Annals of Operations Research

, Volume 193, Issue 1, pp 273–289 | Cite as

Complete voting systems with two classes of voters: weightedness and counting

  • Josep Freixas
  • Xavier Molinero
  • Salvador Roura


We investigate voting systems with two classes of voters, for which there is a hierarchy giving each member of the stronger class more influence or important than each member of the weaker class. We deduce for voting systems one important counting fact that allows determining how many of them are for a given number of voters. In fact, the number of these systems follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. On the other hand, we classify by means of some parameters which of these systems are weighted. This result allows us to state an asymptotic conjecture which is opposed to what occurs for symmetric games.


Voting systems Simple games Weighted games Complete simple games Fibonacci sequence 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Josep Freixas
    • 1
  • Xavier Molinero
    • 1
  • Salvador Roura
    • 2
  1. 1.Dept. de Matemàtica Aplicada 3Universitat Politècnica de CatalunyaManresaSpain
  2. 2.Dept. de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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