It was an historic night. For the first time, candidates for the European Presidency went head-to-head in a live, televised debate as they fought to win the support of hundreds of millions of voters.

Four hopefuls battled to become President of the European Commission, representing the EU’s 500 million citizens.

The winner would set the policy agenda of the Commission, the only body able to propose new EU laws, and represent the EU on the world stage.

Of course, the EU is a democracy, and the debates took place in the run-up to elections, to be held on May 22 in the UK and between May 22 and 25 in other countries.

This isn’t a fantasy. The debates actually took place, at Maastricht University in the Netherlands, on April 28.

There were four candidates - Jean-Claude Juncker of the centre-right European People’s Party, Martin Schulz of the Party of European Socialists, Guy Verhofstadt of the Alliance of Liberals and Democrats for Europe Party and Ska Keller, of the European Green Party. A fifth candidate for the post, Alexis Tsipras of the European Left, declined to take part.

And the European elections later this month may decide who gets to be the president of the European Commission – officially the most powerful post within the European Union.

But you will be forgiven if you missed the debate. It was broadcast on euronews, which is available on satellite and cable services in the UK but not on Freeview. It seems to have passed other broadcasters by.

In the past, the President of the European Commission was appointed by national government leaders meeting together as the European Council, although the European Parliament had to approve the decision.

But things changed when the Treaty of Lisbon came into effect in December 2009.

The treaty states that the European Council must “take account” of the results of the European Elections. This appears to mean the political group that wins the most seats in the European Parliament later this month gets to choose the Commission President. But there is one complication.

It’s not clear that European Council members such as German Chancellor Angela Merkel or David Cameron agree. They’ve been dropping hints that they believe they still have the right to pick a candidate.

So rather than being the final word on the Presidency, the European Elections could be the prelude to a row between national government leaders and the European Parliament.

However, presenters and candidates taking part in the the 90-minute debate, handily available in full on the euronews YouTube channel, seemed in no doubt the forthcoming elections would decide the Presidency.

So who’s standing? The candidates represent parties within the European Parliament which are themselves alliances between national parties.

* Jean-Claude Juncker, a former Prime Minister of Luxembourg, is the candidate of the European People’s Party (EPP), the centre-right group in the European Parliament. British Conservative MEPs were once allied to the EPP but split off, largely because the EPP supports a federal Europe.

Seen as the favourite, his campaign website lists his five priorities as creating jobs and growth; reducing Europe’s dependence on Russia for energy; signing a trade agreement with the US; reforming the Euro, and “to give an answer to the British question”.

* German MEP Martin Schulz is the candidate of the Party of European Socialists, which includes the British Labour Party, although he has been more or less disowned by Labour leader Ed Miliband because he is a supporter for further EU integration. His priorities include cutting youth unemployment and introducing “decent minimum wages across Europe” according to his website.

* Guy Verhofstadt is the candidate for the Alliance of Liberals and Democrats for Europe Party. which includes the Liberal Democrats. He is a former Prime Minister of Belgium and his manifesto calls for “a further decisive step in the European integration as the fuel for new growth in Europe”, as a way of exiting the economic crisis

* German MEP Ska Keller is the candidate for the European Green Party, which includes the Green Party of England and Wales. She calling for a European energy policy with agreed CO2 reduction targets, and an end to austerity.

* Alexis Tsipras is the candidate of the European Left, which includes a number of Communist parties although none from the UK. He is Leader of the Opposition in Greece.

His priorities include ending austerity and transferring power from EU bureaucrats to the European Parliament and national parliaments.

He argues: “The European Union has decayed into an oligarchic and anti-democratic fabric in the service of bankers, multinationals and the super-rich.”

So those are your candidates. And when British voters go to the polls later this month, they could help to decide who gets the top job in the EU – even if they don’t know it.