Prince had many talents but a firm grasp of politics was, perhaps, not among them. In an interview, the late singer recalled his rage when he learned that there were ‘eight presidents before George Washington’. Prince’s teachers had not, as he implied, lied to him as part of some vast political conspiracy. He was simply confused about the early history of the United States, which saw a loose confederation of colonies led by one type of president replaced by a republic led by another.

Rage and confusion over presidents also reigns in advance of the UK’s referendum on whether to remain a member of the EU. ‘Five presidents run Europe – can you name them?’ Michael Gove, UK Secretary of State for Justice and a prominent member of the Leave campaign, asked the audience in his Sky News debate. None could and even Labour MP Stella Creasy – one of Remain’s most fluent members – fumbled her answer.

Gove’s question is straightforward but also slippery. For the record, the Five Presidents head: the European Commission, a powerful administrative body with the authority to propose new EU laws; the European Council, a summit that brings together David Cameron with fellow heads of EU member states; the European Parliament, the EU’s directly elected legislature; the Eurogroup, a meeting of eurozone finance ministers; and the European Central Bank, the institution responsible for setting interest rates in the eurozone.

Asking people to name the five presidents who run Europe is slippery because it asks us to take as given the claim that these office holders are in charge of the EU. Are they really? The term ‘Five Presidents’ does not appear in any EU treaty or law. It is most closely associated with a report on the future of the euro published in June 2015 by the current presidents of the Commission, European Council, European Parliament, Eurogroup and European Central Bank: Jean-Claude Juncker; Donald Tusk; Martin Schultz; Jeroen Dijsselbloem; and Mario Draghi, respectively.

The heads of euro zone countries commissioned this report as part of on-going discussions about how to safeguard the euro from future economic crises. Some of the ideas contained in the Five Presidents’ Report were modest, as in plans to create economic watchdogs in each member state. Others were more radical, including plans for economic, fiscal, financial and political union complete with a eurozone budget capable of fiscal stimulus programmes.

Ambitious though the Five Presidents Report was, ambition should not be confused with authority. Major changes to eurozone governance – such as a eurozone budget – would require treaty changes that could not become law without the backing of member states. Thus far, the member states have shown next to no enthusiasm for the Five Presidents’ more radical ideas. In this narrow sense, Gove’s claim that Messrs Juncker, Tusk, Schultz, Dijsselbloem and Draghi run Europe gives a false impression of how the EU is governed.

Of course, the referendum is not about a report gathering dust in Brussels. It is, above all, about whether British interests are served by remaining in the EU. Thus far, there has been no shortage of informed debate on the economics of this question, But the national interest cannot be reduced to cost-benefit calculation. Even if, as HM Treasury, the Bank of England, the IMF, the OECD and others tell us, the UK gains from membership, voters are entirely right to ask whether they have political control over the EU institutions that bestow such benefits.

In this wider, political sense, Gove’s premise that the Five Presidents run Europe is both inaccurate and misleading. Several institutions are absent from his list, including the Council of Ministers, which brings together ministers from each member state for regular meetings in Brussels. Convenient though it often is for national governments to blame the Commission for unpopular policies, such proposals cannot become law unless national ministers first agree to them in the Council. Along with the European Council, the Council of Ministers is a powerful protector of national interests. It is these institutions – and the British politicians that sit within them – that truly run the EU for better or worse.

Although Prince might be forgiven for his confusion over US presidential politics, Michael Gove knows all too well who runs Europe. As Justice Secretary he has a seat at the table when the Council of Ministers decides on justice and home affairs legislation. Indeed, should the UK vote to remain in the EU and Gove keep his job – to big ifs at this stage – he is in line to assume the presidency of this institution in the second half of 2017. Don’t expect president (in waiting) Gove to tell you this, of course, lest it puncture Leave’s own vast conspiracy about how the EU works.

Dr Dermot Hodson is Reader in Political Economy at Birkbeck College, University of London.