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Section 9.3 Applications of the Apportionment Principle

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Objectives Use the Huntington-Hill principle to assign additional representatives. Use a spreadsheet to compute Huntington-Hill numbers.

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Some Good Advice Once you have used the largest of the Huntington-Hill numbers to apportion a representative, cross that number off so that you do not use it again.

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Huntington-Hill Principle A labor council is being formed from the members of three unions. The electricians’ union has 25 members, the plumbers have 18 members, and the carpenters have 31 members. The council will have seven representatives, with each union having at least one representative. Use the Huntington- Hill numbers listed in Table 9.12 to answer Examples 1 and 2.

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Example 1: Knowing that each union currently has 1 representative, which entries in the Table 9.12 do we use to assign the fourth seat on the council and which union gets that seat? Current Representation ElectriciansPlumbersCarpenters 1312.5162.0480.5 2104.254.0160.2 352.127.080.1 431.3*48.1

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Example 2: Suppose the current council has 5 seats, apportioned so that the electricians and carpenters have 2 seats each and the plumbers have one. Which entries in the table do we use to assign the sixth seat on the council and which union gets that seat? Table 9.12 Current Representation ElectriciansPlumbersCarpenters 1312.5162.0480.5 2104.254.0160.2 352.127.080.1 431.3*48.1

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Huntington-Hill Principle Use the Huntington-Hill principle to apportion the oil consortium board. Recall that Naxxon has 4,700 stockholders, Aroco has 3,700, and Eurobile has 1,600. We will assign the 9 representatives one at a time until we have assigned all of them. A provision on the U. S. Constitution allows us to automatically give each company 1 representative.

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 2 3 4 5 6 7 8 9

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Example 3: 1 – 3 Rep Calculate Huntington-Hill number NaxxonArocoEurobile..\..\Xls\Huntington_Hill Number.xlsx

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 N100 2 A110 3 E110 4 5 6 7 8 9

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Example 4: 4 th Rep Calculate Huntington-Hill number NaxxonArocoEurobile..\..\Xls\Huntington_Hill Number.xlsx

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 N100 2 A110 3 E111 4 N211 5 6 7 8 9

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Example 5: 5 th Rep Calculate Huntington-Hill number NaxxonArocoEurobile..\..\Xls\Huntington_Hill Number.xlsx

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 N100 2 A110 3 E111 4 N211 5 A221 6 7 8 9

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Example 6: 6 th Rep Calculate Huntington-Hill number NaxxonArocoEurobile..\..\Xls\Huntington_Hill Number.xlsx

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 N100 2 A110 3 E111 4 N211 5 A221 6 N321 7 8 9

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Example 7: 7 th Rep Calculate Huntington-Hill number NaxxonArocoEurobile..\..\Xls\Huntington_Hill Number.xlsx

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 N100 2 A110 3 E111 4 N211 5 A221 6 N321 7 A331 8 9

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Example 8: 8 th Rep Calculate Huntington-Hill number NaxxonArocoEurobile..\..\Xls\Huntington_Hill Number.xlsx

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 N100 2 A110 3 E111 4 N211 5 A221 6 N321 7 A331 8 N431 9

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Example 9: 9 th Rep Calculate Huntington-Hill number NaxxonArocoEurobile..\..\Xls\Huntington_Hill Number.xlsx

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Seat Number Goes To # of Reps Naxxon # of Reps Aroco # of Reps Eurobile 1 N100 2 A110 3 E111 4 N211 5 A221 6 N321 7 A331 8 N431 9 E432

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Section 9.2 Assignment Class work: TB pg. 532/2 – 20 Even (Online) Remember you must write the problem and show ALL work to receive credit for this assignment.

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Comparing Methods Apportioning a city council. A city is made up of three boroughs – Alsace, Bradford, and Cambria. Representation on a ten-member city council is allocated in proportion to the population in each of the tree boroughs. Alsace has a population of 23,000, Bradford has 34,000, and Cambria has 14,000. Apportion the ten council seats Using the Hamilton method. Using the Huntington-Hill apportionment principle.

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Example 10: Hamilton Method Apportioning a city council. BoroughsPopulation%Step 1Step 2Step 3 Alsace23,000 Bradford34,000 Cambria14,000 Total: 71,000

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Example 11: Huntington-Hill Principle Huntington-Hill Principle Seat Number Goes To # of Seats Alsace # of Seats Bradford # of Seats Cambria 1 2 3 4 5 6 7 8 9 10

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Example 11: Huntington-Hill Principle Seat Number Goes To # of Seats Alsace # of Seats Bradford # of Seats Cambria 1B010 2A110 3C111 4B121 5A221 6B231 7C232 8B242 9A342 10B352

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Assigning Police Officers Consider the problem of apportioning police officers given in Example 2, page 531. Suppose we still want to apportion the seven officers among the three regions, but the number of incidents per region has changed. The number of related incidents for regions 1, 2, and 3 are listed in the table. How should the seven officers be assigned to the regions, given this new data? Region 1123 incidents Region 2 44 incidents Region 3 79 incidents Total246 incidents

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Example 12: Region 1123 incidents Region 2 44 incidents Region 3 79 incidents Total246 incidents If Given the Next Officer, the Number a Region Would Have Is: Region 1Region 2Region 3 17564.5968.03120.5 22521.5322.671040.2 31260.8161.3520.1 4756.596.8312.1 5504.364.5208.0

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Example 12: Officer Goes To # Region 1 # Region 2 # Region 3 1 2 3 4 5 6 7

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Scheduling Fitness Classes A health club instructor has a course load that allows her to teach six two-credit-hour classes. A pre-registration survey indicates the following interests. 58 want to take high-impact aerobics 32 want to take low-impact aerobics 11 want to take Jazzercise 39 want to take step exercise Assume that the instructor will teach at least 1 class for each activity. a) Use the Huntington-Hill method to apportion the instructor’s remaining two classes among the four activities.

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Example 13: Classes to be Taught Goes To High- Impact Low- Impact JazzerciseStep Class 1 HI 2 LI 3 SC 4 Jazz 5 6

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Section 9.2 Assignment Class work: TB pg. 532/2 – 20 Even (Online) Remember you must write the problem and show ALL work to receive credit for this assignment.

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