I've been listening to the 538 election podcast talking about the Brexit vote while I wait for my son's band concert to start. Having some weirdly ambivalent thoughts about democracy.
I think one of the most pressing problems in any society is making sure that minorities don't get stripped of their rights. This is a non trivial issue to solve. Appointed rulers (i.e. kings) tend to care about disempowered people very little. Entrenched ruling groups, like an established board of directors for a company, tend to empower people that they like personally, and in practice bring in more people who look and think like them.
But then again, mobs of people don't necessarily make informed decisions, and then they can STILL be indifferent to minority rights when voting. So for example, we have the 1964 civil rights act, which prevents anyone in the entire country from discriminating in various arenas. If it was put to a state by state vote, many states might explicitly give preferential treatment to straight white males. But we prevent them from doing that on purpose, because you shouldn't be able to vote away some people's rights.
I'm not British, so I don't have the most thorough understanding of Brexit. But the sense I get is that those who voted "Leave" are most generally the UK equivalent of Trump supporters -- i.e., cranky xenophobic nationalists. This is probably an oversimplification of both countries, but it's the rule of thumb I'm going with for now. I'm hearing that many Brits are experiencing buyer's remorse, having made a "protest vote" without really understanding the impact of the decision, and having ridiculed and dismissed "experts" such as economists, who universally said this vote would be bad news. In the US it seems like a popular stance to oppose "career politicians" and vote for outsiders who haven't held office before. Donald Trump send like the end game if this strategy.
In politics, as in other areas like science and medicine, I think there is definitely something to be said for weighting the input of experts differently than other people. Sure, power corrupts. But also, it would be great if judgement on a law was made more by people who have had time to study the law and understand the issue better.
But on the other hand, we go back to appointed rulers having likely biases against "commoners." So it's a tough thing to figure out a fair system.