Does mathematics have anything to say about whether we should stay in the EU? In one sense, of course, it does. Numbers matter – for example, the fact that we do not send £350 million a week to Brussels.
For a mathematician, however, mathematics is not so much about numbers, important though they are, as it is about abstraction: that is, getting to the heart of problems by stripping away their inessential features and searching for widely applicable general principles. So instead of asking whether we should stay in the EU, I am drawn to a more general question: what is the point of cooperative agreements?
This question, which belongs to the branch of mathematical economics known as game theory, has been much studied. In brief, the answer is that when you have a group of interacting agents, the following situation often arises.
- Each agent has a choice of two options, A and B.
- It is better for everybody if everybody chooses A than if everybody chooses B.
- Each individual agent gains by switching its choice from A to B if the other agents do not switch.
This situation is called the Prisoner’s Dilemma, after a famous illustrative example that concerns two prisoners who have to decide whether to betray each other. Whenever it arises, there is a case for an enforceable cooperative agreement: without an agreement, each agent will tend to act in its own selfish interest and choose B, which will be worse for everybody; with an agreement that forces the agents to choose A, they will all be better off.
Here are just a few of the many examples that apply when the agents are European nation states.
A country is better off if its workers are decently paid, do not work excessively long hours, and work in a safe environment. (If this is not a high priority for you, that just means that you will need other examples to illustrate the abstract principle.)
However, treating workers decently costs money, so if a company is competing with companies from other countries, it will be tempted to gain a competitive advantage by paying its workers less, making them work longer hours, and cutting back on health and safety measures, which will enable it to reduce the price of its product.
More generally, national governments will be tempted to gain a competitive advantage for their whole country by allowing companies to treat their workers less well. And it may be that that competitive advantage is of net benefit to the country: yes, some workers suffer, but the boost to the economy in general reduces unemployment, helps the country to build more hospitals, and so on.
In such a situation, it may benefit an individual country to exercise a B-type option by becoming “the sweatshop of Europe”. If that is the case, then in the absence of a supranational organisation that forbids this, there is a pressure on all countries to do it, and if they do, then there is no competitive advantage any more, so workers end up worse off and there is no compensating gain.
Another example — so obvious that I won’t dwell on it — is the need to combat climate change. Here, option A is to take significant steps to reduce emissions, and option B is not to bother. The world as a whole will be much better off if we all choose option A, but any individual country stands to gain by being selfish and choosing option B. So again we need enforceable supranational agreements. (While the EU cannot combat climate change on its own, it can negotiate with the rest of the world much more efficiently as a bloc.)
A third example is tax harmonisation. Without it, countries are free to compete by setting low rates of VAT and corporation tax. This distorts markets and creates a pressure to race to the bottom. If governments want revenue from these taxes, then they need agreements to set minimum rates, as we have in the EU for VAT but not, so far, for corporation tax.
Next time you hear a Leave campaigner complain about EU control and regulation, ask yourself whether what they really want is to defect from an agreement that is there to deal with an instance of the Prisoner’s Dilemma.
Why do 92% of UK fishermen want to leave the EU? Because they want to overfish while the rest of the EU agrees to quotas. Why does farming minister George Eustice want to leave the EU? Because he wants to be free of the EU’s birds and habitat directive while the rest of the EU’s farmers spend money looking after their birds and wildlife habitats.
Can we trust our government not to succumb to these kinds of agreement-breaking temptations if it is free to do so? No, which is why in areas where international cooperation is needed, international organisations such as NATO, the World Trade Organisation and the EU are needed to enforce it.
Tim Gowers is British mathematician, a professor at the University of Cambridge and winner of a Fields Medal in 1998