Lootman wrote:ursaminortaur wrote:zico wrote:To try to settle the "Is it 8% or 4%" debate?

Imagine the result had been 66.6% Remain and 33.3% Leave.

How best to express this?

a) Twice as many voted Remain as voted Leave.

b) Remain had a 33.3% margin of victory.

I've switched leave and remain around to reflect the 52:48 result since that was what Lootman used to claim the 8% percentage lead

(should actually be 1.08333 recurring as many voted leave as voted remain by that measure). If it was a 66 2/3% versus 33 1/3% victory for leave that would as you say be 2 times as many leave voters as voted remain or as Lootman would have it a 100% margin of victory.

If it was 75% to 25% it would be 3 times which would in his view a 200% margin of victory.

Your 100/0 "infinity" example is just plain silly so I will ignore it.

It's not a percentage of 8.333 recurring. As I noted earlier, it was actually 7.865% more Leave voters than Remain voters. But let's just call it 8% for simplicity.

And please do not put words into my mouth. If Remain had won 66.66% to 33.33% then I would probably have described that as there being twice as many Remain voters as Leave voters. If it were 75/25 then it would be accurate to say that Remain voters were treble the number of Leave voters. And so on.

It's helpful to look at the numbers this way. It means that, on average and rounding, in a room of 25 people there will be 13 Leavers to every 12 Remainers. To reverse the outcome, one of those 25 needs to be switched from Leave to Remain.

And that is 4% of the people in the room - half of the 8% number i cited. QED.

Yes sorry I was using the rounded percentages 52/48 as indicated. You are correct I should have used the actual votes

17,410,742 / 16,141,241 = 1.07865

But you are missing the point that your method stretches out the results in a non-linear manner to give answers in the range 0 to infinity rather than 0 to 100%. To compare margins you have to be comparing them as percentages of the same thing. That works with percentages of the total vote. It doesn't work as percentages of the losers-votes because as the losers vote decreases the denominator in your calculation decreases so the percentage you are dealing with is a percentage of a decreasing quantity rather than of a stable quantity such as the total_votes.

Using your method the actual result is 17,410,742 / 16,141,241 = 1.07865 which is 7.865% more of 16,141,241

Suppose instead though the result had been

16775992 to 16775991 (ie leave winning by 1 vote with the same total number of votes)

Then by your calculation that would be 16775992/16775991 = 1.00000006 which is 0.0000006% more of 16,775,991

but because those are percentages of different things they CANNOT be compared as percentages.

In comparison the standard method provides percentages of the total_vote ie of 33,551,983 which means those percentages can be compared.

Since using your method you cannot compare percentages for different voting patterns with the same voters you cannot use it to produce a figure for the required swing for remain to have won. As you say QED.