Question 11.69
39. A proposed weighted voting system for the New York City Board of Estimate (see Exercise 38) that is based on the populations of the boroughs is . Find a simpler system of weights that yields an equivalent voting system. Do you think this system would satisfy the Supreme Court’s objections?
39.
The borough presidents, taken together, have a total voting weight of 36, and the voting weight of each borough president is more than 1. Thus, the minimal winning coalitions consist of one of the following:
- All three city officials (34 extra votes)
- Two city officials and one borough president (at least 0.8 and not more than 10.3 extra votes)
- One city official and all five borough presidents (0 extra votes)
Therefore, the weighted voting system is equivalent to the system with minimal winning coalitions (a) through (c).
A-29
The Supreme Court would reject this system since— like the system that it was intended to replace—all of the borough presidents wield the same amount of voting power. It is interesting to note that the system where the city officials had 2 votes and the quota was 6, the Banzhaf and Shapley-Shubik models both gave each city official about 19% of the power. With the proposed change, the city officials each had about 29% of the power with the Banzhaf model (27% with the Shapley-Shubik model).