At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {4: 3, 2, 1}. In this voting system, the head coach A has a weight of 3, the assistant coach B has a weight of 2, and the junior varsity coach C has a weight of 1. The head coach has decided that next year the coaching staff should use the weighted voting system {10: 9, 8, 1}. The head coach is still voter A, the assistant coach is still voter B, and the junior varsity coach is still voter C. (a) Compute the Banzhaf power index for each coach under this new system. (Round your answers to the nearest hundredth.) BPI(A) = BPI(B) = BPI(C) = (b) How do the Banzhaf power indices for this new voting system compare with the first Banzhaf power indices? O Measured by the BPI, the head coach gained power. O Measured by the BPI, the assistant coach gained power. O Measured by the BPI, the junior varsity coach lost power. O The BPI of each coach remains the same. Did the head coach gain any power, according to the Banzhaf power indices, with this new voting system? O Yes O No

At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {4: 3, 2, 1}. In this voting system, the head coach A has a weight of 3, the assistant coach B has a weight of 2, and the junior varsity coach C has a weight of 1. The head coach has decided that next year the coaching staff should use the weighted voting system {10: 9, 8, 1}. The head coach is still voter A, the assistant coach is still voter B, and the junior varsity coach is still voter C. (a) Compute the Banzhaf power index for each coach under this new system. (Round your answers to the nearest hundredth.) BPI(A) = BPI(B) = BPI(C) = (b) How do the Banzhaf power indices for this new voting system compare with the first Banzhaf power indices? O Measured by the BPI, the head coach gained power. O Measured by the BPI, the assistant coach gained power. O Measured by the BPI, the junior varsity coach lost power. O The BPI of each coach remains the same. Did the head coach gain any power, according to the Banzhaf power indices, with this new voting system? O Yes O No

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 11CYU

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