# Weighted Voting System, Shapley-Shubik and Banzhaf Distribution and Sequential Coalitions

1) For each weighted voting system , find all dictators (d), veto power players( vp), and dummies (d) ( 7: 7,3,2,1)

2) For the weighted voting system ( 12: 6,4,3,1,1,)

a) Find what percent of the total vote is the quota.

b) In a Shapley-Shubik distribution system , how many sequential coalitions would be formed from this system?

3) Find the Banzhaf distribution ( in percent) for each system.

a) (9: 6,3,2,)

b) (7: 4,3,2,1,1).

https://brainmass.com/math/complex-analysis/weighted-voting-system-38847

#### Solution Preview

Please see the attached file for the complete solution.

1) FOR EACH WEIGHTED VOTING SYSTEM , FIND ALL DICTATORS (D), VETO POWER PLAYERS( VP), AND DUUMIES(D) ( 7: 7,3,2,1)

Solution:

Dictator is a player who has enough votes to pass any motion single-handedly. So Player1 who has 7 votes is the Dictator.

A player that is not a Dictator but can single-handedly prevent any group of players from passing a motion is said to have veto power. There are no veto power players in this system as no player other than the Dictator has enough votes to stop passing the ...

#### Solution Summary

Weighted voting systems, shapley-shubik and banzhaf distribution and sequential coalitions are investigated in the solution. The solution is detailed and well presented.