I'm game if you are

Pairing people off can have some nasty and unexpected side effects. Occasionally, it works: Torvill and Dean spring to mind, as do Crick and Watson. But Blair and Brown, it is becoming increasingly clear, was not a match made in heaven.

Further alliances are likely to be struck in the next few weeks, and similarly disastrous long-term consequences may ensue. What the Labour Party needs now, before it's too late, is the help of a branch of mathematics known as game theory.

Game theory has proved useful to politicians in the past. When John Nash (of A Beautiful Mind fame) invented his "Nash equilibrium", a mathematical trick for settling arguments in a way that offers all parties a mutual advantage, it was applied with great success to cold war politics. It has also proved useful more recently: a government auction of bandwidth to mobile-phone companies in 2001 used Nash's equations to fetch as high a price as possible while keeping the phone companies happy.

So perhaps politicians could use game theory to settle their internal differences. A framework already exists. The "stable marriage problem" is designed to form long-lasting, strife-free alliances.

The maths begins with a familiar scenario - a group of people eager to pair off. The sticking point, as always, is that some people are more desirable as partners than others. The chances are that there is one person who dominates everybody's wish-list, meaning that if the process is left to itself, almost everybody will end up dissatisfied.

But there is a way forward. First, everyone has to rank all the potential partners in order of preference. David says he could work with Andy more easily than he could with Ed, for example. Andy, on the other hand, would rather work with Diane than with David. Unfortunately, Diane ranks Andy lowest of all. And so it goes on, until all the lists are in.

Once the rankings are in, you look for a set of pairings where everybody has the highest-ranking partner that will have them. In 1962, the mathematicians David Gale and Lloyd Shapley proved that it is always possible to find an outcome that is entirely stable - you really can create a situation where there is no partner swap that will make anyone any happier. It's a perfect recipe for long-term stability.

In half a century, however, the stable marriage problem has found only limited practical use. Dating websites could use it to solve all their clients' problems, but perhaps it suits them better to keep dissatisfaction levels high. The only documented case of everyday use seems to be in finding hospital placements for graduating doctors.

This is the perfect moment to apply it to politics. Labour could pioneer a scientifically formed leadership that will take us into an era of stable political partnerships. The downside? Exceedingly dull memoirs.


Michael Brooks holds a PhD in quantum physics. He writes a weekly science column for the New Statesman, and his most recent book is At the Edge of Uncertainty: 11 Discoveries Taking Science by Surprise.

This article first appeared in the 13 September 2010 issue of the New Statesman, France turns right

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Is anyone prepared to solve the NHS funding crisis?

As long as the political taboo on raising taxes endures, the service will be in financial peril. 

It has long been clear that the NHS is in financial ill-health. But today's figures, conveniently delayed until after the Conservative conference, are still stunningly bad. The service ran a deficit of £930m between April and June (greater than the £820m recorded for the whole of the 2014/15 financial year) and is on course for a shortfall of at least £2bn this year - its worst position for a generation. 

Though often described as having been shielded from austerity, owing to its ring-fenced budget, the NHS is enduring the toughest spending settlement in its history. Since 1950, health spending has grown at an average annual rate of 4 per cent, but over the last parliament it rose by just 0.5 per cent. An ageing population, rising treatment costs and the social care crisis all mean that the NHS has to run merely to stand still. The Tories have pledged to provide £10bn more for the service but this still leaves £20bn of efficiency savings required. 

Speculation is now turning to whether George Osborne will provide an emergency injection of funds in the Autumn Statement on 25 November. But the long-term question is whether anyone is prepared to offer a sustainable solution to the crisis. Health experts argue that only a rise in general taxation (income tax, VAT, national insurance), patient charges or a hypothecated "health tax" will secure the future of a universal, high-quality service. But the political taboo against increasing taxes on all but the richest means no politician has ventured into this territory. Shadow health secretary Heidi Alexander has today called for the government to "find money urgently to get through the coming winter months". But the bigger question is whether, under Jeremy Corbyn, Labour is prepared to go beyond sticking-plaster solutions. 

George Eaton is political editor of the New Statesman.