Politics in Europe these days can have a paradoxical quality. So it is that Europeans will go to the polls next month in an election that will be both significant and meaningless for a legislative body that is simultaneously influential and impotent. Meet the European Parliament.

Elections for the European Union’s Continentwide parliament are generally a low-turnout snooze compared with national elections, but the EU’s sheer size means these votes are still among the world’s largest democratic exercises. About 198 million ballots were cast in the 2019 round, compared with some 158 million votes in America’s 2020 presidential election, 168 million in Indonesia’s elections this spring, and 120 million in Brazil in 2022.

Europeans next month will elect the 720 members of the legislature that constitutes one-third of the EU’s governing structure, the other two parts being the bureaucracy in the European Commission and the heads of national governments in the European Council. What powers will those lawmakers exercise?

Formally, a lot. The European Parliament must approve new legislation alongside the other two branches, and it has grown more effective over the years at creating legislation and blocking ideas proposed by the other two branches that lawmakers don’t like. The Parliament also elects the president of the Commission, who becomes the most prominent single figure in EU politics.

Practically, it depends. National leaders retain individual vetoes over many decisions, meaning the Parliament can govern only with unanimous consent of those other politicians. Legislating remains a matter of bargaining within the Council rather than a process of forming a consensus between a majority of the Parliament and a majority of the Council.

Ditto the appointment of a Commission president. Europe periodically flirts with establishing a “leading candidate” system, in which the leader of the largest party in the newly elected Parliament would become leader of the Commission—akin to a prime minister. Such a model may emerge eventually, and should bolster the legitimacy and accountability of the Commission. But for now presidents are foisted on a (sometimes more, sometimes less) willing Parliament after horse trading among national presidents and prime ministers.

The subtler issue is that the European Parliament lacks an institutional sense of itself. Lawmakers campaign as members of their own country’s political parties; European “parties” are merely the umbrella coalitions like-minded national parties form with each other once they reach Brussels and the Parliament’s other seat in Strasbourg, France.

Legislators are beholden to party leaders back home, especially if they have ambitions in national politics. It’s as if Ron DeSantis called the shots for every Republican member of Florida’s U.S. House delegation, while Gavin Newsom directed California’s Democratic members. In a chicken-and-egg conundrum, this is both a cause and an effect of a fragmentation that makes it hard to talk about “European” as opposed to national public opinion and politics.

The perception that these forces produce an impotent legislature traditionally led Europeans to assume the result of European Parliament elections would be meaningless. This encourages voters to use these elections to send messages rather than shape policy outcomes. They tend to be a field day for protest parties of left and right. Which leads us back to the chicken-and-egg dilemma: Is the European Parliament ineffective because it’s larded up with fringe politicians, or is it larded up with fringe politicians because it’s ineffective?

Yet this year’s vote could have big practical consequences. In part this is because members of the Parliament are becoming savvier at exercising their powers. After the 2019 election, national-government leaders in the Council thwarted the Parliament’s plan to place the leader of its largest party grouping (Manfred Weber of the center-right European People’s Party) atop the Commission. But lawmakers did extract policy concessions as the price for narrowly approving Ursula von der Leyen , preferred choice of Germany’s then-Chancellor Angela Merkel .

The consequences may be substantial this time around, precisely because of those feedback loops between European-level and national politics. Issue One will be immigration, which is expected to drive a lot of voters toward protest parties. The presence of those lawmakers in the European Parliament can shift the debate on Continentwide approaches to stemming inflows, while such an outcome will frighten national governments into tougher action on matters such as welfare eligibility for migrants and deportation of those who enter illegally.

To cite another example, German commentators have belatedly noticed that national parties opposed to the forced march toward electric vehicles are likely to be the big winners in that country’s European Parliament vote. This signal from the EU’s largest economy could force Brussels to dial back the EU’s grand climate ambitions, a reversal that’s already under way amid Ms. von der Leyen’s fears of an embarrassing electoral rebuke in June. Such a result also could push Berlin to do the same closer to home.

It’s a reminder that elections have consequences, even in the EU. European politicians are learning they ignore these votes at their peril, and that’s a good reminder for the rest of us, too.