Homework 5: Game Theory (2016)

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. Without assuming each "state" has to get 1 seat, how would a house with 14 seats be apportioned to states with population A = 460, B = 280, C = 160, and D = 100

using::

a. The rounding rule version of i. Webster; ii. Adams; iii. Jefferson

Clearly indicate the "adjusted" district size you use in your calculation.

b. The table algorithm version of i. Webster; ii. Adams; iii Jefferson

If any seats are "shared" by states due to there being a tie, indicate this.

2. Determine the i. Coleman power, ii. Banzhaf power, iii. Shapley-Shubik power and iv. Deegan -Packel for the weighted voting game below, whose players are 1, 2, 3, 4 and where the quota is 14.

[14; 9, 7, 6, 4]

The weights are listed in the order of the players' names. State what the winning coalitions and minimal winning coalitions for this game are.