Ordinary elections are simple. Once the votes are counted and the number of seats in Parliament determined, you know who will govern for the coming years.

There are two exceptions to this rule. One is elections involving Winston Peters in the kingmaker role. The other is any elections to the European Parliament.

Europe has just gone to the polls (i.e. the – still – 28 member states of the European Union) in the world’s second-largest democratic vote after India. There is a new European Parliament with 751 elected MEPs.

Yet we do not have any sense what this will mean.

If you are watching this from New Zealand and you only pay marginal attention to European affairs, this election will utterly confuse you. So, let’s try to make some sense of it together.

To start with, there are European political groups in the new Parliament that voters only vote for indirectly via national parties.

For example, there is the Alliance of Liberals and Democrats for Europe (ALDE), which might be called a liberal political grouping. Yet it unites parties from across Europe that have little in common.

ALDE includes: the UK Liberal Democrats, a social-democratic party; Austria’s NEOS, a free-market party; and La République En Marche!, the heterogeneous movement of French President Emmanuel Macron. ALDE is liberal only in a very liberal interpretation of that word.

The next confusing factor is the role of lead candidates. Since the last election in 2014, the two main groupings have campaigned with so-called lead candidates. These are politicians nominated to become the President of the next European Commission (the EU’s ‘government’) in case their groupings win the election.

Sounds logical and similar to national elections. But it is not that simple.

The problem is there is no automatism. Under European treaty law, the President of the European Commission is elected by the European Parliament. However, the candidate first needs to be nominated by the European Council, i.e. the heads of Europe’s national governments.

Thus we have the strange situation in which neither the European Parliament nor the European Council alone can decide on the next head of the European Commission. The choice of the President is therefore bound to lead to much haggling.

This is especially true after this election because it is not just the position of European Commission President (and members of the European Commission) which need to be filled. Also, the European Central Bank needs a new President, as does the European Council and the European Parliament. Plus, the EU has to appoint a new High Representative for Foreign Affairs and Security Policy.

To complicate matters further, and even though there is no legal requirement for it, a balance must be found between various national and political interests. All major party groupings have to be represented according to their strength, and no country or group of countries can become too dominant.

With the election result Europe’s voters just delivered, this becomes an almost impossible task. Because for the first time in the European Parliament’s history, the two major political groupings from the centre-right and centre-left no longer command a majority.

The European People’s Party (EPP) as the grouping of centre-right parties won 179 seats. Its centre-left counterpart, the Progressive Alliance of Socialists and Democrats (S&D), got 150 seats. Each grouping lost just under 40 seats. In third place, the aforementioned ALDE now holds 107 seats, up 39 from the last election.

It means that President Macron has effectively made himself Europe’s Winston Peters. Without Macron’s support channelled through ALDE, it will be challenging to put together a majority in the European Parliament. Otherwise, the EPP and S&D would have to rely on the bloc of Green parties, which might be too hard to swallow for some EPP members.

The rest of the European Parliament mainly consists of populist and extremist parties on the fringes, which neither of the more moderate party groupings would want to rely on.

Macron had never left any doubt that he did not like the concept of lead candidates. Just days before the election, he backed Michel Barnier, the EU’s chief Brexit negotiator, for the top Commission job.

This is not without irony because Barnier does not even belong to Macron’s own ALDE grouping. Instead, he is a former vice-president of the EPP and thus a conservative. But from Macron’s perspective, Barnier’s political leanings probably matter less than the fact that he is French.

By blocking the EPP’s actual lead candidate, the German Manfred Weber, Macron could, therefore, install his compatriot Barnier as the next Commission President while still gifting the job to the EPP.

Strangely, this might work even for German Chancellor Angela Merkel. She had to back Manfred Weber’s candidacy not least because he is a member of her CDU’s Bavarian sister party. Still, just like Macron, Merkel never had much sympathy for the lead candidate system either.

By sacrificing her compatriot and party ally Weber, Merkel might even gain something she would want even more. Germany could then claim the position of the next ECB President as compensation. The Germans also have a well-qualified candidate for the job in Bundesbank President Jens Weidmann, who happens to be a former economic advisor to Merkel.

The above scenario is not a prediction. It is meant as an illustration of what kind of negotiations Europe can expect over the coming days and weeks.

The number of positions to fill and the arithmetic of the election result lead to almost limitless combinations of parties, candidates, and nationalities. It is a gigantic pan-European power play that is only insufficiently described as democratic.

Perhaps that is not how elections usually conclude, but this is the European Parliament. It is constituted in its very own way, and European affairs follow their own logic.

If you are a New Zealander watching this strange process with a sense of disbelief from afar, do not be too puzzled: Most Europeans do not understand it either.