14.4 Flaws of the Apportionment Methods 945 Just as we have discovered that voting methods can have flaws, apportionment methods can also have flaws. In this section, as we did in Section 14.2 with voting methods, we will consider several reasonable properties that an apportionment method should have. Then we will see examples in which these properties are violated. Problems with apportionment can occur in a variety of ways. Population changes, changes in the number of items to be apportioned, and the addition of one or more groups can lead to problems with apportionment. Recall from Section 14.3 that the quota rule states that an apportionment for every group under consideration should always be either the upper quota or the lower quota. Hamilton’s method, which satisfies the quota rule, would appear to be a reasonable and fair apportionment method. As we will discuss in this section, though, Hamilton’s method can result in some serious flaws. Recall from Section 14.3 the situation in which a college receives a grant to purchase 50 laptops that will be placed in four different libraries on campus. Suppose that before the laptops are purchased the price of the laptops decreases enough so that 51 laptops can now be purchased and apportioned to the four libraries. Because of a flaw in the apportionment method to be used, it is possible that one of the libraries would receive fewer laptops with 51 laptops being apportioned than with 50 laptops being apportioned. In this section, we will discuss this flaw and other flaws with apportionment methods. Flaws of the Apportionment Methods SECTION 14.4 LEARNING GOALS Upon completion of this section, you will be able to: 7 Determine if a given apportionment demonstrates the Alabama paradox. 7 Determine if a given apportionment demonstrates the population paradox. 7 Determine if a given apportionment demonstrates the new-states paradox. Why This Is Important With each new census taken, the number of representatives in the United States Congress allocated to various states may change. How these representatives are assigned can make an important difference in the laws and bills that are passed. b) Determine the apportionment that was used with Jefferson’s method. 7, 1, 2, 2, 8, 14, 4, 5, 10, 10, 13, 2, 6, 2, 19 c) Compare the apportionments from parts (a) and (b). Which state(s) benefited from Jefferson’s method? Which state(s) were at a disadvantage from Jefferson’s method? Benefited: Virginia; Disadvantage: Delaware 46. Legislative Seats A country with a population of 10,000,000 has 250 legislative seats to be apportioned among four states, where each state has a different population. Determine a population for each state in which Hamilton’s method, Jefferson’s method, Webster’s method, and Adams’ method all lead to the same apportionment of the 250 legislative seats. Many answers are possible. * 47. Police Officers A police department has 210 new officers to apportion among six precincts. The department plans to apportion the officers based on the number of crimes committed during the previous year in each precinct. Suppose that the number of crimes committed in each precinct is different and that the total number of crimes committed in all six precincts was 2940. Determine the number of crimes committed in each precinct such that Hamilton’s method, Jefferson’s method, Webster’s method, and Adams’ method all lead to the same apportionment of the 210 new officers. Many answers are possible. Answers will vary. One possible answer is A: 743, B: 367, C: 432, D: 491, E: 519, F: 388. Research Activities 48. House of Representatives Do research and write a report on the apportionment method used in the House of Representatives in 1872. Include in your report a description of the method used. 49. Huntington–Hill Method Do research and write a report on the Huntington–Hill method, also known as the method of equal proportions, the current method used to apportion the representatives in the House of Representatives. Include historical background and describe how the method works. *See Instructor Answer Appendix Jasminko Ibrakovic/Shutterstock
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