a. Verify that the weighted voting systems [ 12 : 7 , 4 , 3 , 2 ] and [ 24 : 14 , 8 , 6 , 4 ] result in exactly the same Banzhaf power distribution. (If you need to make calculations, do them for both systems side by side and look for patterns.). b. Based on your work in (a), explain why the two proportional weighted voting systems [ q : w 1 , w 2 , ... , w N ] and [ c q : c w 1 , c w 2 , ... , c w N ] always have the same Banzhaf power distribution.
a. Verify that the weighted voting systems [ 12 : 7 , 4 , 3 , 2 ] and [ 24 : 14 , 8 , 6 , 4 ] result in exactly the same Banzhaf power distribution. (If you need to make calculations, do them for both systems side by side and look for patterns.). b. Based on your work in (a), explain why the two proportional weighted voting systems [ q : w 1 , w 2 , ... , w N ] and [ c q : c w 1 , c w 2 , ... , c w N ] always have the same Banzhaf power distribution.
Solution Summary: The author explains how the Banzhaf power distribution gives a complete distribution of the contribution of every player in the voting system.
a. Verify that the weighted voting systems
[
12
:
7
,
4
,
3
,
2
]
and
[
24
:
14
,
8
,
6
,
4
]
result in exactly the same Banzhaf power distribution. (If you need to make calculations, do them for both systems side by side and look for patterns.).
b. Based on your work in (a), explain why the two proportional weighted voting systems
[
q
:
w
1
,
w
2
,
...
,
w
N
]
and
[
c
q
:
c
w
1
,
c
w
2
,
...
,
c
w
N
]
always have the same Banzhaf power distribution.
During busy political seasons, many opinion polls are conducted. In apresidential race, how do you think the participants in polls are generally selected?Discuss any issues regarding simple random, stratified, systematic, cluster, andconvenience sampling in these polls. What about other types of polls, besides political?
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Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL