The false premise in your post is that "being well-informed" would lead you to a particular conclusion. Governing isn't like building a dam. You'd be insane to build a dam by getting random people on the street to design it. But the principles underlying governance aren't predictable like the principles underlying engineering. You're not going to find prominent engineers at leading universities disagree about whether concrete with a particular compressive strength will hold back a particular amount of water. Yet, you had a number of prominent economists on the pro-Brexit side: http://www.wsj.com/articles/pro-brexit-economists-make-case-....

At the end of the day, on most issues (obviously there are exceptions), the "informed" class is just guessing or following a particular ideology. Was NAFTA good for the average American? 20 years later economists still can't definitively answer that question!