51% means that there's a 51 in 100 chance of it working.
With votes, however, the margin is the number of votes that'd need to change for the result to change. So a 2% shift from Leave->Remain would have given a Remain result.
Personally, I think a referrendum should have at least a 10 percentage point lead (5% margin) before it could be considered a majority. I.e. 60:40.
As low as a 2% margin doesn't seem like democracy, as that figure can be easily skewed either way, by hosting it on the day Glastonbury starts, for instance, meaning a lot of younger voters will be away from the town with the polling station.
Bear in mind, that Farage said that if it was a narrow Remain vote, he'd be demanding a re-run. So a lot of the prominent Leavers are only claiming it's democracy in action because they got their own way. That said, a lot of remainers are doing the same.
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