CHAPTER 14 Test 957 40. Determine each region’s apportionment using Adams’ method. 4, 3, 3 41. Determine each region’s apportionment using Webster’s method. 5, 2, 3 42. Suppose that the post office purchases one additional truck. Using Hamilton’s method, does the Alabama paradox occur if the number of trucks is increased from 10 to 11? Yes. The apportionment is 5, 2, 4. Region B loses one truck. Apportioning Biology Sections In Exercises 43– 47, Miami Dade College plans to offer 23 sections of three different biology courses: Anatomy and Physiology (A), Introduction to Biology (B), and Biochemistry (C). The sections will be apportioned based on preregistration as shown in the table below. Course A B C Total Number of students 311 219 160 690 43. Determine the apportionment for each course using Hamilton’s method. 11, 7, 5 44. Determine the apportionment for each course using Jefferson’s method. 11, 7, 5 45. Determine the apportionment for each course using Adams’ method. 10, 7, 6 46. Determine the apportionment for each course using Webster’s method. 11, 7, 5 47. Suppose that the following table shows the final registration for each course. If the 23 sections are reapportioned using Hamilton’s method, does the population paradox occur? No. The apportionment with the additional population is still 11, 7, 5. Course A B C Total Number of students 317 219 162 698 Apportioning Seats In Exercises 48–52, a country has two states, A and B, and 50 seats in the legislature. The population of each state is shown in the table below. State A B Total Population 4420 45,580 50,000 48. Determine each state’s apportionment using Hamilton’s method. 4, 46 49. Determine each state’s apportionment using Jefferson’s method. 4, 46 50. Determine each state’s apportionment using Adams’ method. 5, 45 51. Determine each state’s apportionment using Webster’s method. 4, 46 52. Suppose that a third state, C, with the population shown in the table below, is added along with five new seats. Does the new-states paradox occur using Hamilton’s method? State A B C Total Population 4420 45,580 5400 55,400 Yes. The new apportionment is 5, 45, 5. State B loses a seat. Test CHAPTER 14 Lunch Choices In Exercises 1– 6, the employees of an advertising firm are planning to have lunch delivered to a meeting. Their choices are deli sandwiches (D), pizza (P), and burgers (B). The preference table follows. Number of Votes 4 3 3 2 First D P B P Second P B D D Third B D P B 1. How many members voted? 12 2. Does any choice have a majority of votes? No 3. Determine the winner using the plurality method. Pizza 4. Determine the winner using the Borda count method. Pizza 5. Determine the winner using the plurality with elimination method. Deli sandwiches 6. Determine the winner using the pairwise comparison method. Deli sandwiches Favorite Animal In Exercises 7–11, the children of Happy Faces Preschool are voting on their favorite classroom animal. The choices are hamster (H), iguana (I), lemming (L), and salamander (S). The results of the election are given in the following preference table. Number of Votes 43 30 29 26 14 First S L I H H Second L H H I I Third I I L S L Fourth H S S L S
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