Homework 5: Game Theory (2016)
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
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
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.