When Utah sued the federal government over the 2000 census, a census-taking technique called “hot-deck imputation” was on the hot seat. Utah was none too happy to have lost a representative based on its population estimate, so it argued that “imputation”—inferring who lives in a residence by looking at like neighbors—was essentially “sampling,” which is prohibited by statute.
At the oral argument, the Court seemed receptive to the State’s argument. But then Solicitor General Ted Olson stood up and tossed out the following “metaphor,” as he called it:
[Say] the Court asked the library of this Court to ascertain the number of books [. . .], but sampling was not permitted to do that, so that the librarian could not go to every third shelf, multiply, count the books, multiply by three and get the census.
But if the librarian went to those shelves and counted every particular volume and found that there was a space here on that shelf, a space this big on the next shelf, and a space this big on another shelf, for example, the imputation would be saying, “Well, all the books or the books right next to this are this size, and therefore that space a book is missing, so we know we have a book, and we will impute one book to that space or two books to [that] space.”
So that the sampling technique is completely discrete from the imputation technique.
The Justices’ skeptical tone softened. “I’d like to understand this better,” said Justice Breyer. “In the library, you look and see that everything around the book is a history book and so then you impute the characteristic of being a history book to the one that’s missing. That’s your analogy of what goes on here, is that right?”
As you can […]