14.3 Apportionment Methods 929 received a number of representatives based on its population. Article 1, Section 2, of the Constitution of the United States includes the statement “Representatives shall be apportioned among the several states according to their respective numbers.” What the constitution did not say is how the apportionments are determined. In this section, we will discuss four different apportionment methods. The goal of apportionment is to determine a method to allocate the total number of items to be distributed in a fair manner. One of the most important examples of apportionment is in determining the representation of governing bodies. However, any time a fixed number of undividable items must be distributed to multiple entities, it can be considered an apportionment problem. Some examples include determining how many police officers should be assigned to each precinct in a city or determining how many nurses should be assigned to each shift at a hospital. In this section, we will discuss four different apportionment methods: 1. Hamilton’s method 2. Jefferson’s method 3. Webster’s method 4. Adams’ method We begin by considering a problem facing First Physicians Organization, a healthcare provider that operates five medical clinics. The organization has recently hired 60 doctors. Since the clinics do not all serve the same number of patients, the organization decides to apportion the 60 doctors based on the number of patients who visit each clinic in a given week, as shown in Table 14.25. Table 14.25 First Physicians Organization Clinic A B C D E Total Patients 246 201 196 211 226 1080 If the organization wants to distribute the doctors based on the number of patients served at each clinic, it would take each clinic’s number of patients served and divide it by the total number of patients. For example, clinic A would be entitled to , 246 1080 or 22 %, 7 9 of the doctors. Similarly, clinic B would be entitled to , 201 1080 or 18 %, 11 18 of the doctors and so on. Dividing the number of patients at each clinic by the total number of patients leaves a fractional part of a doctor. Since a clinic cannot have a fraction of a doctor, the organization has a problem. How can it apportion the doctors so that each clinic receives its fair allotment? Before we discuss how to apply apportionment methods, we will introduce some important terms used in this section, standard divisor and standard quota . The standard divisor is determined by dividing the total population under consideration by the number of items to be allocated. The total population in the previous illustration is the 1080 patients given in Table 14.25. Did You Know? Too Young to Run for Congress According to the United States Constitution, a senator must be at least 30 years of age, a U.S. citizen for at least 9 years, and a resident of the state in which they are elected. If you do not want to wait until you are 30 years old to become a member of Congress, you may run for office in the House of Representatives. Members of the House must be at least 25 years of age, a U.S. citizen for at least 7 years, and a resident of the state in which they are elected, but not necessarily a resident of the congressional district they hope to represent. Standard Divisor To obtain the standard divisor when determining apportionment, use the following formula. Standard divisor total population number of items to be allocated = For our doctor problem, the standard divisor is determined as follows: Standard divisor total number of patients number of doctors to be allocated 1080 60 18 = = = The standard quota for a particular group is determined by dividing the population of the group by the standard divisor. Richard Ellis/Alamy Stock Photo
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