I stand corrected: More learned Supreme Court counsel advise me that it is fair to infer that Justice Alito voted on the application to vacate the Eighth Circuit’s stay of execution.
On the eminently reasonable (but not compelled) assumption that Alito voted with the majority, his vote is entirely unremarkable. Alito had earlier that same day just been designated Circuit Justice for the Eighth Circuit. The Eighth Circuit had voted 9-1 to stay the execution. Alito was encountering the Court’s arcane practices in capital cases for the first time. In these circumstances (and completely apart from the merits of the matter, which I haven’t looked at), a decision not to vacate the Eighth Circuit’s stay order is eminently understandable.