SHOW ALL WORK Foreman and Sons is a family owned corporation. Three generations
ID: 426035 • Letter: S
Question
SHOW ALL WORK Foreman and Sons is a family owned corporation. Three generations of Foremans (George I, George II and George III) are involved in its management but their names notwithstanding, the Foremans are not all the same when it comes to making decisions. George I has 3 votes, George II has 2 votes and George III has 2 votes. A majority of 4 (out of 7) is needed to carry a motion. a. What is the shorthand notation for the Foreman and Sons Corporation? b. List ALL sequential coalitions, indicating for each sequential coalition the PIVITOL player c. How is the power divided among the 3 Georges if the Shapley Shubik Power Index is used? (Need this by Sunday evening)
Explanation / Answer
a) Shorthand for Foreman and Sons Corporation can be F&S Corp.
b) Sequential coalition is the order in which the player joins the coalition. Here, players are the 3 Georges. Let's list the coalitions:
1. George 1> George 2> George 3.
So first George 1 gives vote, then George 2, and then George 3
This gives 3 votes+ 2 votes = 5 votes. Thus, as the votes become more than 4 (majority). This makes George 2 a Pivitol player. Pivitol player is the one who's vote provides the coalition a win.
Similarly we work the other coalitions:
(G1, G3, G2) - pivitol player - G3
(G2, G1, G3) - G1
(G2, G3, G2) - G3
(G3, G1, G2) - G1
(G3, G2, G1) - G2
c) Shapley Shubik Power Index = No. of times a player is pivitol / n!
N! = 3! = 3*2*1= 6
Thus, power of G1 = 2/6 = 1/3
G2 = 2/6 = 1/3
G3 = 2/6 = 1/3
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