Abstract
In this chapter, we provide a review of some recent results on power indices related to work done by the research group SaGaTh. We review axiomatic characterizations of several of the most important indices in the literature. Furthermore, we include a power index based on a desirability relation and two new power indices based on quasi-minimal winning coalitions. Finally, we summarize some results in other areas related with power indices.
This chapter is a reissue based on the work of José M. Alonso-Meijide, Balbina Casas-Méndez and M. Gloria Fiestras-Janeiro (2011), A review of some recent results on power indices, Essays in Honor of Hannu Nurmi, a special number of Homo Oeconomicus 28 (1/2): 143–159
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Notes
- 1.
In this research program more colleagues were involved. We specially want to thank our coauthors Mikel Álvarez-Mozos, Mario Bilbao, Carlos Bowles, Francesc Carreras, Joseph Freixas, Julio R. Fernández, Flavio Ferreira, Manfred J. Holler, Silvia Lorenzo-Freire, Stefan Napel, Andreas Nohn, Guillermo Owen, and Alberto Pinto for the discussions and contributions to this research topic. More information about members and working areas of the group is available in the website http://eio.usc.es/pub/io/xogos/.
- 2.
We will use shorthand notation and write \(S\cup i\) for the set \(S\cup \left\{ i\right\} \) and \(S\backslash i\) for the set \(S\backslash \left\{ i\right\} .\) We will denote by \(s\) the number of members in a finite set \(S\).
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Acknowledgments
We wish to thank the suggestions and comments of the referees. This research received financial support from Ministerio Español de Ciencia y Tecnología through Project ECO2008-03484-C02-02 and from Xunta de Galicia through Project INCITE09-207-064-PR.
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Alonso-Meijide, J., Casas-Méndez, B., Fiestras-Janeiro, M. (2013). A Review of Some Recent Results on Power Indices. In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_12
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