This case history involves Nassau County, New York, which is the geographic region on Long Island just to the east of New York City. Nassau County's government took the form of a Board of Supervisors, one representative for each of various municipalities, who cast a block of votes. Not only did Nassau County use weighted voting, but weighted voting was also used for the counties of New York State other than the 5 counties in New York City.

Here are the weighted voting systems used at various times by Nassau County. The passing quota shown reflects the number of votes needed to pass "ordinary legislation." Some special voting situations required larger quotas than the numbers shown.

	1958	1964	1970	1976	1990
Hempstead (H₁)	9	31	31	35	29
Hempstead(H₂)	9	31	31	35	29
North Hempstead	7	21	21	23	15
Oyster Bay	3	28	28	32	22
Long Beach	1	2	2	2	7
Glen Cove	1	2	2	2	6
Total votes	30	115	115	129	108
Quota to pass	16	58	63	71	65

The numerical weights were chosen to try to take into account the populations of the different municipalities, which were quite disparate. It is easy to see that in 1958, Oyster Bay, Long Beach and Glen Cove were dummies (!) and that North Hempstead had the same power as Hempstead 1 and Hempstead 2 because any two of these communities formed a minimal winning coalition. You should check for yourself that in 1964 there were also dummies. After 1964 the quota was raised to guarantee that no community was a dummy. However, eventually Nassau County converted to having a county legislature because of the difficulties of using a weighted voting system in a situation where there were so few players and such large differences in the populations of the communities.

Still, this approach to governance has its own problems. District lines cut across what had often been natural historical political entities. Furthermore, though the districts served by each member of the county legislature could be made approximately equal in population, this could not be done in a way that avoided some members of the legislature being tempted to vote in an identical way because, though they are different people, they have identical interests, given the geographical communities that they serve. To the extent that it is desirable that every member of the legislature act in an independent manner, this has been hard to achieve.