Rebecca Brown and Andrew Martin have posted this draft on SSRN (forthcoming, NYU Law Review).  Here is the abstract:

This is an empirical piece prepared for a conference entitled Testing the Constitution, held at the University of Chicago Law School. Brown and Martin collaborated to design a survey experiment aimed at testing some of the factual claims made by the Supreme Court in Citizens United v. FEC. The paper shows that there is a demonstrable harm to the electorate’s faith in democracy, and argues that these findings supply a government interest, separate from prevention of corruption, in regulating campaign spending.