The city of New Coventry decides to elect a mayor using the Electoral College weighted voting system, with the voters being the three boroughs of the city. Each borough is awarded two city Senators and city Representatives according to their population, which results in Newburgh having 8 Representatives, Oldburgh having 7, and Middleburgh having 1.

 

(a) Use our standard notation to write the weighted voting system for electing a mayor in New Coventry. 

(b) What is the Shapley-Shubik index for each borough in the New Coventry mayoral elections?

 (c) Are there any dictators, dummies, or voters with veto power in the mayoral election process? Justify your answer.