A weighted voting system for voters A, B, C, D, and E is given by {35: 29, 11, 8, 4, 2}. The weight of voter A is 29, the weight of voter B is 11, the weight of voter C is 8, the weight of voter D is 4, and the weight of voter E is 2. a. What is the quota? b. What is the weight of the coalition {A, D, E}? c. Is {A, D, E} a winning coalition? d. Which voters are critical voters in the coalition {A, C, D, E}? e. How many coalitions can be formed? f. How many coalitions consist of exactly two voters?
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Given weighted voting system is: { 35: 29,11, 8, 4, 2 }
(a) Quota of the given voting system is 35.
(b) Weight of the coalition {A, D, E} = 29+4+2= 35
(c) Yes, {A, D, E} is a winning coalition because its weight is equal to quota.
(d) Critical voter in the coalition {A, C, D, E) is voters A.
(e) Total number of coalitions formed is 2n - 1 where n is number of voters. Therefore,
Total number of coalitions formed = 25 — 1 = 32 - 1 = 31
(f) There are 10 coalitions consist of exactly two voters. i.e. {A,B}, {A,C}, {A,D}, {A,E}, {B,C}, {B, D}, {B, E}, {C, D}, {C, E} and {D, E)