Jeffersons Method and the Quota Rule

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Jeffersons Method and the Quota Rule
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The Quota Rule

• Upon apportionment, each state should receive
  either its Upper Quota or Lower Quota.
• A lower-quota violation occurs when a state
  receives less than its lower quota, an
  upper-quota violation occurs when a state
  receives more than its upper quota.

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Again with the controversy???

• When using Hamiltons Method, recall that every
  state received either its
• LOWER QUOTA (standard quota rounded down)
• Or its
• UPPER QUOTA (standard quota rounded up)
• for its final apportionment.
• Hamiltons Method is said to adhere to the
• QUOTA RULE
• at all times
• BUT...

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How about JEFFERSONS METHOD?

• There are applications in which
• DIVISOR METHODS cause a
• QUOTA RULE VIOLATION
• that is
• some state receives MORE THAN its Upper Quota
• or LESS THAN its Lower Quota
• as its final apportionment.
• (Remember the QUOTA RULE is not a law
• it just seems fair, thats all!)

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Quota Rule violation EXAMPLE

• There are 6 public schools in Techno Town.
• Their enrollments are given in the chart on the
  next slide.
• One year, the district has purchased 300
  computers, and wishes to award each school a
  number of computers based on their enrollment.
• Use Jeffersons Method to award the computers.

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Jeffersons Method handout
2 computers left to distribute
Find a new modified divisor.
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And so it goes...

• School B had a LQ of 166 computers
• But was awarded 168 computers
• Not a major problem
• But someone might complain.
• The arguments over this controversy become more
  intense when, for example, some states
  apportionment to Congress violates the quota rule.

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Another alternative Adamss Method

• Proposed by John Quincy Adams to solve the
  upper-quota violations of Jeffersons Method.
• Uses a modified divisor and rounds the modified
  quotas upward.
• Apportions to each state its modified upper
  quota.

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Adamss Method handout
4 computers too many!
Find a new modified divisor.
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A new problem!

• School Bs upper-quota violation is solved, but
  replaced by another quota violation.
• Now instead of receiving 168 computers (one more
  than its upper quota), School B receives 165
  computers (one less than its lower quota).
• Certainly the Principal at School B will not be
  happy.

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Websters MethodA compromise

• Daniel Webster proposed a compromise method.
• He hoped to solve the quota rule violations by
  using conventional rounding.
• But of course that doesnt always work, so we
  often have to employ a modified divisor.

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• Websters Method sounds like a good alternative,
  but is still not perfect.
• It does not create any paradoxes, BUT
• Although it was created to solve quota rule
  violations, it is still subject to them, though
  not as frequently.

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The lesser of two controversies?

• As you continue reading about apportionment
  methods in your text
• you may not be surprised to learn that
  mathematicians have actually proven that there is
  no perfect method of apportionment.
• Check it out for yourself!
• And remember fairness depends on whos
  defining it!