[Lurking Libertarian]

Who wrote the majority opinion and how in the world did they justify it?

Scalia, and the rationale is federal preemption: Congress in the Motor Voter Act said that states "must accept" federal registration forms (which require a sworn statement that the voter is a citizen, but no other proof), so states cannot (under the Supremacy Clause) contradict the federal law.

[windsorknot]

So, thank the asshats that passed the Motor Voter Act.