958 CHAPTER 14 Voting and Apportionment 7. How many children voted? 142 8. Which animal wins this election if the plurality method is used? Salamander 9. Which animal wins this election if the Borda count method is used? Iguana 10. Which animal wins this election if the plurality with elimination method is used? Hamster 11. Which animal wins this election if the pairwise comparison method is used? Lemming 12. Violating the Head-to-Head Criterion Which voting method(s)—plurality, Borda count, plurality with elimination, or pairwise comparison—violate the head-to-head criterion using the following election data? Plurality method, Borda count method, and plurality with elimination method Number of Votes 86 60 58 52 28 First W Y Z X X Second Y X X Z Z Third Z Z Y W Y Fourth X W W Y W 13. Voting for a Logo Design The park rangers in Yosemite National Park are holding a contest to choose a new logo design. The four logo choices for their stationery are El Capitan (E), a sequoia tree (S), a mule deer (M), and a waterfall (W). The 35 rangers rank their choices according to the following preference table. Number of Votes 18 10 4 3 First E M W S Second M W M M Third S E S E Fourth W S E W Using the data provided, does the Borda count method violate the majority criterion? Yes, El Capitan has a majority of first-place votes but mule deer wins. Apportioning Legislative Seats In Exercises 14–20, a country has three states and 30 seats in the legislature. The population of each state is shown in the following table. State A B C Total Population 6933 9533 16,534 33,000 14. Determine each state’s apportionment using Hamilton’s method. 6, 9, 15 15. Determine each state’s apportionment using Jefferson’s method. 6, 9, 15 16. Determine each state’s apportionment using Adams’ method. 6, 9, 15 17. Determine each state’s apportionment using Webster’s method. 6, 9, 15 18. If the number of seats in the legislature increases to 31, does the Alabama paradox occur using Hamilton’s method? No. The apportionment is 6, 9, 16. 19. Suppose that in 10 years the states have the following population and 30 seats are apportioned. If the seats are reapportioned, does the population paradox occur using Hamilton’s method? No. The apportionment is 6, 9, 15. State A B C Total Population 7072 9724 17,030 33,826 20. Suppose that a fourth state with the population shown in the table below is added, with five additional seats for a total of 35 seats. Does the new-states paradox occur using Hamilton’s method? No. The apportionment is 6, 9, 15, 5. State A B C D Total Population 6933 9533 16,534 5100 38,100
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