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, Volume 22, Issue 2, pp 658–673 | Cite as

A generating functions approach for computing the Public Good index efficiently

  • Michela ChessaEmail author
Original Paper

Abstract

In the past years, a combinatorial method based on generating functions was introduced to compute Shapley–Shubik, Banzhaf and other indices for weighted majority games exactly and efficiently. In this paper, taking inspiration from what has already been done, in view of the efficiency of the generating functions method, we define a generating function for computing the Public Good index, maintaining the property of exactness of the resulting algorithm. The main difference with the existing algorithms derives from the fact that the Public Good index takes into account only minimal winning coalitions and counts how many swings of a player involve them. Moreover, we study the computational complexity of the algorithm and we evaluate the Public Good index for the vote share of the Russian Duma in 1995.

Keywords

Public Good index Generating functions Minimal winning coalitions 

Mathematics Subject Classification (2000)

91A12 

Notes

Acknowledgements

The author thanks Vito Fragnelli for some useful discussions and two anonymous referees for the interesting suggestions.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MilanMilanItaly

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