The Washington Post headline bluntly declares "Brexit is a reminder that some things just shouldn't be decided by referendum."
Writer Emily Badger, whose focus is generally on urban policy, brings up American ballot initiatives—particularly those in California—as an example of how referendums can lead to bad outcomes, or rather outcomes that certain people don't like.
After talking about a handful of Brits who publicly regret their vote (keep in mind that millions of people voted to leave), Badger points out correctly that public referendums can be used to undermine democratic institutions, both purposefully by special interest groups ranging from public sector unions to private corporations by directing taxes and government programs in their directions and by simple and not-so-simple unintended (or unpublicized) consequences.
Still, even when making this point, Badger commits some possibly unconscious biases to print when she writes about California, "Back in 1978, California voters generously decided in a ballot measure to cap their own property taxes in a way—amending the state constitution—that has hobbled ever since California's ability to generate revenue and create reasonable housing policy." The bold emphasis is mine to point out that her idea of a problematic referendum seems to inherently be anything that restrains the authority of the state. California's ability to generate revenue has most assuredly not been hobbled even with this one restriction. It's got some of the highest taxes and fees in the country. She uses "hobbled" to describe the idea that there are limits to what the state of California can afford to do, assuming that these are things that should be done.
But what should also be obvious during this entire "populist" vs. "elites" political battle happening both in the United States and Europe is that representative democracy under legislators has also led to taxes and government programs being directed to interest groups and all sorts of unintended or unpublicized consequences. And it's an issue that some these same people do not want to seem to deal with. Instead, we get the "uneducated poor people voting against their own self-interest" arguments, like we see about Wales.
These responses are of the "These communities get more money from the European Union than they pay in" vein. We have seen similar arguments about American states who get more "money" from the federal government than they pay in taxes. Such an argument ignores the fact that these targeted communities don't actually get more "money" than what they pay into the pool; what they get is more government administration and programs put together by various interest groups that tend to direct these subsidies to those with the right connections (in other words—"elites").
A read through how that money is used in Wales looks like a lot of the same kind of "redevelopment" spending we see in the United States that somehow gets a lot of money into the hands of various private developers and government projects and is prone to deep levels of corruption and cronyism. So the overall irony is that actually it's the higher-educated "elites" who benefit most from such a expansive multinational administration, and yet they probably don't realize how self-interest influenced their own votes. (Note that Bernie Sanders responded to the Brexit vote as evidence that voters see a "rigged economy" in the United Kingdom that benefits the wealthy and connected, and there is a chunk of people on the left who agree.)
But let's pull back to the larger issue of voting over one's own sovereignty. Yes, deciding whether to remain in the European Union has tied to it a whole bunch of complicated issues over immigration, trade, regulatory power, and many other concerns. But, the same is true whenever you are casting a vote over who will have legislative and administrative power over your life. Whether you're voting for an MP, a congressman, a president, or even a judge, attached to that vote is a directive over very complicated policies, like immigration, trade, and criminal justice.
So how is a vote whether to remain or leave the European Union on a fundamentally different level from a vote for MP or president? Is there something dramatically different about the choice of who represents you within your country and who you are granting the authority over significant parts of your life versus how many people in other countries you are permitting to do the same?
The question of who rules over you is an elemental, central component of having a democratic republic. Treating Brexit like it's just some complicated but very broad referendum is ignoring the nature of the question behind it. If British citizens shouldn't get to vote whether to be in the European Union because they don't "understand" all the issues involved, then why should they even get to vote on their legislators? Indeed, why have them vote at all?