Last week, in RNC v. Mi Familia Vota, the Supreme Court granted a partial stay of a district court order enjoining portions of Arizona's election laws that require proof of citizenship for voter registration. The question splintered the justices. Justices Thomas, Alito and Gorsuch would have stayed the district court order (allowing the Arizona law to take effect) in full, while all four female justices (Kagan, Sotomayor, Barrett and Jackson) would have denied the stay request across-the-board. Thus the Chief Justice and/or Justice Kavanaugh made the difference (possibly "or" because only one of them needs to have voted with the female justices to deny part of the stay request).
Over at the Election Law Blog, there is a little debate over whether this order violates the "Purcell Principle," which seeks to prevent meaningful changes to election laws or election administration in the run up to election day.
Rick Hasen thinks the order violates the principle, because it alters and complicates the rules governing voter registration. Although he's not a fan of Purcell, he thinks the Supreme Court should be criticized for not applying it consistently. He writes: