Chief Justice Roberts in today’s opinion (which I am now editing for our casebook supplement): “As in Davis, we do not need empirical evidence to determine that the law at issue is burdensome. See 554 U.S., at 738–740 (requiring no evidence of a burden whatsoever).”
I’ve written about the Court’s wildly inconsistent approach to evidence in the campaign finance cases before, most recently in my Michigan Law Review article on Citizens United.