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Unformatted text preview: of voters is called a coalition. De…nition
A coalition is said to be winning if passage is guaranteed by yes votes from
exactly the members of the coalition. Coalitions that are not winning are
losing. Example
In EEC, the coalition of France, Germany, and Italy is a winning coalition
whereas the coalition of France, Germany, and Luxembourg is a losing
coalition. Van Essen (U of A) Y/N 10 / 30 Coalitions
De…nition
If adding more voters to a winning coalition makes another winning
coalition, then the yesno voting system is said to be monotone.
For monotone yesno voting systems, one can concentrate on minimal
winning coalitions: those winning coalitions with the property that
deleting one member causes it to go from a winning coalition to a
losing coalition. Example
In EEC, the coalition of France, Germany, and Italy is a winning coalition,
but the winning coalition of France, Germany, Italy, and Luxembourg is
not. Van Essen (U of A) Y/N 11 / 30 Ways to describe a Yesno Voting System 1 One can specify the number of votes each player has and how many
votes are needed for passage. 2 One can explicitly list the winning coalitions. Every yesno system can
be described in this way. 3 One can use a combination of (1) and (2) with provisos which often
involve veto power. Van Essen (U of A) Y/N 12 / 30 Weighted Voting Systems De…nition
A yesno voting system is said to be a weighted voting system if it can be
described by specifying real number weights for the voters and a real
number quota – with no provisos or mention of veto power – such that a
coalition is winning precisely when the sum of the weights of the voters in
the coalition meets or exceeds the quota. Example
The EEC is a weighted voting system. Van Essen (U of A) Y/N 13 / 30 The U.N. Security Council is a Weighted Voting System It turns out that the UN Security Council is a weighted system. This
is surprising since the description of the voting system includes the
mention of veto power.
To show that a voting system is weighted one must produce weights
for each voter and a quota such that the winning coalitions are
precisely the ones whose weigh...
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This note was uploaded on 04/08/2014 for the course ECON 497 taught by Professor Vanessen during the Spring '12 term at Alabama.
 Spring '12
 Vanessen
 The Land

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