And suppose we had a three-way people's vote and the result was

May's deal 30%
No deal 22%
Remain 48%

Then what?

That is why we have to use some form of eliminating transferable vote system. Yes, actually agreeing what form is a problem in its own right, but it has to come up with a result where the is a clear winner. Anna Subry's approach of eliminating the weakest - No deal in your example - and redistributing the second preference to whichever of "May's deal" and "Remain" they preferred will end up with one above 50%, which would be the winner. Now, if some of these Brexiteers are telling the truth that they really do prefer remain to May's deal, then Remain would be highish 50's or low 60's and a clear win. However, I suspect they are not and we would end up again at an almost 50-50 split. And I cannot see that ending well.

There has been quite a lot of talk of the Condorcet system. I don't think is a good idea partly for technical reasons but mainly because it does not eliminate options, so would indeed end up with the sort of result Steve listed, probably with no-one above 50%. That also, I think, makes ongoing division near certain.