Unit 3 Math

Hamilton’s method

1. divide the total population of all the states by the total number of reps (this is called the divisor)

2. Divide each states population by the divisor to determine for many reps it should have (these are called quotas

3. Cut off decimal parts of all quotas (these are called lower quotas)

   1. Add up the remaining whole numbers. This will always be less of equal to the total number of reps

   2. Usually off by a few

4. Assuming that the total for lower quota was a bit smaller, we look at the decimal, assign the remaining reps, one each, to the states whose decimal was the highest.

Jeffersons method

Same as Hamilton’s BUT instead of just adding the left overs to the highest decimal point, you reduce the divisor and recalculate the quotas with the ADJUSTED DIVISOR.

Websters method

1. divide total population by number of reps to get the standard divisor

2. divide each state population by the standard divisor to get the quota

3. round all the quotas to the nearest whole number and add them up

4. if the total of than the number of reps, reduce the divisor and recalculate the quotas using the adjusted divisor

Hamilton’s method hint

looks at highest decimals

Jefferson’s Method hint

reduces divisor and recalculates everything (more annoying)

Webster’s Method Hint

round to the whole number and usually we will have too many so we increase the divisor and try again

Current Method

Huntington Hill

Gerrymandering

when districts are drawn based on political affiliation of the constituents usually to the advantage of those drawing the boundary

cracking

where there are some of each but the same majority in nearly every district

packing

packing all the same voters into one district

efficiency gap

each party only needs 50 % of the district and anything more is wasted and for the losing party, it is all wasted

websters method does not always follow the…

quota rule

Quota rule

The Quota Rule says that the final number of representatives a state gets should be within one of that state’s quota. Since we’re dealing with whole numbers for our final answers, that means that each state should either go up to the next whole number above its quota, or down to the next whole number below its quota.

Alabama Paradox

house added more reps due to growing population so they had to reapportion. There were not enough reps for every state to gain and something weird ended up happening where Alabama lost a rep even though they had no pop change.

Hamilton’s method does obey the…

quota rule

The New States Paradox

Oklahoma became a state and needed to take 5 reps from other states. Something weird was that Maine gained a rep.

Population Paradox

population grew over ten years so they reapportioned and Virginia grew faster than Maine but Virginia ended up losing a rep to Maine.