Dissatisfaction with the European Union is on the rise, as Sunday’s elections in Italy showed. Now, even some mathematicians are mad at Brussels. In a paper uploaded recently to the arXiv server, Friedrich Pukelsheim of the University of Augsburg in Germany and Geoffrey Grimmett of the University of Cambridge in the United Kingdom decry the European Parliament’s reallocation of seats from the departing United Kingdom to other EU member states.

The duo complains that members of the European Parliament (MEPs) have ignored their own long-standing aim to assign seats using a clean, transparent formula, instead reverting to a more familiar approach: bargaining behind closed doors. That is bad news for European democracy, the mathematicians say, because it means that midsize countries are overrepresented in the Parliament. In their paper, they bemoan what they see as MEPs’ failure to explain how they converted population figures into seats. The Parliament, the pair writes, has missed an opportunity “to proceed from the dark ages to an era of enlightenment.”

A formula “pleases us, the academics, because it is a systematic way of responding to inevitable population changes,” Pukelsheim tells Science. “But it is frowned upon by politicians.”

EU citizens can only vote for MEP candidates of their own country, but the number of national delegates isn’t directly proportional to population size; if it were, Germany would get 200 times as many seats as tiny Malta. So the Parliament has always used a compromise that gives large countries a bigger say without drowning out the small ones. The European Union’s constitutional Treaty of Lisbon, signed in 2007, stipulated a maximum and minimum number of seats for each member state—96 and six, respectively—and also imposed a ceiling on the total number, 751.

But how to assign seats to individual countries within those limits is up to the Parliament itself. In 2007, MEPs proposed introducing an “undisputed mathematical formula” to implement the concept of “degressive proportionality,” stipulated in what was then the draft of the Lisbon Treaty. It meant that smaller member states can never have more seats than bigger ones, but do get more seats per million citizens.

At a 2-day workshop in Cambridge in 2011, held at the request of the European Parliament’s Committee on Constitutional Affairs (AFCO), Grimmett, Pukelsheim, and other experts devised a formula to do just that. The Cambridge Compromise, as it became known, assigned each member state five seats regardless of its size, and then allocated the remainder in proportion to population, but rounded up so that every country has at least six seats.

MEPs blithely ignored their advice in 2013, ahead of elections the following year, settling instead on a “pragmatic” division of seats that violated the principle of degression several times over; there were many examples of a bigger country having more MEPs per million citizens than the next biggest country or countries.

Pukelsheim and Grimmett had another chance to push the Cambridge Compromise at a second AFCO-organized workshop, held in Brussels in January 2017, where the key issue was what to do with the 73 seats to be freed up after the United Kingdom leaves the European Union in March 2019. (Three other mathematical formulae were discussed as well.) But the experts were ignored again. In January, AFCO decided to recycle 27 of the United Kingdom’s seats to create a new 705-seat assembly, but once more assigned the seats through negotiations.

The biggest loser appears to be France, which would have gained an extra 12 seats over its 2014 allotment under the Cambridge Compromise (assuming the United Kingdom’s seats were simply removed from the Parliament), but which ended up with just five more. By contrast, Hungary and Sweden each ended up with four more seats than the formula would give them; another five countries get three more seats.

In a report to the Parliament, the MEPs in charge the redistribution efforts, Danuta Maria Hübner from Poland and Pedro Silva Pereira from Portugal, said it will only be possible to agree on a formula when “the political context is ripe” for a discussion that also includes a review of the separate voting system in the European Council, which experts regard as slightly biased against citizens from midsize member states. In any case, they wrote, an agreement should wait until the United Kingdom has left the European Union.

The new allocations were backed by fellow MEPs at a plenary session on 7 February, with 552 voting in favor and 109 against. They are likely to be approved by the European Council, which comprises the heads of government of the member states, in June.

Pukelsheim is disappointed that MEPs have once more favored backroom dealing over mathematical rigor, arguing that the seats freed up by Brexit gave them the excuse to adopt a new system without unseating anyone. He is optimistic that they will settle on a formula for the next round of elections in 2024 but remains cautious. “The status quo is so enormously inert they essentially hate to touch it,” he says.