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Section 9.2

Section 9.2. The Huntington-Hill Apportionment Principle. Objectives. Understand and use the Huntington-Hill Principle. The method currently being used in the U. S. House of Representatives. Key Concept:.

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Section 9.2

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  1. Section 9.2 The Huntington-Hill Apportionment Principle

  2. Objectives • Understand and use the Huntington-Hill Principle. The method currently being used in the U. S. House of Representatives.

  3. Key Concept: • Apportionment Criterion – When assigning a representative among several parties, make the assignment so to give the smallest relative unfairness.To avoid the Alabama Paradox, we will use the Apportionment Criterion.

  4. Example 1: • Using the Apportionment Criterion • State A, with a population of 41,440 presently has seven representatives. State B, with a population of 25,200 has 4 representatives. • Determine the relative unfairness of the apportionment if we give an additional representative to state A.

  5. Example 2: • Using the Apportionment Criterion • State A, with a population of 41,440 presently has seven representatives. State B, with a population of 25,200 has 4 representatives. • Determine the relative unfairness of the apportionment if this representative is given instead to state B.

  6. Example 3: • Using the Apportionment Criterion • State A, with a population of 41,440 presently has seven representatives. State B, with a population of 25,200 has 4 representatives. • Use the apportionment criterion to decide which state should receive the additional representative.

  7. Note: • Sometimes the Apportionment Criterion violates the Hamilton Method for Apportionment.

  8. Example 4: • Using the Hamilton Method • State A, with a population of 41,440 presently has seven representatives. State B, with a population of 25,200 has 4 representatives. Determine who gets the extra representative.

  9. Key Concept: • The Huntington-Hill Apportionment Principle – If states X and Y have already been allotted x and y representatives, respectively, then state X and Y should be given an additional representative in preference to state Y provided that(population of Y)2 < (population of X)2 y * (y + 1) x * (x + 1) • Otherwise, state Y should be given the additional representative. We will often refer to a number of the form (population of X)2 as a Huntington-x * (x + 1)Hill number.

  10. Historical Highlight • TB pg. 523/Is There a Perfect Apportionment Method?

  11. Example 5: • Using the Huntington-Hill Apportionment Principle • There are 320 full-time nurses and 148 part-time nurses at Community General Hospital. The nursing supervisor has chosen four full-time nurses and two part-time nurses to serve on a committee to evaluate proposed nursing guidelines. Use the Huntington-Hill apportionment principle to decide whether the seventh nurse on the committee should be full-time or part-time.

  12. Example 6: • According to a recent census, Iowa had a population of approximately 2.8 million people and 6 representatives to the U. S. House of Representatives; and Nebraska had a population of 1.6 million people and 3 representatives. Use the Huntington-Hill apportionment principle to determine which state is most deserving of an additional representative.

  13. Example 7: • Apportioning Representatives Among Three States • Assume that the oil consortium board currently has 2 members from Naxxon, 2 from Aroco, and 1 from Eurobile. Use the Huntington-Hill apportionment principle to decide which company should receive the next member on the board.

  14. Section 9.2 Assignment • TB pg. 524/2 – 28 Even (online also) • Must write problem and show ALL work to receive credit for this assignment.

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