From a libertarian viewpoint—that is, from the point of view of giving priority to the value of individual liberty—it is not obvious whether Brexit or Remain is the best solution. And there is something wrong in what a British Conservative politician asked rhetorically: “What is liberty if not to govern ourselves?”
As Benjamin Constant explained, a liberty so described would be “ancient liberty,” the liberty of 50% plus 1 (at best) to “govern ourselves,” which means the power of 50% plus 1 (at best) to govern the rest. Constant also called ancient liberty “collective freedom.” “Modern liberty,” on the other hand, is individual liberty: to all extent possible, it allows each individual to govern himself. It is at the very least misleading to describe this system as “governing ourselves.”
One objection is that individual liberty can be guaranteed only by a state where libertarian-leaning people “govern themselves” in the sense that they are not governed by a foreign tyrant. Ultimately, we meet Anthony de Jasay’s argument that the only function of a “capitalist state,” or minimal state, would be to prevent a takeover by a non-minimal state, that is, by a state actually intent on governing. Governing and being governed, that is the problem.
The validity of the objection does require libertarian-minded people agreeing to every individual governing himself, and fundamentally disagreeing with “governing ourselves.” Seeing clearly through this might call for James Buchanan’s social contract theory. In the case of Brexit as in other “sovereignty” conflicts, it is not clear where the worst Leviathan danger lies.