Cite as: 572 U. S. ____ (2014) 29 Opinion of ROBERTS, C. J. to prove, pointing to eight FEC cases that did not proceed because of insufficient evidence of a donor’s incriminating knowledge. See post, at 24–25. It might be that such guilty knowledge could not be shown because the donors were not guilty—a possibility that the dissent does not entertain. In any event, the donors described in those eight cases were typically alleged to have exceeded the base limits by $5,000 or less. The FEC’s failure to find the requisite knowledge in those cases hardly means that the agency will be equally powerless to prevent a scheme in which a donor routes millions of dollars in excess of the base limits to a particular candidate, as in the dissent’s “Example Two.” And if an FEC official cannot establish knowledge of circumvention (or establish affiliation) when the same ten donors contribute $10,000 each to 200 newly created PACs, and each PAC writes a $10,000 check to the same ten candidates—the dissent’s “Example Three”— then that official has not a heart but a head of stone. See post, at 19–20, 25. The dissent concludes by citing three briefs for the proposition that, even with the aggregate limits in place, individuals “have transferred large sums of money to specific candidates” in excess of the base limits. Post, at 26. But the cited sources do not provide any real-world examples of circumvention of the base limits along the lines of the various hypotheticals. The dearth of FEC prosecutions, according to the dissent, proves only that people are getting away with it. And the violations that surely must be out there elude detection “because in the real world, the methods of achieving circumvention are more subtle and more complex” than the hypothetical examples. Ibid. This sort of speculation, however, cannot justify the substantial intrusion on First Amendment rights at issue in this case. Buckley upheld aggregate limits only on the ground that they prevented channeling money to candidates beyond