Annals of Operations Research

, Volume 222, Issue 1, pp 317–339 | Cite as

Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum

  • Josep Freixas
  • Sascha Kurz


This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class as well. Second, we focus on the special case of bipartite complete games with minimum, and we compare and rank these games according to the behavior of some efficient power indices of players of type 1 (or of type 2). The main result of this second part establishes all allowable rankings of these games when the Shapley-Shubik power index is used on players of type 1.


Simple game Weighted and complete games Enumerations Shapley-Shubik power index Banzhaf power indices 



The authors are grateful to the two referees of this paper for their interesting comments and also for their exhaustive reports that contributed to improve the original submitted version.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics III and High Engineering School (Manresa Campus)Technical University of CataloniaBarcelonaSpain
  2. 2.Department of Mathematics, Physics and Computer ScienceUniversity of BayreuthBayreuthGermany

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