…n particular, it's not clear why we should accept this as a standard for legitimacy after the fact. To the best of my knowledge, Grayling did not express any concern about referendum procedures before Remain lost the referendum, or following the very narrow Welsh devolution referendum of 1997.
OK, so I suspect that given you ignored all my other points and questions across all other articles, you’ll ignore this one and in this, I’m going to take a completely opposite position and state that you are a statistician, so should know a lot better than this!
Voting is a statistical sampling exercise. Like any such exercise, when any form of threshold is involved, that threshold should be set at a point to form a statistically significant change. This can be through the use of 95/99 confidence intervals, outside which it is considered sufficient to beat chance.
In a two option referendum, that chance is 50:50. The one place you do not ever set the threshold therefore, is 50%. The EU operate the 55% qualifying membership majority (with the caveat of a 35% of population representation in their blocking minority) in no small part for this reason. It is akin to selling people the sugar pill or homeopathy after a scientific or medicinal licensing study. Inherently, its garbage. Plus, the table is like saying “everyone else defrauds the government of benefits, so why shouldn’t we?”. Rubbish!
Your point on the application of the same approach as the 70's is noted, but is naturally also weak on the part of the government. The vote and subsequent evolution of the EU brought into scope the rights of people who were allowed into the UK realm as equivalent citizens, but didn’t have the right to vote at the time. The UK is not the same as it was in 1972. We’d have to strip away all technologies, legislature and indeed, both ourselves to go that far back in time. Not happening.