Alas, history tells us that the people with "rational" opinions are no better to rule than the ones with "irrational" ones. At least not in the long run.
As a fellow EU-citizen I am absolutely horrified by the chaos currently unfolding in the UK, but dismissing the entire voting process while referring to "democracy yada yada" is far scarier than the outcome of a democratic election will ever be.
I think the above poster's point is that plenty of government decisions are not voted on by referendum, and shouldn't be. The consequences of Brexit are complex and far-reaching, more so than countless other types of decisions that are not directly voted on. So why should we expect The People to know any better?
They're not random, you're supposed to vote for them.
And they're supposed to represent your general opinion. They're supposed to have an education in politic/economics/&c. which makes them better equipped to make informed decisions. And it's supposed to be their full time job.
Just like anyone can bake bread at home with no tools / minimum knowledge but the bakery at the corner of the street will make better bread.