It's a Brussels murder mystery that would flummox even Hercule Poirot: Who killed the Spitzenkandidat?

Accusations are flying over the death of the "lead candidate" system for choosing the president of the European Commission, the EU's most powerful job. It's a crime story that's also a political drama — played out over multiple summits including a day-and-night marathon earlier this week — about how the European Union should be governed.

Making the case particularly fiendish: Some confessions may not be all they seem and some of the most indignant accusers are also prime suspects.

Manfred Weber, the German center-right candidate, has pointed the finger at an unholy alliance of French President Emmanuel Macron and Hungarian Prime Minister Viktor Orbán.

French officials and others suggest Weber look closer to home — at himself and his European People's Party (EPP).

Members of the European Parliament blame leaders of EU member countries, who cast aside the lead candidate system to choose German Defense Minister Ursula von der Leyen on Tuesday as their surprise nominee for the Commission presidency. But MEPs themselves are also accused of sabotaging a system they claim to hold dear.

In time-honored tradition, POLITICO's in-house detectives — combining the steeliness of Taggart, the empathy of Montalbano, and the method of Maigret — have gathered the suspects to go through the case against each one, before revealing the truth.

The European Parliament: Senior MEPs came up with the system before the 2014 European Parliament election. It was meant to work like this: Pan-European alliances of national parties would each nominate a Spitzenkandidat, or lead candidate, ahead of the election. That person would also be their candidate to be European Commission president. The European Council, made up of national leaders, would then nominate the candidate of the winning party, who would then be confirmed by the Parliament. MEPs argued the system brought more democracy to the choice of Commission chief.

Many national government leaders didn't like the system. They noted that the EU's governing treaties require only that they take "into account" the Parliament election when selecting the nominee for Commission president. And they stressed they have their own democratic legitimacy as elected leaders. Critics of the concept also noted that voters in the EU election still choose from national parties — and the vast majority of voters are completely unaware of the pan-European alliances and their lead candidates. But the system prevailed in 2014, with the EPP's lead candidate Jean-Claude Juncker of Luxembourg appointed Commission president — in part because it was hard to say no to someone who had served for 18 years as a head of government.

This time around, the concept got muddier. Some MEPs insisted it should work as last time — with the candidate of the party that comes first in the election claiming the Commission presidency. But others argued that any Spitzenkandidat who could command a majority of votes in the European Parliament could become Commission president. That left open the possibility that different parties could band together behind one Spitzenkandidat.

In picking Weber, the EPP increased the chances that EU leaders would reject their candidate as unqualified to run the EU executive.

That ambiguity made it even harder to explain an obscure concept to ordinary voters, and set the stage for a bitter post-election battle, with different camps interpreting the system in different ways. Juncker admitted on Friday that the process this time around was "not very transparent."

The German language: Choosing a long German word (admittedly not so long by German standards) to describe something and expecting it to be easily understood and liked across Europe was probably über-optimistic.

European People's Party: The Continent's predominant political alliance, which includes Angela Merkel's Christian Democrats and other center-right parties from across Europe, took a big risk by choosing Weber as its lead candidate. The Bavarian is a veteran MEP and leader of the EPP group in the European Parliament. But he has no experience of senior executive public office. For decades, Commission presidents have previously served as heads of national governments or senior ministers. In picking Weber rather than former Finnish Prime Minister Alexander Stubb, the EPP increased the chances that EU leaders would reject their candidate as unqualified to run the EU executive and choose a non-Spitzenkandidat. (In nominating Weber, the EPP also ignored a tradition that the Commission chief should be able to speak French — a move sure to go down badly with Paris.)

Guy Verhofstadt and Europe's liberals: Verhofstadt, until recently leader of the liberal group in the European Parliament, and the liberal ALDE alliance were enthusiastic backers of the Spitzenkandidat last time around. But as they moved towards a tie-up with Macron — an outspoken critic of the system — Verhofstadt changed tack. The former Belgian PM justified the U-turn by saying he'd hoped transnational lists of candidates would feature in the election, allowing voters to choose a Spitzenkandidat directly. The liberals ended up nominating a Spitzenteam — a slate of candidates for top EU jobs — who were not seen as true "lead candidates" by other parties. Their change of heart meant one of the Parliament's major groups was no longer behind the system.

Emmanuel Macron: As a newcomer on the EU stage who does not belong to either the main center-right or center-left families, Macron made no secret of his disdain for the Spitzenkandidat system. The system offered no obvious advantage to him or his centrist political group. He repeated many of the long-held criticisms of the system, including that the lead candidates were not known to most European voters. For the system to make any sense, Macron argued, the EU should introduce transnational lists of candidates, allowing voters across the bloc to vote for the same parties and leaders.

Macron also made very clear — too clear, to the taste of some Germans — that he did not think Weber was up to the job. In doing so, he weakened the Spitzenkandidat system — although he was willing to accept another lead candidate, current Commission First Vice President Frans Timmermans of the Party of European Socialists.

Viktor Orbán: The Hungarian leader, champion of "illiberal democracy," claimed credit for killing two Spitzenkandidaten — Weber and Timmermans. But Orbán is a late convert to the anti-Spitzenkandidat camp. As recently as March, he said he would support Weber "until the end." His U-turn came only after the German, who has long sought to cultivate good relations with Orbán, supported his party's suspension from the EPP. And neither Hungary alone nor the four-strong Visegrad Group of central and eastern European governments was big enough to kill the Spitzenkandidat alone. In the case of Weber, they were helped by Macron, plus socialist and liberal leaders. With Timmermans, they were assisted by...

EPP prime minsters: A group of EPP national leaders, including Ireland's Leo Varadkar, Bulgaria's Boyko Borisov and Croatia's Andrej Plenković rebelled against a compromise plan championed by Merkel, which would have given Timmermans the Commission presidency and made Weber president of the Parliament. That plan would have put two "lead candidates" in top EU positions. But the conservative rebels decided they wanted the EPP to hold onto the Commission presidency above all, even if it meant ditching the Spitzenkandidat system. "The vast majority of the EPP prime ministers don’t believe that we should give up the presidency of the Commission quite so easily, without a fight," Varadkar declared on Sunday. Some leaders from the EPP rebel countries also complained that Weber had struck a deal that secured jobs for himself and Timmermans without telling them, according to diplomats.

Manfred Weber: Weber was the Spitzenkandidat of the party that finished first in the European Parliament election, albeit with fewer seats than last time. But Weber could not persuade other pro-EU parties in the Parliament to rally behind him. If he had been able to demonstrate he commanded a majority, it would have been much harder for EU leaders to reject him. He was also unable to get his parliamentary group to back the deal championed by Merkel, which would have preserved the Spitzenkandidat system by putting Timmermans in the Commission presidency.

EPP MEPs: After an all-night session, some EU leaders were still trying on Monday afternoon to pursue a package that would have made Timmermans Commission president. But then came word from a meeting of EPP MEPs in Strasbourg that they would not vote to confirm any nominee who did not come from their party family. With Weber out of the running, the largest group in Parliament decided that keeping hold of the Commission was more important than the Spitzenkandidat system it had long defended.

All Spitzenkandidaten and MEPs: Weber was not the only lead candidate who couldn't put together a majority in Parliament. Nor could Timmermans, or Competition Commissioner Margrethe Vestager, who emerged as the liberals' choice for the Commission. And MEPs from the main pro-EU groups were not willing to make the compromises necessary to establish such a majority. That handed the whip hand to national leaders to pick someone else — resulting in the surprise choice of von der Leyen.

So who killed the Spitzenkandidat? It's an outcome familiar to fans of Poirot — all of them did.