956 CHAPTER 14 Voting and Apportionment Number of Votes 34 24 23 21 12 First P R N B B Second R B B N N Third N N R P R Fourth B P P R P a) Which brand is favored over all others in a head-to-head comparison? Ragu b) Which brand wins if the plurality method is used? Prego c) Which brand wins if the Borda count method is used? Tie between Newman’s Own and Barilla d) Which brand wins if the plurality with elimination method is used? Barilla e) Which brand wins if the pairwise comparison method is used? Ragu f) Which voting method(s) in parts (b) through (e) violate the head-to-head criterion? * 34. Selecting a Band The Southwestern High School Class of 1986 is organizing its 35-year class reunion and is trying to pick out a band to play at the reunion. The choices are REO Speedwagon (R), Boston (B), Journey (J), and Fleetwood Mac (F). The class members have ranked their choices as indicated in the following preference table. Number of Votes 34 25 15 9 4 First B F R J J Second F J J R R Third R R F B F Fourth J B B F B a) Is one band favored over all others in a head-to-head comparison? Yes, Fleetwood Mac b) Which band is chosen if the plurality method is used? Boston c) Which band is chosen if the Borda count method is used? Fleetwood Mac d) Which band is chosen if the plurality with elimination method is used? REO Speedwagon e) Which band is chosen if the pairwise comparison method is used? Fleetwood Mac f) Which voting methods in parts (a) through (e) violate the head-to-head criterion? The plurality method and the plurality with elimination method 35. Violating the Majority Criterion Which voting method(s) violate the majority criterion in the following election data? The Borda count method Number of Votes 36 20 8 6 First A B C D Second B C B B Third D A D A Fourth C D A C 36. Violating the Monotonicity Criterion Using the following tables, determine which voting method(s) violate the monotonicity criterion. First Election Number of Votes 28 24 20 10 First A B C C Second C A B A Third B C A B Second Election Number of Votes 36 24 20 2 First A B C C Second C A B A Third B C A B The plurality with elimination method 37. Violating the Irrelevant Alternatives Criterion Using the following table, determine which voting method(s) violates the irrelevant alternatives criterion. Assume that candidate D drops out prior to the conclusion of the election. Number of Votes 24 16 16 16 8 4 5 First B B E C A D D Second A A A D E B E Third D E C E D A A Fourth E C D B B E B Fifth C D B A C C C The pairwise comparison method and the Borda count method 14.3, 14.4 Postal Service Apportionment In Exercises 38– 42, a post office in the city of Riverside has three regions in which to distribute the mail and 10 new mail trucks. The trucks are to be apportioned based on the number of houses in each region, as shown in the table below. Region A B C Total Number of houses 2592 1428 1980 6000 38. Determine each region’s apportionment using Hamilton’s method. 4, 3, 3 39. Determine each region’s apportionment using Jefferson’s method. 5, 2, 3 *See Instructor Answer Appendix
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