New mathematical properties of the Banzhaf value

Dragan, Irinel

doi:10.1016/0377-2217(95)00292-8

Cited by 50 publications

(21 citation statements)

References 7 publications

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“…There are other characterizations of the Bz semivalue, but they are only valid in the domain of all TU-games (Dragan 1996;Owen 1982). We will mention only the one introduced by Owen (1982), where a proportionality axiom closely related to the one we have employed here is also used.…”

Section: Discussionmentioning

confidence: 99%

A new axiomatization of the Banzhaf semivalue

Albizuri¹,

Ruiz²

2001

Span Econ Rev

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A new characterization of the Banzhaf semivalue on the domain of monotonic simple games is given. We use the well-known valuation and dummy axioms plus two additional properties. The first one simply requires that the power-index be bigger for those players belonging to more winning coalitions. The second one is the proportionality axiom introduced by Owen in (1982) which is suitable for those simple games that represent an indirect voting process. JEL classification: C71

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Section: Discussionmentioning

confidence: 99%

A new axiomatization of the Banzhaf semivalue

Albizuri¹,

Ruiz²

2001

Span Econ Rev

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“…(For additional material on the Banzhaf value and the original Banzhaf power index, we refer the reader to Banzhaf 1965;Coleman 1971;Dubey and Shapley 1979;Lehrer 1988;Feltkamp 1995;Dragan 1996, andCarreras andFreixas 2000. ) We can then ask for similar indices that should reflect the protectionist viewpoint adopted along this paper.…”

Section: Blocking Power Indicesmentioning

confidence: 99%

Protectionism and blocking power indices

Carreras

2009

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“…also [18,17]) and gave rise later, among others, to the coalitional q-binomial total power property [10,3,11] and the p-multinomial total power property [12,13]. It reduces to this latter if B = B n but it also extends efficiency, to which it reduces if B = B N .…”

Section: Remark 313mentioning

confidence: 99%

Coalitional multinomial probabilistic values

Carreras

Puente

2015

European Journal of Operational Research

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We introduce a new family of coalitional values designed to take into account players' attitudes with regard to cooperation. This new family of values applies to cooperative games with a coalition structure by combining the Shapley value and the multinomial probabilistic values, thus generalizing the symmetric coalitional binomial semivalues. Besides an axiomatic characterization, a computational procedure is provided in terms of the multilinear extension of the game and an application to the Catalonia Parliament, Legislature 2003Legislature -2007, is shown.

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New mathematical properties of the Banzhaf value

Cited by 50 publications

References 7 publications

A new axiomatization of the Banzhaf semivalue

A new axiomatization of the Banzhaf semivalue

Protectionism and blocking power indices

Coalitional multinomial probabilistic values

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