The Hoede-Bakker index modiﬁed to the Shapley-Shubik and Holler-Packel indices
AbstractWe present some modiﬁcations of the Hoede-Bakker index deﬁned in a social network in which players may inﬂuence each other. Due to inﬂuences of the other actors, the ﬁnal decision of a player may be diﬀerent from his original inclination. The modiﬁcations presented in the paper are deﬁned for an arbitrary probability distribution over all inclination vectors. In particular, they concern the situation in which the inclination vectors may be not equally probable. Furthermore, by assuming special probability distributions over all inclination vectors, we construct modiﬁcations of the Hoede-Bakker index that coincide with the Shapley- Shubik index and with the Holler-Packel index,respectively. We present a practical example in which the concepts in question are applied to Dutch parties, and a theoretical example in which we show how the modiﬁcations can be calculated.
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Date of creation: 2010
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Publication status: Published, Group Decision and Negotiation, 2010, 19, 6, pp. 543-569
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Hoede-Bakker index; inclination vector; probability distribution; Shapley-Shubik index; Holler- Packel index;
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- Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
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