Practice Test Questions Instructions: Show necessary work. 1. Acounty is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. Find the rounded quota for the Hillcrest district. b) 3 ) Old Tewn 19,682 c) 2 9 o9 Wison il | 908 fi 4 2. The given table shows the preference schedule for an election with four candidates (Alina, Beatriz, Candice and Diane). Use the plurality method to find the complete ranking of the candidates. Choose the correct answer below. a) CLABD b) A,D,C,B c) D,CAB d) D,B,CA e)] CLB,AD f) MNone of the above answers. 3. Consider a four person weighted voting system with voters A, B, C and D. The winning coalitions are: {A.B.C,D}, {A,B,C}, {A,B,D}, {A,C,D}and {4, B). From this information we know that: a) Dis a dummy voter. b) Cand D are both dummy voters. c) Ais a dictator. d) A has veto power. e) A and B have veto power. 4. Given the weighted voting system [15: 7,7,6,5,3], in which sequential coalition is the last player (Ps) pivotal? a) {77,653} b) {7,5,7.3.6) c) {53,677} d) {6,53,7,7) e) {57,367} f} MNone of the above. 5. Consider the following weighted voting system [13: 11, 10, 2, 1]. In coalition {P1, P3, PA], which players are critical? a) A. P1, P3 and PA b) B. P, and P3 c) C. P, and PA d) D. P, only e) E. None of them are critical. 6. Consider the weighted voting system [q: 38, 27,19,16]. Assume that this system has no dictators and that q is at minimum a majority. For what values of the quota is {P], P3) a winning coalition? a) {P1, P3] is always a losing coalition. b) 51 through 100 c) 38 through 57 d) 51 through 57 e) None of the above answers. 7. The given table shows the preference schedule for an election with four candidates ( A, B, C, and D). Use the plurality-with-elimination to find the complete ranking of the candidates. Choose the correct answer. a) D, A, C, B Number of Voters 21 17 11 8 6 1 b) B, D, A, C 1st D BAACA C) B, D, C, A 2nd A C CB DB 3rd C d) A, D, B, C A B CBD 4th B D D D AC e) None of the above answers. 8. An election is held to choose the chair of a department at a university. There are 5 candidates. The preference schedule is given. How many first-place votes are needed for a simple majority selection? Number of Voters 47 38 19 a) 71 15 12 9 b) 70 1st choice B A F A C c) 47 d) 94 2nd choice C F B D e) 93 f) None of the above answers. 3d choice E D E E 4" choice D 5" choice 4 A A9. If the initial calculations leading to Webster's apportionment result in an over-apportionment of seats, what would be the best thing to do next? a) Use a randomly chosen divisor. b) A seat is taken from the state with the smallest residue. c) A seat is taken from the state with the largest quota. d) Modify the divisor by choosing a divisor that is smaller than the standard divisor. e) Modify the divisor by choosing a divisor that is larger than the standard divisor. 10. A small country consists of five regions: Nairobi, Sila, Mandoul, Kanem, and Emnedi. According to the country's constitution, the 120 seats in the legislature are fairly distributed to the states according to their populations. This table shows each state's standard quota. Find the apportionment using Hamilton's method. State N S M K E Standard quota 38.66 29.87 20.3 17.9 13.27 a) Nairobi > 38 Sila > 29 Mandoul > 20 Kanem > 17 Emnedi > 13 b) Nairobi -> 39 Sila > 30 Mandoul > 21 Kanem > 18 Emnedi > 14 c) Nairobi > 39 Sila > 30 Mandoul > 20 Kanem > 17 Emnedi > 13 d) Nairobi > 38 Sila > 30 Mandoul > 20 Kanem > 18 Emnedi > 13 e) Nairobi > 39 Sila > 30 Mandoul > 20 Kanem > 18 Emnedi > 13 11. Determine the pairwise comparison winner. Rank 33 voters 26 voters 20 voters 17 voters 16 voters 10 voters First choice Fernando Roger Emily Emily Roger Lisa Second choice Lisa Lisa Roger Lisa Fernando Emily Third choice Emily Emily Lisa Fernando Lisa Fernando Fourth choice Roger Fernando Fernando Roger Emily Roger a) Emily b) Roger c) Lisa d) Fernando e) It is a tie 12. Determine the Shapley Shubik and Banzhaf power distribution for [8: 5, 4, 3] a) 01 = $,02 =2,03 = =. The Banzhaf power distribution is the same. 1 b) 01 = 7,02 =;,03 = 0. The Banzhaf power distribution is the same. INNI c) = =,02= 2,03 = 2 B1 = . B2 = =. B3= NINGIN 1) G=02 =03 = BBB=13. Which of the statement(s) is true about the given graph? a) It has an Euler path. b) It has an Euler circuit. c) It has a bridge. d) Both (b) and (c) e) Both (a) and (c) 14. Which of the following describes an Euler path in the given graph? B a) A, B, C, D, F, E, C, A, G, F, A, D b) G, A, B, C, D, F, E, C, A, F, D, A, G, F A c) G, F, E, C, D, A, B d) B, A, D, F, G, C, E e) None of the above. )An Euler path is not possible in the given graph. 15. How many edges must be added to the following graph in order to optimally Eulerize it? A a) 0 b ) c) N d) 3 e) 4 f) More than 4