Homework 5: Game Theory (2018)

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 we have 4 political parties A, B, C, and D with votes 100, 80, 70, and 50 respectively, to which we want to assign a non-negative integer number of seats in a "parliament" (legislature) which has size h (for house size) where h equals 13 seats. It is not insisted upon that a party get at least one seat. How many seats should be given to each party if:

a. Webster's Method with the calculations done using both the divisor/rounding rule approach and the "table method" associated with Webster's method.

b. D'Hondt's Method with the calculations done using both the divisor/rounding rule approach and the "table method" associated with Webster's method.

c. Adams's Method with the calculations done using both the divisor/rounding rule approach and the "table method" associated with Webster's Method.

2. Repeat 1. using only the table method approach with h = 14.

3. Do the results of 1. and 2. show an occurrence of the Alabama Paradox? (This refers to getting fewer seats with a larger house size.)

4. Do the results in 1. or 2. show a violation of "quota?" (Quota means that a party would get its ideal quota rounded up or down to the nearest integer.)