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In apportioning its state legislative seats, the State of Wyoming made provisions to allocate to each county at least one state representative. With the state's total population and its sixty-four House seats, the ideal apportionment would have been 7,337 persons per representative. Given the guarantee of county representation, Niobrara County, with a population of less than half the ideal (2,924), was allocated a House seat.

Did the State of Wyoming violate the equal protection clause of the Fourteenth Amendment by allocating one of its state House seats to a county with a population considerably lower than the average population per state representative?

The Court upheld the Wyoming apportionment scheme and found no Fourteenth Amendment violations. Justice Powell argued that using counties as legislative districts and assuring at least one representative per county supported "substantial and legitimate state concerns." Since the population variations in the Wyoming plan were the result of the consistent application of a nondiscriminatory and legitimate state policy, the plan was consistent with the Constitution. Any dilution of voting strength which the constituents of the other sixty-three representatives may have experienced as a result of Niobrara's relatively small population was minimal and irrelevant given the advantages of the Wyoming scheme.