Social Choice_Lecture 6_Yes-No Voting

Denition a coalition is said to be winning if passage

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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 yes-no voting system is said to be monotone. For monotone yes-no 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 Yes-no 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 yes-no 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 yes-no 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.

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