See problems 31 and 32 for information about the UN Security Council. Problems 31 and 3...

See problems 31 and 32 for information about the UN Security Council.

Problems 31 and 32:

The Security Council is a branch of the United Nations that is in charge of maintaining international peace and security. The Security Council is made up of five permanent member countries: the United States, China, France, the United Kingdom, and the Russian Federation. It also includes 10 countries elected for 2-year terms. On January 1, 2002, the 2-year terms began for Guinea, Mexico, Syrian Arab Republic, Bulgaria, and Cameroon. On January 1, 2003, the 2-year terms began for Angola, Chile, Germany, Pakistan, and Spain. When voting, every member has one vote, but in order for a resolution to pass, all five permanent members, as well as at least four of the elected members, must vote in favor of the resolution. If one permanent member votes against a resolution, then the resolution will not pass.

31. a. In 1997, a resolution to demand a halt to the construction of a new housing settlement in the Jabal Abu Ghneim area of East Jerusalem was put to a vote by the Security Council. There were 13 votes in favor, 1 vote against (made by the United States) and 1 abstention. Did the resolution pass or fail?

b. Suppose that only Pakistan, Germany, and Mexico vote against a resolution. Would the resolution pass or fail?

32. a. In 1997, the Security Council voted on a resolution involving a cease-fire in Guatemala. There were 14 votes in favor, 1 vote against (made by China) and 0 abstentions. Did the resolution pass or fail?

b. Suppose only Bulgaria, Cameroon, Chile, Angola, Spain, Pakistan, and Guinea vote against a resolution. Would this resolution pass or fail?

Each member of the UN Security Council has one vote, but each vote does not carry the same weight. Suppose we assign each elected member’s vote a weight of 1, and let w represent the weight of each permanent member’s vote. In order to pass a resolution, all five permanent members and at least four of the elected members must vote in favor of the resolution; thus, when 5w + 4 ≥ quota, the resolution will pass. On the other hand, a resolution will fail even if all 10 elected members vote in favor as long as one permanent member votes against a resolution; thus, when 4w + 10 < quota, the resolution will fail.

a. If we combine the inequalities, we have 4w +10 < 5w + 4. Solve, and determine the smallest whole number w that satisfies the inequality.

b. What is the smallest quota for the weighted voting system?

c. Express the weighted voting system using the proper notation.