The fairest way to reach a decision
It is concerning that the country is almost split down the middle between EU remainers and leavers, and the difference between the two groups of only 3.8 per cent is extremely small.
Upon looking into the statistical significance of the figures I discovered the following.
First, May’s Theorem states that simple majority voting is the only anonymous, neutral, and positively responsive social choice function between two alternatives (K.O. May, Econometrica, 20, 680 – 684, 1952). Put simply, this means that the Yes/No referendum vote on leaving the EU was the fairest way to reach a decision.
The next question to ask is whether the result was statistically reliable since it was so close.
The answer to this is offered by the Z-test for the difference between two proportions, ie the proportion that voted Yes and the proportion that voted No.
With 51.9 per cent voting Yes, and with a total of 33.57 million voters, the result of the calculation is 160, which far exceeds the conventional numerical threshold for a reliable result.
This means the referendum result was reliable.
The reason for its reliability lies in the large number of participating voters.
We may therefore conclude that statistically speaking the British people voted convincingly to leave the EU.
However, I do not believe the statistics adequately deal with the current situation with the country roughly split in two.
It seems intuitively wrong to take half the country in a direction they do not want, whichever way the election went, and this is why I believe that a binding decision to leave should only be made after the negotiations are complete, and May’s Law means that this should be by refendum.