Question 11.35
5. The various weighted voting systems used by the Board of Supervisors of Nassau County, New York, turned out to be the mathematical quagmire described in Spotlight 11.4 (page 480). Before the county’s weighted voting was declared unconstitutional by a federal district court in 1993, it was changed several times. The weights in use since 1958 were as follows:
| Weights | |||||||
|---|---|---|---|---|---|---|---|
| Year | Quota | ||||||
| 1958 | 16 | 9 | 9 | 7 | 3 | 1 | 1 |
| 1964 | 58 | 31 | 31 | 21 | 28 | 2 | 2 |
| 1970 | 63 | 31 | 31 | 21 | 28 | 2 | 2 |
| 1976 | 71 | 35 | 35 | 23 | 32 | 2 | 3 |
| 1982 | 65 | 30 | 28 | 15 | 22 | 6 | 7 |
Here, is the presiding supervisor, always from the community of Hempstead; is the second supervisor from Hempstead; and , , , and are the supervisors from the remaining districts: North Hempstead, Oyster Bay, Glen Cove, and Long Beach.
- List the dummy voters in each year.
- Suppose that the two Hempstead supervisors always vote together. Now list the dummy voters in each year.
5.
(a) In 1958, , , and were dummies. In 1964, , , and were dummies. There were no dummies in 1970 and after.
(b) In 1958 and 1964, the Hempstead supervisors would be dictators; , , , and would be dummies. Following 1970 there would have been no dummies until 1982, when G was a dummy.