 15, 8010, Graz, Austria

    Daniel Eckert & Christian Klamler

Authors
  1. Daniel Eckert
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  2. Christian Klamler
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Editors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121, Padova, Italy

    Francesca Rossi

  2. LAMSADE-CNRS, University of Paris Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France

    Alexis Tsoukias

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Eckert, D., Klamler, C. (2009). A Geometric Approach to Paradoxes of Majority Voting in Abstract Aggregation Theory. In: Rossi, F., Tsoukias, A. (eds) Algorithmic Decision Theory. ADT 2009. Lecture Notes in Computer Science(), vol 5783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04428-1_2

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  • DOI: https://doi.org/10.1007/978-3-642-04428-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04427-4

  • Online ISBN: 978-3-642-04428-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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