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.