On the Felsenthal Power Index

Josep Freixas () and Dani Samaniego ()
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Josep Freixas: Departament de Matemàtiques de la Universitat Politècnica de Catalunya
Dani Samaniego: Departament de Matemàtiques de la Universitat Politècnica de Catalunya

Group Decision and Negotiation, 2023, vol. 32, issue 6, No 1, 1273-1288

Abstract: Abstract The paper that introduces the Felsenthal index is titled: ‘A well-behaved index of a priori P-Power for simple n-person games.’ In 2016, Felsenthal introduced his index for simple games. His definition does not base on the axiomatic approach. Then, Felsenthal regarded some properties and proved that his index satisfies a list of six reasonable and compelling postulates. Three of the properties that he regarded refer to the weighted games, but this fact does not reduce the definition of his index to weighted games. He proves that none of seven well-known efficient power indices proposed to date satisfies the list of postulates, indicating for each of them which of the six postulates violate. In this paper we extend some of his postulates, originally defined for weighted games, to simple games. The main objective of the article is to answer three open questions motivated in his article. In particular, we prove that his index may not be the unique one fulfilling the six proposed postulates, provide an axiomatic characterization for his index and, propose an impossibility result, which is obtained by adding a new postulate to a sublist of the postulates he considered. We also remark the existence of some alternative compelling postulates which are not satisfied for the index.

Keywords: Distribution of an asset; Efficient power indices; Decision and negotiation; Fair distributions among agents (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10726-023-09843-z

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