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Maths shows that this week’s Brexit votes won’t solve the UK’s crisis

The UK House of Commons is voting to try to agree on a solution to Brexit, but game theory suggests it has chosen a particularly bad way of doing so, says Petros Sekeris
UK Prime Minister Theresa May is making a statement in the House of Commons
Deal pusher: Theresa May is still fighting to get her unpopular Brexit deal through parliament
Mark Duffy/UK Parliament/Handout/EPA-EFE/Shutterstock

At 7 pm tonight, the UK House of Commons will try yet again to break the Brexit deadlock. MPs have decided to proceed with an array of indicative votes whereby a series of potential outcomes, including the no-deal option, will be proposed to the Speaker of the house, John Bercow. Bercow will then compile a shortlist of some of them for all MPs to vote on in a strict yes/no manner.

Prime Minister Theresa May then has the option to decide which of these outcomes to officially subject to voting in the House. This may all seem a sound idea given the looming deadline, and yet one needs to be careful because – as with any voting procedure – this process can be manipulated.

For starters, what should the prime minister do if two or more options get a majority? And what if none of them does – should May still propose the most popular one? Ultimately, most MPs are likely to prefer an option that will give extra time to the UK, or at least one that will require a reassessment from Brussels and thereby delay the process. If so, this will be good news for the UK, subverting the European Union’s strategy of forcing the UK parliament to choose between the two “evils” of a hard Brexit and an unpopular deal.

Such deal-making falls within the purview of game theory,  a branch of mathematics dedicated to analysing the potential outcomes of multi-party negotiations.

On the ballot paper tonight, there are likely to be three scenarios: a no-deal option (which includes alternative deals unacceptable to the EU), May’s deal and other proposals that require further discussions – including a new referendum.

Hard Brexiteers are likely to exclusively vote for the first option. The majority of MPs prefer some deal to no deal, and are thus likely to opt for one of the new options rather than May’s proposal. But if the Speaker includes too many options, it may be self-defeating because each single choice is likely to attract fewer positive votes. That puts a great deal of responsibility on Bercow to narrow down the number of options so as to avert a catastrophic outcome. Ideally, there should be just three options on the table.

With tonight’s vote decided in such haste, the procedure may not have been sufficiently thought through. Even the voting system, for example, can have a dramatic impact on the outcome. A preferential vote, for instance, would have brought forward a single “winner” and resolved some dilemmas, while sequentially voting on one option after another would have given more power to Mr Bercow to orient the outcome when selecting the voting order. As it is, the result of the vote is likely to be more uncertainty, and further delay in the negotiations with Brussels.