ANSWERS A-51 32. a) C wins the election by plurality with elimination. b) When the order is changed A wins. Therefore, the monotonicity criterion is not satisfied. c) No. If B drops out, A is the winner by plurality with elimination. Therefore, the irrelevant alternatives criterion is not satisfied. 33. a) Ragu b) Prego c) Tie between Newman’s Own and Barilla d) Barilla e) Ragu f) Plurality method, Borda count method, and plurality with elimination method all violate the head-to-head criterion. 34. a) Yes, Fleetwood Mac b) Boston c) Fleetwood Mac d) REO Speedwagon e) Fleetwood Mac f) The plurality method and the plurality with elimination method 35. The Borda count method 36. The plurality with elimination method 37. The pairwise comparison method and the Borda count method 38. 4, 3, 3 39. 5, 2, 3 40. 4, 3, 3 41. 5, 2, 3 42. Yes. The apportionment is 5, 2, 4. Region B loses one truck. 43. 11, 7, 5 44. 11, 7, 5 45. 10, 7, 6 46. 11, 7, 5 47. No. The apportionment with the additional population is still 11, 7, 5. 48. 4, 46 49. 4, 46 50. 5, 45 51. 4, 46 52. Yes. The new apportionment is 5, 45, 5. State B loses a seat. CHAPTER TEST, PAGE 957 1. 12 2. No 3. Pizza 4. Pizza 5. Deli sandwiches 6. Deli sandwiches 7. 142 8. Salamander 9. Iguana 10. Hamster 11. Lemming 12. Plurality method, Borda count method, and plurality with elimination method 13. Yes, El Capitan has a majority of first-place votes but mule deer wins. 14. 6, 9, 15 15. 6, 9, 15 16. 6, 9, 15 17. 6, 9, 15 18. No. The apportionment is 6, 9, 16. 19. No. The apportionment is 6, 9, 15. 20. No. The apportionment is 6, 9, 15, 5. 13. a) 7, 16, 9, 11, 11 b) Yes. Division B loses a printer to division A even though the population of division B grew faster than the population of division A. 15. a) 8, 40 b) Yes. The apportionment is now 9, 39, 7, and group B loses a manager. 17. a) 7, 26 b) No. The apportionment is 7, 26, 7. REVIEW EXERCISES, PAGE 954 1. a) Comstock b) No 2. a) Michelle b) Yes 3. Number of Votes 3 2 1 1 3 First B A D D C Second A C C A B Third C D A B A Fourth D B B C D 4. Number of Votes 2 2 2 1 First C A B C Second A C A B Third B B C A 5. 11 6. Chipotle Mexican Grill 7. Domino’s Pizza 8. Chipotle Mexican Grill 9. Three-way tie, no winner 10. Chipotle Mexican Grill 11. 110 12. Volleyball 13. Soccer 14. Volleyball 15. None, a three-way tie 16. Soccer 17. Yes, American Music 18. American Music 19. American Music 20. American Music 21. American Music 22. No 23. Seattle 24. Las Vegas 25. Las Vegas 26. Las Vegas 27. A tie between Chronicles of Narnia and Where on Earth Is Carmen Sandiego? 28. Where on Earth Is Carmen Sandiego? 29. A tie between Chronicles of Narnia and Where on Earth Is Carmen Sandiego? 30. No. A has a majority, but B wins by the Borda count method. 31. No. B wins by the Borda count method, but A is preferred over each of the other candidates using head-to-head comparisons.
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