Seeing red

Given that those who bothered to vote in the 2016 referendum were split more or less straight down the middle, it stands to reason that our democratically elected parliamentary representatives, assuming they are following their mandate, should be equally split straight down the middle, and no amount of parliamentary debate is going to change that.

I imagine that were there to be a second referendum, the country would still be split more or less straight down the middle. Perhaps a larger percentage of the electorate would bother to vote and perhaps the line would be drawn fractionally on the other side, but there would still be an impasse.

We need a tie-breaker and I have a couple of suggestions which are no more barmy than another 40 months of argument in the House of Commons;

Either we resolve this simply with a single round of Rock, Paper, Scissors between Gina Miller and Boris Johnson,

or, given that the argument is ultimately about “sovereignty”, couldn't we just get our Sovereign to cast the deciding vote and earn the biscuits we have all been paying for throughout her busy and difficult life? 
Couldn't she now do something a little-bit-useful in return?