B
ANZHAF
R
EVIEW
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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
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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
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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.