A floterial district is a legislative district that includes several separate districts that independently would not be entitled to additional representation, but whose combined population entitles the area to another seat in the legislative body. It is a technique that a state may be authorized to use to achieve more equal apportionment by population during redistricting.
In common usage, a floterial district is not just a multi-town district, but a multi-town district that "floats" over towns that already elect one or more legislators. For example, a city due more than five representatives but not quite six might elect five representing the city itself, and one more in a floterial district that includes some neighboring towns whose small populations, alone, would not merit even a single representative.
2 U.S.C. § 2a, based on the Reapportionment Act of 1929, reapportions the U.S. House to the states following each decennial census. If a state received additional representatives but failed to redistrict, the additional representatives would be elected at-large, so the entire state would be a floterial district. This has occurred in many states. However, subsequent decisions of the U.S. Supreme Court, such as Reynolds v. Sims (the "one man, one vote" decision), now oblige the states to redistrict.
New Hampshire litigation
In 1982, U.S. District Court in Boyer v. Gardner upheld New Hampshire's reapportionment of the 400-person House of Representatives using floterial districts. The plaintiffs had taken issue with the "aggregate method," which compares the relative voting power of the group of districts with both floterial and dedicated representatives, and had asked the court to consider the "component method." For example, a small town paired with a large city in a floterial district would be unlikely ever to control that House seat.
However, after the reapportionment of 2002, the New Hampshire Supreme Court found that towns and wards with floterial districts elect different numbers of representatives, the floterial scheme is "complicated and often confusing", and the floterial scheme is not specified in the state constitution. Finding that none of the plans submitted to it correctly used figures from the 2000 census and that all of them had political components, the court redistricted the state into 88 districts, none of them floterial, and all but five electing multiple representatives.
Legislators and voters were dissatisfied that the larger districts in the court's plan valued numerical equality over more local representation. Consequently, the New Hampshire constitution was amended in 2006 to guarantee a representative for each town or ward "within a reasonable deviation from the ideal population for one or more representative seats" and to explicitly authorize floterial districts for fine-tuning.