Critical analysis is overrated. At least in America, democracy worked just fine for two hundred years before modern methods of conveying information to the public. People vote based on their guts and their values and that works pretty well.

There isn't really any better option. The basic problem is that political science isn't a science. It's cargo cult science. (What passes for "analysis" among the wonktitude drives the engineer in me bonkers). On an issue like Brexit, there is nobody who can predict with anything approaching scientific certainty what the outcomes of the two choices will be. You can dress up your choice however you like, referencing reports of this or that expert (who all have conflicting opinions), but at the end of the day is imagine most Remain voting was also done based on a gut-feeling commitment to Pan-Europism.