Often, The Girlfriend and I are deadlocked on a decision where neither of us expresses a strong preference — for instance, which restaurant to go to. In those situations, we each pick a side and play rock-paper-scissors. Then, once the decision is “real,” we gauge how we actually feel about it and have the option to revise it.
The basic insight behind this method is that there is an unbridgable gap between the hypothetical and the real. We can’t really judge how we will feel about a choice, for instance, until we’ve actually made it and feel locked in. Merely entertaining the possibility does not predict our real reaction — in a weird way, in order to make an informed decision, we have to have already made it and know how it feels.
Hence I support the Brexit do-over referendum, on purely psychological grounds. The British public was clearly short-sighted in their decision because they were too focused on the — completely legitimate and justified — pleasure of defying the establishment and weren’t thinking about the longer-term consequences. In the cold light of day, they realize that the frisson of defiance is not worth it.
In short, now that UK voters know what the morning after actually feels like, they are finally in a position to make the decision for real. A second referendum would therefore be more legitimate than the original. Or to save time, Parliament could simply implement the policy that the public’s gut reaction to the Brexit vote clearly indicates.
An und für sich 
Herodotus reports that the Persians made all their decisions twice, once drunk, and once when sober, and they were only binding if they were the same both times.
The problem is that polling seems to suggest most people who voted Leave are very happy with the result, and it’s hard not to feel that any attempt to do it over would be seen as a massive betrayal by a large proportion of already very alienated and angry people. It’s a total mess, but I’m not sure there’s any such easy way out of it.
The beauty of my approach is that it’s potentially open to infinite regress. “Now that you know what it feels like to choose it again in the cold light of day, would you still choose it?” Etc., etc.
The eternal brecurrence of the same.
This has generally been the EU’s approach to referendums (referenda?) in the past.
I think the EU approach hasn’t so much been “now in the cold light of day, the citizens of country X realize they want to vote again” so much as the EU telling them “you will hold new ones until you get it right”, even if the actual citizenry thought they got it right the first time.
I think this is good on why a second referendum would actually be pretty dangerous: http://www.vice.com/en_uk/read/how-to-benefit-from-brexit
I am trying to think through the choice of the referendum through the prism of Lacan’s double blackmail of “your wallet or your life”! We were supposed to vote in due to the cataclysmic uncertainty of an out vote. Zizek states that faced with a forced choice we should choose the worse option. I am struck by the proximity of a protest vote and a refusing of a blackmail. Ultimately what distinguishes the two is that in the former case relies upon an interpassivity i.e. I vote one way with the expectation that the majority would vote the other for me. To the shock of the protest voter they actually won, and some have buyers remorse. It will be interesting as to whether we can fully assume the referendum result so that it breaks the lock of the double blackmail.
Having said all of this, I am haunted by the prospect that I have understood the double blackmail in a wrong sense. The mandated “right choice” was in fact to leave the EU.
…hence as Ben implies above, EU is happy to let UK leave.