Decidability in complex social choices

  • Gennaro Amendola
  • Luigi Marengo
  • Davide Pirino
  • Simona Settepanella
  • Akimichi Takemura
Article
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Abstract

In this paper, we develop on a geometric model of social choice among bundles of interdependent elements (objects). Social choice can be seen as a process of search for optima in a complex multidimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and probabilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima (called local and u-local) are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.

Keywords

Social choice Object construction Hyperplane arrangement Probability Tournament Algorithm 

Mathematics Subject Classification

05C20 52C35 91B10 91B12 91B14 

JEL Classification

D03 D71 D72 

Notes

Acknowledgments

We are very grateful to anonymous referees for very useful suggestions. Simona Settepanella was partially supported by the Institute for New Economic Thinking, INET inaugural Grant \(\sharp\)220.

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Copyright information

© Japan Association for Evolutionary Economics 2015

Authors and Affiliations

  • Gennaro Amendola
    • 1
  • Luigi Marengo
    • 2
  • Davide Pirino
    • 3
  • Simona Settepanella
    • 4
  • Akimichi Takemura
    • 5
  1. 1.eCampus UniversityNovedrateItaly
  2. 2.Department of Business and ManagementLUISS UniversityRomeItaly
  3. 3.Scuola Normale SuperiorePisaItaly
  4. 4.Department of MathematicsHokkaido UniversitySapporoJapan
  5. 5.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan

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