The Supreme Court's decision in June in Arizona v. Inter Tribal Council  did not resolve very much. Arizona had a proof-of-citizenship requirement it wanted to include as a part of its voter registration process. The requirement would have been something beyond what the national mail voter registration form (or "Federal Form") includes.

The Election Assistance Commission could allow Arizona to include that requirement, but it had not done so. In part, it had not done so because it lacked a quorum, which means it could not do business. But in part, according to the Court in Inter Tribal , it was because Arizona failed to make a proper request of the EAC.

Nine justices agreed on one thing: it is possible for Arizona's position to win in the end. Two justices simply thought Arizona could win that day, while seven deferred until the proper procedures had been followed. 

In fact, the seven-justice majority agreed that "it would raise serious constitutional doubts if a federal statute precluded a State from obtaining the information necessary to enforce its voter qualifications." (It might be noted that the Supreme Court in Northwest Austin Municipal District No. 1 v. Holder  used the language "serious constitutional questions" for purposes of the Voting Rights Act, only for the justices in Shelby County v. Holder to divide as to how to answer those "serious questions.")

The Court then continued,

Arizona did not challenge that agency action (or rather inaction) by seeking APA review in federal court, but we are aware of nothing that prevents Arizona from renewing its request. [Footnote: The EAC currently lacks a quorum—indeed, the Commission has not a single active Commissioner.  If the EAC proves unable to act on a renewed request, Arizona would be free to seek a writ of mandamus to “compel agency action unlawfully withheld or unreasonably delayed.” It is a nice point, which we need not resolve here, whether a court can compel agency action that the agency itself, for lack of the statutorily required quorum, is incapable of taking.  If the answer to that is no, Arizona might then be in a position to assert a constitutional right to demand concrete evidence of citizenship apart from the Federal Form.] Should the EAC’s inaction persist, Arizona would have the opportunity to establish in a reviewing court that a mere oath will not suffice to effectuate its citizenship requirement and that the EAC is therefore under a nondiscretionary duty to include Arizona’s concrete evidence requirement on the Federal Form. Arizona might also assert (as it has argued here) that it would be arbitrary for the EAC to refuse to include Arizona’s instruction when it has accepted a similar instruction requested by Louisiana.

Arizona and Kansas took the seven-justice majority at its word. Both Arizona (PDF) and Kansas (PDF) heard from the EAC after making a request, and in each case the EAC answered that it must defer the State's request as it lacked a quorum.

Accordingly, these States filed a complaint (PDF) in Kansas federal court. (Perhaps in an unsurprising litigation decision, Arizona joined Kansas in the potentially more-hospitable realm of the Tenth Circuit rather than its home jurisdiction of the Ninth Circuit.)

The States largely tracked the Supreme Court's advisory path in this litigation. And now we shall see where it leads.