930 CHAPTER 14 Voting and Apportionment For our doctor problem, the standard quota for clinic A is determined as follows: Standard quota for clinic A number of patients at clinic A standard divisor 246 18 13.67 = = ≈ We will round all standard divisors and standard quotas to the nearest hundredth. Standard Quota To obtain the standard quota when determining apportionment, use the following formula. Standard quota population for the particular group standard divisor = Clinic A B C D E Total Patients 246 201 196 211 226 1080 Standard quota 13.67 Example 1 Determining Standard Quotas Determine the standard quotas for clinics B, C, D, and E of the First Physicians Organization and complete Table 14.26. Use 18 as the standard divisor, as was determined above. Table 14.26 First Physicians Organization Now try Exercise 11 Solution The standard quota for clinic B is 11.17, 201 18 = rounded to the nearest hundredth. The other standard quotas are determined in a similar manner. Table 14.27 shows the completed table. Table 14.27 First Physicians Organization Clinic A B C D E Total Patients 246 201 196 211 226 1080 Standard quota 13.67 11.17 10.89 11.72 12.56 60.01 The standard quota represents the exact number of doctors each clinic would receive if we were able to divide a doctor into fractional parts. Notice that the sum of the standard quotas is slightly above 60, the total number of doctors due to rounding. 7 Now we introduce two more important definitions, the lower quota and the upper quota. The lower quota is the standard quota rounded down to the nearest integer. The upper quota is the standard quota rounded up to the nearest integer. For example, clinic A has a lower quota of 13 and an upper quota of 14, clinic B has a lower quota of 11 and an upper quota of 12, and so on. How should we round the standard quotas so that each clinic receives its fair share? If we were to use conventional rounding and round each clinic’s standard quota to the nearest integer, clinic A would receive 14 doctors and clinic B would receive 11 doctors. Clinics C, D, and E would receive 11, 12, and 13 doctors, respectively. The total number of doctors needed would be 61. Since there are only 60 doctors to
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