**Game Theory Practice: Apportionment (Spring, 2013)**

Prepared by:

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk__

1. Suppose one has a country with four states A, B, C, and D with populations respectively of 80, 70 50, and 20. The legislature for the country has 20 seats.

Assume each state is entitled to at least one seat.

a. Find the exact fair share of each state.

b. Find the ideal district size for each state.

c. Use Hamilton's method to apportion the legislature.

d. (i) Use the rounding rule approach to Webster's method to apportion the legislature.

ii. Use the "table method" approach to Webster's method to apportion the legislature.

e. (i) Use the rounding rule approach to Jefferson's method to apportion the legislature.

ii. Use the "table method" approach to Jefferson's method to apportion the legislature.

f. (i) Use the rounding rule approach to Adams's method to apportion the legislature.

ii. Use the "table method" approach to Adams's method to apportion the legislature.

g. For each of these 4 apportionments compute the number of representatives per person for each state, and the number of people per representative for each state. Which states are underrepresented and which are over-represented?

2. Repeat the above question for a house size h of 15.