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Section 9.3

Section 9.3. Applications of the Apportionment Principle. Objectives. Use the Huntington-Hill principle to assign additional representatives. Use a spreadsheet to compute Huntington-Hill numbers. Some Good Advice.

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Section 9.3

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  1. Section 9.3 Applications of the Apportionment Principle

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

  3. 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.

  4. 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.

  5. 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?

  6. 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?

  7. 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.

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

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

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

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

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

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

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

  15. 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.

  16. 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.

  17. Example 10:Hamilton Method

  18. Example 11:Huntington-Hill Principle

  19. Example 11:Huntington-Hill Principle

  20. 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?

  21. Example 12:

  22. Example 12:

  23. 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. Use the Huntington-Hill method to apportion the instructor’s remaining two classes among the four activities. Scheduling Fitness Classes

  24. Example 13:

  25. 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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