Uh, methodological point: There are two kinds of public debates, expert/analytical and popular/rhetorical.
The first is rigorous but not accessible to the public, and if we're talking about technocrats in Brussels or their local "sympathizers", which is what "expert/analytical" is code for to a lot of people, local people are going to think they're lacking legitimacy making decisions by themselves without public input -- there's some kind of vague distrust -- even if their stats are good. They'll also get slammed for not knowing or distorting local conditions or opinion if not being outright hostile to the hoi palloi.
The second is accessible but seriously swayed by manipulation and methods that are explicitly barred from analytical debates because they're so misleading, emotional rhetoric, appeals to fear, etc, and any use of statistics is almost sure to be next to worthless because they're not used in a rigorous way. But again making decisions without any democratic input at all, you're not going to get public acceptance. So you can't just not have a mushy public debate either.
So you have this trap where you have to have both, but both seem almost carefully crafted to undo the work of the other. Any major public debate is a rope-walking exercise not so much in negotiating between the two as making sure we at least don't fall completely off to one side, and one ideally serves as the check to the other. Easier done in theory than practice, and it's not even easy to figure out in theory.
Edit: This is pretty much, incidentally, my research area, the negotiation between international expert bodies and democratic decisionmaking, and most of my case studies were WTO, EU, or NAFTA.