Competing interpretations of one person, one vote [updated with a note on additional alternatives]
For over fifty years—since the 1964 case of Reynolds v. Sims, the Supreme Court has required states to draw legislative districts based on the "one person, one vote" principle. Recently, the Court decided to hear Evenwel v. Abbott, a case that raises the issue of which people should be counted in the determining the population of a district. The state of Texas has drawn its legislative districts on the basis of equalizing total population. The conservative plaintiffs in the case argue that only voters should be counted (or at least that districts must be drawn in such a way as to equalize both the total population and the voting population).
The two sides in the case, the lower court decision, and most commentators seem to assume that these are the only two possible metrics. But there are at least two other possibilities, each of them supported by plausible theories of democratic representation.
One alternative approach is to count all citizens, regardless of whether they are eligible to vote, but exclude all non-citizens. Many citizens are not permitted to vote because they are minors, they have committed felonies that exclude them from the franchise, or they are mentally disabled. But, on some theories of democratic legitimacy, governments have a special obligation to citizens, and all citizens are entitled to representation, regardless of whether they are allowed to vote. Non-citizens, by contrast, are assigned a lower status and the government has fewer obligations to them.
Another plausible approach would count all legal residents, regardless of whether they are citizens, but exclude illegal immigrants. The theory here is that states have strong obligations to all those whose residency they have legitimized, but few or no obligations to those whose very presence is illegal. I am no fan of immigration restrictions myself, and I think the moral legitimacy of most of them is questionable at best. But many people argue for a sharp distinction between legal and illegal immigrants, and this approach to representation fits that intuition.
The total population and voter population standards also have their normative justifications. The former is based on the idea that all of the people living in the state are subject to its laws, and therefore are entitled to at least some form of consideration in representation formulas; the latter on the theory that voters are the only ones who can actually participate in elections, and therefore it makes little sense to make a vote in District A more potent than one cast in District B merely because the latter has more residents who are ineligible for the franchise. There are also a variety of other arguments that can be made for or against the various metrics.
Thus, we have at least four plausible alternative approaches to counting the relevant population of legislative districts: total population, legal population, citizen population, and voter population. The Court could also choose to let states choose between some or all of the different approaches. But that could mean that an important constitutional principle would be applied in widely varying ways in different states.
It is worth noting that three of the four theories—total population, legal population, and citizen population—all implicitly assume that the voting population is a good proxy for the interests of the non-voters who are counted in the representation formula. Those who vote provide a kind of "virtual representation" for those who do not. If the eligible voters of a given district are not good proxies for the nonvoters who count in the formula, then the nonvoters will not benefit from the extra representation the district gets by counting them. If the voting population is actively hostile to the interests of the nonvoting group included in the formula, then the extra representation might actually harm the latter instead of benefiting them. The relevant historical precedent here is the harm caused to African-Americans when southern states were able to count them as part of the population relevant to the allocation of congressional districts, while simultaneously denying them the right to vote. In this case, counting nonvoting African-Americans actually strengthened the pro-segregation bloc in Congress, by increasing the number of representatives elected by segregationist southern whites.
The three more restrictive metrics—legal population, citizen population, and voting population, have a different potential flaw. As Nathaniel Persily points out, we don't have a reliable way of measuring them, because "[w]e have no national citizen database that tells us how many citizens live in each district around the country." We also often don't have reliable data on the number of eligible voters in a given district either.
From an originalist point of view, it is quite possible, as Justice Scalia has suggested, that the one person one vote principle is simply not required by the Constitution. On this view, states should be allowed to draw widely unequal legislative districts, just as the federal Constitution gives some states far more per capita representation in the Senate than others. So long as states don't discriminate on the basis of race, sex, religion, or other suspect classifications, they can draw their legislative districts however they want.
But if you are a living constitutionalist, or simply unwilling to jettison longstanding precedent, then it is worth considering the full range of plausible interpretations of the one person, one vote principle.
UPDATE: I have made minor improvements in the wording of this post.
UPDATE #2: I should add that these four options do not exhaust the range of theoretically possible alternatives. There is an almost infinite variety of ways to classify and categorize populations. For example, we could draw legislative districts based on the number of people over 18, the number of citizens over 18, or—for that matter—the number of right-handed people or the number of people with green eyes. I have chosen to consider these particular four models because they seem to map on relatively well to various widely believed normative theories of democracy and representation.