Banzhaf Review

Banzhaf Review - BANZHAF REVIEW PAGE 1 OF 2 PAGES 5/12/2008...

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B ANZHAF R EVIEW PAGE 1 OF 2 PAGES 5/12/2009 1. A senate with nine Red party members, nine Green party members, and one independent decides issues by simple majority according to the model [ ] . 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 : 10 Prior to any vote, the nine Reds caucus and decide to vote as a bloc of nine, deciding on their vote by simple majority according to the model [ ] , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 : 5 and the nine Greens also caucus and vote as a bloc of nine, also deciding in caucus according to the same simple majority model. The independent is not bound by any caucus and therefore decides on his vote all by himself. a. If A is a Red senator, describe all the winning coalitions in which A is critical. How many are there? The answer is the Banzhaf power of each Red senator, and obviously also of each Green senator. b. If B is the independent senator, describe all winning coalitions in which B is critical. How many are there? The answer is the Banzhaf power of the independent senator. c.
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Banzhaf Review - BANZHAF REVIEW PAGE 1 OF 2 PAGES 5/12/2008...

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