Summary from class Feb 13 2013

Today in class we covered another method of Apportionment called The Huntington-Hill Method.  This method was adopted until 1941 after several methods by several different politicians(in some case their own) failed to fix the problem.  I mean I can see how this confusion was going on with the addition of new states joining the Union after the Civil War and in fact at each census the population would change resulting in changes + or - for some states.  But the states would end up trying to sue or declare it unconstitutional but nothing ever really got anywhere.  So there are 435 seats in the house 200 held by Democrats, 232 by Republicans, and 3 vacant. 
The Huntington-Hill Method has the same first three steps as the Hamilton method.  
1.Find the total population 
2.Calculate the ideal district size, also known as the Standard Divisor: total population ÷ house size
3.Calculate the Quotas: state population ÷ standard divisor
But after that things start to get a little complicated and steps cant be skipped.
4.Then we find each states upper quota in which we round up, then each states lower quota in which we round down.
5.Then we take the geometric mean of each states upper and lower quota.
6.After that we then create a tentative apportionment as follows.  If the quota is less then Q* then we use the lower quota.  If the quota is greater than or equal to Q* use the upper quota.
7.Sometimes we might still have a seat to give out.  So lets find out who would get the seat.  Calculate the critical divisor for each state.  Remember if there are too many seats divide the state population by the geometric mean of the states tentative apportionment N and N-1.  If there are too few seats, do the same thing but use N and N+1.
8.If the tentative apportionment is too large the state with the smallest critical divisor loses a seat.  If the tentative apportionment were too small the seat with the largest critical divisor would gain a seat.
9.You may still need to do some work if the correct house size still hasnt been achieved.  We would recalculate the critical divisors of the states whose apportionment has changed and repeat the process.

Extension-- Huntington-hill method of apportionment

We first learned the simple method of Hamilton for apportionment, well at least simple compared to the die hard method created by Huntington and Hill. However they are both similar due to the first three steps. They are; find the total population, calculate the ideal district size, and calculate the quotas. Simple right? For that part yes, it gets much more difficult. From there you must find each states upper quota and lower quota then find the geometric mean. Then you create a tentative apportionment and calculate the critical divisor for each state. So on and so on.

Edward Vermilye Huntington was a great mathematician of his time. He spent most of his career at Harvard. During world war one he would actually create important statistics for generals of the army. It was among that time when he learned of the apportionment ideas of Joseph A. Hill. He began to study and revise Joseph's thoughts. He then came up with a method he referred to as "the method of equal proportions" otherwise known as the Huntington-Hill method. This is the current method used in congress today to decide how many seats each state receives. It was signed into law the year he retired from Harvard, November 15th, 1941.

After researching methods such as Webster's, Dean's, and Jefferson's, I believe this method shall be used for a very long time. Although great, not perfect. There were many extensive debates about which method to use. This went on for a long time at the beginning of the 20th century until the speaker of the house, Nicholas Longworth, suggested a team of mathematicians be sent out to find the right method. They then found Huntington's to work the best, thus the current method being used.

Extension-Feb-7-2013

In class we discussed Hamilton's method of apportionment. This method is mostly used to decide how many seats are given to the House of Representatives. While it has its flaws it is widely accepted by most of the US. However, there are more methods of apportionment other than Hamilton's.

One such method is Jefferson's method. This method is similar to Hamilton's and follows the same guidelines up until the numbers are rounded down to the lower quota. If the total number added up by the lower quota is not correct, by trial and error, find a "modified" district size. When the state size is divided by the new district size and rounded down the number must be equal to the modified district size. In short, the number of seats does not change, it is the district size that must be changed. The only problem this method is said to have is the fact that it violates the Quota Rule. I tried to understand what the Quota Rule was, but came up with nothing. Perhaps Kira will touch on this next class.

There are multiple other forms of apportionment that have the same problem as Jefferson's. While Hamilton's method has more than one, these other methods only violate the Quota Rule. Maybe we should look into using another type of apportionment in order to select seats for Representatives.

An extension of Hamiltonian apportionment

  Extension 2-6-2013



In class the apportionment was discussed. Apportionment is the procedure through which representation in congress and other democratic bodies are used. The method we discussed was Hamilton’s method (named after Alexander Hamilton). While at first glance the method looks fair, pragmatic and democratic we notice an incredible flaw.

 Who could believe that a state could gain a seat(s) by actually losing citizens from its district? Well this is quite possible and does happen rarely under the Hamilton method. This travesty is named the Alabama paradox. The paradox is named after Alabama because that is the state in which it first occurred. The constitution demands that we use apportionment in the status quo, through the Hamilton method. No, it does not say Hamilton method in the constitution even though he is accredited with the method in the document. This was first discovered after reading the 1880 census, I always wonder if it were noticed prior.

 Uimately, I am a firm believer in this imperfect, normally consistent method. It works, and reflects demographic trends accurately for the most part. Are you all in favor of Hamilton’s method or do you disagree? Remember that if you do you should provide a pragmatic alternative that answers the criticism of the method.

Extension 01-30-2013

When talking about apportionment in our last class we mentioned the United States’ House of Representatives as an example.  There are of course other countries which have to deal with apportionment in their legislatures.  One of these countries is Canada.  The Canadian parliament consists of the House of Commons, the Senate, and the Queen.  Only the House of Commons is elected by the people of Canada.  The Senate members come into office by the recommendation of the Prime Minister.  The Queen is represented in Canada by the Governor General, who is chosen by the Queen based on the advice given to her by the Prime Minister.  When the Queen is in Canada she “performs many important ceremonial duties”.

Since the only elected body is the House of Commons, I will focus on them.  In order to be elected to the House of Commons one must get the most votes in her or his constituency, which is similar to the term district.  A candidate can win an election “even if he or she gets less than half of the total votes”.  This indicates that the U.S. is not the only nation that uses the Plurality method of voting.  There are 308 seats total in the House of Commons.  These seats “are distributed roughly in proportion to the population of each province and territory”.  Bigger population equals more seats in the House of Commons.  Additionally, “Every province or territory must have at least as many Members in the Commons as it has in the Senate”. 

http://www.parl.gc.ca/About/Parliament/GuideToHoC/index-e.htm