What would the U.S. apportionment look like with Huntington-Hill, Hamilton, Jefferson, and Webster Apportionment? Click Here for a Spreadsheet with the Answers.
If you Want Extra Practice with the Electoral College -- You can calculate and see if the results of the 2000 Election would have been different with these different apportionment Methods.
Find some places and situations (governments, institutions, organizations) in the U.S. or in the world where some of the apportionment methods we have seen are used. Which method is used in your state's House of Representatives?
Try to look up the current figures for the populations of the U.S. and of your home state. According to these numbers, do you think your home state is overrepresented, underrepresented, or appropriately represented in the U.S. House of Representatives?
Small Country that uses Hamilton's Method of Apportionment has three states of Population 540, 2430, and 7030, respectively.
a) Compute the apportionment with the house size 10 and with house size 11. Which state got the extra representative?
b) Suppose the country stays with a house of size 11, but the population of the smallest state decreases by 10 decreases while the population of the other two states increases by 70 and by 940, respectively -- Yielding new populations of 530, 2500, and 7970. How is apportionment affected? Do your calculations demonstrate any paradoxes?
In a particular country, there are three states with populations with 241,00; 339,000; and 420,000.
a) Hamilton Method is used to apportion h = 10 seats. What is the result?
b) The largest state seceded from the union, leaving just two states with population 241,000 and 339,000. How would Hamilton's method apportion h = 6 seats to this new two-state union? What paradoxes do you notice?
Assume the House of Representatives has 10 seats. Four States: Ambivalence -- Population 8,000; Boredom -- Population 9,000; Confusion -- Population 24,000; Depression -- Population 59,000. What is the apportionment with:
a) Hamilton Method?
b) Jefferson Method?
c) Adams Method?
d) Webster Method?
a) A small country, Æ, has 5 states, A, B C, D and E, with populations of 6,893; 1,763; 5,972; 8,991, and 3,327 respectively. The country has decided to implement a new branch of government with proportional representation. There are 55 seats available. Using Hamilton apportionment determines the distribution of seats for each state. Be sure to identify any paradoxes you come across.
b) A civil war broke out in the neighboring country. County Æ accepts 2,000 refugees. 394 go to State A, 942 go to state B, 228 go to state D, and 436 go to state E. Now determine the distribution of seats with this new population.
c) The civil war has ended and your neighbor would like to implement proportional representation in their government. There are only 3 states in this country. State X with 8,000 people, state Y with 6,398 people, and state Z with 3,214 people. Using Hamilton apportionment, find the distribution of seats when there are 45 seats and when there are 50 seats.
d) A new state is added to the neighboring country. This new state ß has a population of 4,762. Find the distribution with 60 seats using the Hamilton Method.
Questions 4, 5, and 6 Taken from The Mathematics of Politics by Robinson and Ullman
Mariela Duran - Grace Jackson - Hannah Quiroz