This article in the Wall Street Journal (Subscription required) covers an important case in whcih the Supreme Court allowed the Census bureau to use statistical methods. They had previously blocked the use of sampling. Although even the census bureau came out saying that the sampling method used previously did not necessarily “improve accuracy” (the measure used by the court), it isn’t exactly clear from the new ruling whether another sampling method might not be legal if it could be shown to be more accurate than current methods.Sampling could be very important for impoverished inner cities that tend to be undercounted.
“Writing for the court’s slim 5-4 majority, Justice Stephen Breyer said”we conclude that the use of ‘hot-decking imputation’ violates neither the statute nor the Constitution.”
Justice Breyer said this method was substantially different than one rejected by the high court in a 5-4 ruling in 1999. The court ruled at that time the use of overall sampling didn’t meet the constitutional test of being an "actual enumeration" of the population. Regarding Thursday’s ruling, "The consequence is that the census can breathe a sigh of relief that it doesn’t have to worry that everything it does will be subject to constitutional scrutiny," said Nathaniel Persily, a law professor at University of Pennsylvania law school in Philadelphia, who has written extensively on redistricting and the census. "The decision makes clear the Census bureau can use other methods besides head counting in order to achieve the most accurate count," he said.”