Brexit: how to hold a second referendum

You can enable subtitles (captions) in the video player

So you want a new Brexit referendum, but there are three realistic options: no deal, the negotiated deal, or remain. If you ask the public whether they support any one of these, you'll get a resounding raspberry, so that won't find the settled will of the people.

If you ask people in a sequential process, first question, do you want no deal? Yes or no. Second question, if you want a deal, do you want the negotiated deal or to remain? The problem is, the order in which you ask the questions will affect the result you get, so that doesn't work either.

But don't give up. There is, perhaps, a solution. For that, we have an 18th century French revolutionary to thank, Nicolas de Condorcet. Condorcet worked out that if you have multiple options, let's say A, B, and C, and if you ran three head to head contests where A versus B, A versus C, B versus C. Then if, for example A beat B and A beat C, you can be pretty sure that A is the will of the people.

The beauty of the Condorcet method is this can be done on one simple ballot. Let's put our three Brexit options on the table. No deal, deal, and remain. Three options and boxes for first and second choice. And I'm going to put an X in the first preference and second preference. The third preference is obvious, so I don't need to write it down.

Look, first preference - remain. Second preference - deal. It's clear that in any head to head referendum for my preferences, remain beats deal, remain beats no deal, and deal beats no deal.

One ballot, pretty simple. X is in the box and you can count it three ways for three head to head contests. If there were lots of people like me, you would get remain wins both contests and it is clearly the will of the people. So we could stop there.

The Condorcet method should be attractive to Theresa May because second preferences always matter in this way of counting and it helps options which are unloved but are accepted compromises. But even with this clever Condorcet method, you could get an inconclusive result. You can get remain beating deal, remain losing to no deal, and deal beating no deal.

Here, the people's will goes round in a circle, just like the game rock, paper, scissors. If this happened, you'd need a tie breaker, something like which option had the highest number of first preferences? That would be a bit messy, but at least it's clear.

So should we look to a French mathematician for the resolution to the Brexit impasse? Well, it might help the prime minister get what she wants and live to fight another day. But don't tell the prime minister what happened to Nicolas de Condorcet after the French Revolution.