Three into two doesn’t go

By their nature, if referenda are to be used only for matters of the greatest import, a clear answer must be forthcoming and therefore only binary outcomes can be permitted. In fact, though the Brexit referendum voting slip had just Remain or Leave printed on them, the Leave campaign was a coalition of two different perspectives. Michael Gove and Boris Johnson wanted to leave the loss of sovereignty implied by being a member of the EU with its automatic imposition of any Brussels regulations, but did not wish to lose the ability to trade freely with the EU, particularly in financial services where the UK dominates Europe. Many in wealthy parts of the UK voted Leave for this reason. For Nigel Farage on the other hand, the key issue was control of immigration – the EU’s freedom of movement for people in the single market was not acceptable and many in the poorer parts of the UK voted Leave for this reason.

The UK thus finds itself in a situation of intransitive preferences, known as Condorcet’s paradox. This occurs when a society prefers A over B and B over C and C over A. For a single individual this is obviously inconsistent, but in a society of many different points of view, this state of affairs is quite possible.

The referendum shows that the UK prefers Leaving the EU to Remaining in it. However, leaving the EU requires that we have to choose between continuing to be part of the Single Market with its economic benefits and having constraints of the freedom of movement of EU citizens. EU leaders have made it quite clear that this is the price to be paid to be part of the single market.

Thus it is entirely possible that there is majority preference to Remain rather than no longer be part of the single market but have control of immigration, ie Remainers plus many of the richer Leave voters, and a different majority preference to Remain rather than not have control of immigration and continue to have full participation in the single market, ie Remainers plus many of the poorer Leave voters.

Theory shows that for society as a whole such intransitive preferences have no good solution and this is where the UK finds itself today – wanting to Leave but with no plan and the world laughing at it.

Boris Johnson, now in campaigning mode to be the next Prime Minister, proclaims that the UK can have both, but David Cameron has already admitted that the UK must choose. The next Prime Minister will thus have to choose between the interests of business and the City and the poor. As a Conservative the obvious course may be to save the interests of business, but such a course of action will further alienate the poorer sections of the country and boost the support for UKIP and its anti-immigration stance.

There is already speculation that France would be prepared to offer the new prime minister zero tariffs on goods (where the Eurozone has a large surplus with the UK) and controls on immigration from the EU but no passporting rights for UK banks in to the EU. This would be exactly what the Farage wing of Leave would accept, but do great damage to the City and Conservative supporters.

As ever in politics there will likely be a compromise with some damage to the UK’s access to the single market in services in exchange for some flexibility on EU freedom of movement.