14.3 Apportionment Methods 931 Did You Know? Mathematical Contributions from Political Leaders m Alexander Hamilton (1757–1804) As a result of his distinctive service in the Revolutionary War, Hamilton became George Washington’s aide-de-camp and personal secretary in 1777. In 1789, Washington appointed Hamilton as the first secretary of the treasury. Hamilton and Thomas Jefferson were strong political adversaries. In 1804, Hamilton was killed in a duel with Aaron Burr, who was serving as Jefferson’s vice president. Hamilton , the musical, based on the life story of Alexander Hamilton, won 11 Tony Awards in 2016, including Best Musical. distribute, conventional rounding of standard quotas can be problematic. We need a more sophisticated apportionment method to avoid the problems that can occur with rounding standard quotas. We will now discuss the first of our four apportionment methods, Hamilton’s method. Hamilton’s Method Mathematically, Hamilton’s method is the easiest to apply. HAMILTON’S METHOD To use Hamilton’s method for apportionment, do the following. 1. Calculate the standard divisor for the set of data. 2. Calculate each group’s standard quota. 3. Round each standard quota down to the nearest integer (the lower quota). Initially, each group receives its lower quota. 4. Distribute any leftover items to the groups with the largest fractional parts until all items are distributed. PROCEDURE Example 2 Using Hamilton’s Method for Apportioning Doctors Use Hamilton’s method to distribute the 60 doctors to the First Physicians Organization clinics discussed in Example 1. Solution Table 14.28 includes the standard quotas (row 2) calculated from Example 1, along with the lower quotas (row 3) and the apportionment using Hamilton’s method (row 4). Table 14.28 First Physicians Organization Now try Exercise 27 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 Lower quota 13 11 10 11 12 57 Hamilton’s apportionment 14 11 11 12 12 60 The sum of the lower quotas is 57, leaving three additional doctors to be distributed. Since clinics C, D, and A, in this order, have the three highest fractional parts (0.89, 0.72, and 0.67, respectively) in the standard quota, each receives one of the additional doctors using Hamilton’s method. Note that with Hamilton’s method, each clinic receives either its lower quota or its upper quota of doctors. Also note that the total number of doctors apportioned by Hamilton’s method is 60, which is what we expected. 7 Library of Congress Prints and Photographs Division [LC-DIG-ppmsca-17523] We use the word group in Steps 2, 3, and 4 as a general term. However, group could refer to a state, a school, or even an individual.
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