the members of the Suprem Court are 9 justices one vote each

the members of the Suprem Court are 9 justices, one vote each, and a majority is needed for a decision. The relative power of each justice is therefore 1/9. Three justices, who shall remain nameless, decide to use the following process to increase their power: They will meet privately to discuss each case, and agree that each will vote according to the majority decision from their private discussion. What are the new Banzhaf and Shapley-Shubik indices of the court? (b). If you find that the other six justices have lost power under this procedure, what can they do to counter this process?

Solution

a)

What are the new Banzhaf and Shapley-Shubik indices of the court?

if they are only 3 and all of them have the same power

then the indices of the court is 1/3

If you find that the other six justices have lost power under this procedure, what can they do to counter this process?

they can\'t do anything because the power is now lost