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Journal of Difference Equations and Applications Volume 17, 2011 - Issue 7: Dynamics, Games and Applications I. In honour of Mauricio Peixoto and David Rand
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Original Articles

Two new power indices based on winning coalitions

J. M. Alonso-Meijide Department of Statistics and Operations Research, Faculty of Sciences of Lugo, University of Santiago de Compostela, Santiago de Compostela, Spain
,
F. Ferreira ESEIG, Instituto Politécnico do Porto, Rua D. Sancho I, 981, 4480-876, Vila do Conde, PortugalCorrespondence[email protected]
,
M. Álvarez-Mozos Department of Statistics and Operations Research, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain
&
A. A. Pinto Departamento de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal
Pages 1095-1100 | Received 10 Mar 2009, Accepted 14 Jul 2009, Published online: 21 Jul 2011
 
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Abstract

Deegan and Packel (1979) and Holler (1982) proposed two power indices for simple games: the Deegan–Packel index and the Public Good Index. In the definition of these indices, only minimal winning coalitions are taken into account. Using similar arguments, we define two new power indices. These new indices are defined taking into account only those winning coalitions that do not contain null players. The results obtained with the different power indices are compared by means of two real-world examples taken from the political field.

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Acknowledgements

This research received financial support from the Spanish Ministry of Science and Innovation and FEDER through Project ECO2008-03484-C02-02/ECON, from the FPU program of the Spanish Ministry of Science and Innovation, from Fundação Calouste Gulbenkian and from Programs POCTI and POCI by FCT and MCTES. F. Ferreira thanks ESEIG/IPP and CMUP for their financial support. A.A. Pinto also thanks Centro de Matemática da Universidade do Minho for its financial support.

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