ANSWERS A-47 SECTION 14.4, PAGE 951 8. b) Yes. If the number of printers is increased, office B loses a printer, where as offices C and D gain a printer. 13. 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. b) Yes. The apportionment is now 9, 39, 7, and group B loses a manager. REVIEW EXERCISES, PAGE 954 3. 10. Number of Votes 2 3 2 1 First D C B C Second B D D B Third C B C D 62. a) If there were only two columns, only two of the candidates were the first choice of the voters. If each of the 15 voters cast a ballot, one of the voters must have received a majority of votes because 15 cannot be split evenly. b) An odd number cannot be divided evenly, so one of the two first-choice candidates must receive more than half of the votes. SECTION 14.2, PAGE 922 16. No. C wins by plurality with elimination, but A is favored over each of the other candidates using head-to-head comparisons. 21. No. C wins by plurality with elimination. If the voters change their preference, B wins by plurality with elimination. 22. No. B wins by plurality with elimination. If the voters change their preference, A wins by plurality with elimination. 23. Yes. D wins by pairwise comparison. If the voters change their preference, D still wins by pairwise comparison. 24. Yes. A wins by the Borda count method. If the voters change their preference, A still wins by the Borda count method. 25. No. B wins by pairwise comparison. If A, C, and E drop out, D wins by pairwise comparison. SECTION 14.3, PAGE 942 46. Answers will vary. One possible answer is A: 3,250,000, B: 1,750,000, C: 2,265,000, D: 2,735,000 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 31. No. B wins by the Borda count method, but A is preferred over each of the other candidates using head-to-head comparisons. 32. c) No. If B drops out, A is the winner by plurality with elimination. Therefore, the irrelevant alternatives criterion is not satisfied. 33. f) Plurality method, Borda count method, and plurality with elimination method all violate the head-to-head criterion.
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