As Constitutional Reform Minister at the time, I had responsibility for the detailed election rules set out in the European Union Referendum Act 2015. Since those rules would have included any provision for a super-majority of the kind that is suggested in the petition, it might help if I explain why we did not include such a super-majority in that Act, which was passed by Parliament last year.
There was not much discussion of super-majorities when Parliament debated the 2015 Act, but had that subject come up, I suspect that there would have been widespread opposition to it from campaigners on both sides of the debate. No matter what the issue at hand may be, a super-majority gives an in-built advantage to the status quo. It tilts the playing field deliberately in favour of no change. In other words, it would rightly have been seen as a pretty transparent attempt to give the remain campaign an enormous—and in the eyes of many, unfair—advantage. Leave supporters would have denounced it in ringing terms. Equally importantly, more thoughtful remain campaigners would probably have felt uncomfortable too.