One great virtue of representative democracy is that it allows for mistakes to be corrected. Wrong’uns can be booted out of office and bad policies can usually be reversed*. Under plebiscites, it is not so. These reveal the “will of the people” which must be obeyed. Whereas representative democracy is a system of checks and balances, plebiscites are battles of wills in which the victor wins permanently. As Mrs Thatcher said, plebiscites are “a device of dictators and demagogues.”
This is why there’s a big difference between Brexit and Trump: one can be voted out and his damage repaired; whereas in the other, this is much less likely.
Sensible polities set high bars for permanent changes, for example by requiring supermajorities for constitutional change. These help ensure that big changes will usually not be made in a fit of passion and regretted later**. Plebiscites, by contrast, permit radical changes even with slender majorities.
The distinction between the two systems would not be so sharp if plebiscite campaigns were conducted rationally and honestly and votes cast by reasonable, well-informed citizens. But this, of course, was not the case. What we had was one of the foulest spectacles in recent British history, scarred by lies (pdf) and racism which resembled no more than toddlers screaming “I want, I want”, with the same narcissistic denial of reality and over-inflated sense of entitlement***. It was a triumph of the id over the ego. If anyone had wanted to design something to vindicate Jason Brennan, they couldn’t have done better.
To be clear, the issue here is not whether Brexit is right or wrong. It is: can we be so confident that Brexit is right as to make a (largely) irrevocable change on that basis? In a narcissistic age in which we've largely lost the capacity for self-reflection, the distinction between these two questions isn't sufficiently appreciated.
All of this raises some paradoxes.
One is that perhaps the biggest thing I’ve learned in my adult life is that social affairs are complex and that knowledge and rationality are tightly bounded. This should have led to greater antipathy to plebiscites and to more respect for checks and balances. In fact, we’ve seen the opposite.
Paradox two is that traditionally it has been Conservatives who have been most sceptical of radical change and most leery of passions in politics. And yet it is these who have embraced plebiscitary politics. It cannot be stressed enough that Conservatives are no longer conservative.
Paradox three is that all this is being pointed out by a Marxist, and Marxists have historically supported some radical and violent changes. In truth, though, this isn’t a paradox. The change we favour now is gradual and consensual. It is we Marxists who are cool-headed and reasonable, and our opponents who are hysterical anti-conservatives.
* There are exceptions. For example, Thatcher’s sale of council houses was intended to be very difficult to reverse
** Again, this isn’t always so, as the US’s 18th amendment demonstrated.
*** I’m not saying this applies to all Brexiters or even most. But theirs were the loudest voices and perhaps the ones that tipped the balance.