Imagine an EU led, 12 months from now, by Angela Merkel and Christine Lagarde That would catch the world’s attention. Is Europe at last getting its act together, the Americans and Asians might wonder.

Regrettably, it will not happen. Under the EU’s eccentric methods of allocating its top jobs, it cannot happen. With their muddy and contradictory notions of Europe’s international role, it is a fair bet the EU’s 28 national leaders would not even want it to happen.

What a wasted opportunity. In Ms Merkel, fresh from her victory in Germany’s parliamentary elections, and relishing her responsibilities as the pivotal decision maker in the eurozone crisis, there is a supremely well-qualified candidate to replace Herman Van Rompuy as president of the European Council, which groups the EU’s heads of government.

In Ms Lagarde, managing director of the International Monetary Fund and a former French finance minister, there is an excellent choice to fill the shoes of José Manuel Barroso as president of the European Commission, the EU’s executive arm.