Consider the weighted voting system (17: 15, 8, 4, 3). (a) Fill in the table below. If a coalition does not win, use O for the number of critical players. Coalition (P1, P2, P3, P4} Weight Number of Critical Players (P1, P2, P3} (P1, P2, P4} {P1, P3, P4} {P2, P3, P4} (P1, P2) (P1, P3} {P1, P4} (P2, P3) {P2, P4} {P3, P4} (b) Find the Banzhaf score (critical count) for each player: P1: P2: P3: ☐ P4: (c) Find the Banzhaf index for each player (please enter your answer as a fraction): P1: P2: P3: P4:

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 12CYU
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Consider the weighted voting system (17: 15, 8, 4, 3}.
(a) Fill in the table below. If a coalition does not win, use O for the number of critical players.
Coalition
(P1, P2, P3, P4}
Weight Number of Critical Players
{P1, P2, P3}
{P1, P2, P4}
{P1, P3, P4}
{P2, P3, P4}
(P1, P2)
(P1, P3)
(P1, P4}
{P2, P3)
{P2, P4}
(P3, P4}
(b) Find the Banzhaf score (critical count) for each player:
P1: P2:
P3:
P4:
(c) Find the Banzhaf index for each player (please enter your answer as a fraction):
P1: P2: P3: P4:
Transcribed Image Text:Consider the weighted voting system (17: 15, 8, 4, 3}. (a) Fill in the table below. If a coalition does not win, use O for the number of critical players. Coalition (P1, P2, P3, P4} Weight Number of Critical Players {P1, P2, P3} {P1, P2, P4} {P1, P3, P4} {P2, P3, P4} (P1, P2) (P1, P3) (P1, P4} {P2, P3) {P2, P4} (P3, P4} (b) Find the Banzhaf score (critical count) for each player: P1: P2: P3: P4: (c) Find the Banzhaf index for each player (please enter your answer as a fraction): P1: P2: P3: P4:
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