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The Owen and the Owen-Banzhaf Values Applied to the Study of the Madrid Assembly and the Andalusian Parliament in Legislature 2015-2019

“…In a similar way and according to Lemma 3.1, for u {1,2,4,5,6,7} we obtain The computing technique based on the multilinear extension has been applied to many coalitional values: to the Owen value in (Owen and Winter, 1992); to the Owen-Banzhaf value in (Carreras and Magana, 1994); to the quotient game in (Carreras and Magana, 1997); to the coalitional semivalues in (Amer and Giménez, 2003); to the Alonso-Fiestras value in (Alonso et al, 2005); to the symmetric coalitional binomial semivalues in (Carreras and Puente, 2011); and to the coalitional multinomial probabilistic values in (Carreras and Puente, 2013). In next theorems we present a new method to compute the Owen and the Owen-Banhaf values by means of the multilinear extension of the game.…”

“…The multilinear extension of a cooperative game was introduced in (Owen, 1972) and then it was applied to the calculus of the Shapley value. The computing technique based on the multilinear extension has been applied to many values: to the Banzhaf value in (Owen, 1975); to the Owen value in (Owen and Winter, 1992); to the Owen-Banzhaf value in (Carreras and Magana, 1994); to the quotient game in (Carreras and Magana, 1997); to the binomial semivalues and multinomial probabilistic indices in (Puente, 2000); to the coalitional semivalues in (Amer and Giménez, 2003); to the α-decisiveness and Banzhaf α-indices in (Carreras, 2004); to the Alonso-Fiestras value in (Alonso et al, 2005); to the symmetric coalitional binomial semivalues in (Carreras and Puente, 2011); to all semivalues in (Carreras and Giménez, 2011); and to coalitional multinomial probabilistic values in (Carreras and Puente, 2013).…”