It doesn't take long to see all sorts of questions that the distinction draws. Should we count people who can vote or people who do vote? How does that shift the priorities of the official who wins the right to represent the district?
What might not be as obvious is that the effect of broad switch to focus on possible voters would be large. In order to be able to vote, you need to meet three criteria: 1) You must be a citizen, 2) you must be over 18 years old and 3) you must not have had your right to vote rescinded, say for a felony conviction. The Census Bureau's American Community Survey calculates the number of people across the United States who meet the first two standards. And we can use that data to get a picture of the places in which the largest percentage of the population can't actually cast a ballot.
You'll notice two things right away. First, urban areas (New York. Chicago, Miami, Atlanta) have a greater percentage of the population that fails to meet either or both of the first two criteria. And, second, the Southwest has similarly high percentages. (The first point, as Phillips notes in her piece, is why a switch to this sort of apportionment would favor rural areas -- and accordingly, Republicans.)
Why the disparity? As we've noted before, it's in part linked to areas with a high Hispanic population. Those areas often have a larger percentage of non-citizens. The graph below compares the citizen voting-age population (CVAP) with the density of the Hispanic population in congressional districts.
That's not only a function of citizenship. The median age among Hispanics in America is also lower than among other groups. In some places, that's a larger factor than citizenship status. For example in Utah, which in the 2010 Census had the lowest median age of any state, the percentage of people too young to vote is higher.
As Derek Muller of Pepperdine University pointed out in an e-mail, the case before the Supreme Court doesn't look at congressional district boundaries, though an argument in support of focusing on CVAP in general could result in similar changes to the House map.*
We can't wrap this up without noting another important point. During the 2010 Census, a great deal of emphasis was placed on getting an accurate count from all residents, including those who immigrated illegally. Often, such residents are wary of revealing themselves to the government, meaning that they are under-counted and communities with large undocumented communities are under-represented in politics. In other words, an increased focus on those eligible to vote already exists to some degree -- likely to the detriment of the same states that would lose even more seats on the second map above.
There's essentially no way in which politicians will ever fairly and uniformly represent the population. The question before the Supreme Court is an interesting one that could have wide ramifications. But in terms of it ensuring a fairer system, the jury is very much out.
* Muller also pointed out that in an original version of this post, we conflated redistricting with reapportionment. The latter, in which the number of House seats in each state is divvied up, depends heavily on the 14th Amendment, which specifically mandates "counting the whole number of persons in each state, excluding Indians not taxed." The post has been corrected.