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Wednesday April 13
th
Banzef weighted voting
Concerned with how weighting affects power distribution ( sometimes it does not)
the total number is 7
(3,2,2)
so the Decision rule
is 4
and the minimum winning coalition is the minimum number of partners where one
defection can defeat the coalition so we rewrite
(4;3,2(i),2(ii)
so most people see player 3 as the most influential; Banzef does not thinks so
the minimum winning coalitions are as follow for
(4;3,2(i),2(ii) )
(3,2(i) )
(3,2(ii) )
(2(ii),2(i) )
But the grand coalition is not a minimum winning coalition
((3,2(ii), 2(i) )
so in a table showing the critical defectors ( can they affect it)
the decision rule is the minimum win number 4
3 is it a critical
defector
2(i) is it a
critical
defector
(2(ii)is it a
critical
defector
(3,2(i)
X
X
(3,2(ii)
X
X
(2(i),(2(ii)
X
X
Total number
of critical
defectors
2 OUT OF 6
or .33 is the
banzef index
2 OUT OF 6
or .33 is the
banzef index
2 OUT OF 6
or .33 is the
banzef index
so the three vote member is no more critical than the other 2 members so even
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This note was uploaded on 05/04/2011 for the course POLITICS V53.0810 taught by Professor Stevenjbrams during the Spring '11 term at NYU.
 Spring '11
 stevenjbrams

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