SHE was born to Lutheran ministers known to be both tough and principled. As a child, she thought it unfair that pupils were not allowed to sell fruit and milk in school and successfully lobbied for change. In her office in Brussels she keeps a statue of a raised middle finger, a gift from a trade union when she was deputy prime minister of Denmark, as a reminder that there will always be critics.

It shouldn’t have come as a surprise that Margrethe Vestager, the European Union’s competition commissioner, took a tough line against Google this week. The size of the fine the tech giant will have to pay for abusing its monopoly in online search, €2.4bn ($2.7bn), sets a record for European antitrust penalties (see chart). Yet more important than the amount is that she provided a rough guide to how the European Commission plans to deal with online firms which not only dominate a market, but essentially are the market.

In the 2000s Microsoft got into trouble because it had expanded its Windows monopoly by bundling it with its web browser. By comparison, Google’s infraction seems minor. In 2002 it launched a price-comparison service called Froogle, later renamed Google Shopping. In 2008 it changed how this service works. According to the commission, the new version systematically favoured Google’s own comparison-shopping results by giving them prominent placement at the top of its generic search results and demoting links to rival offerings to pages further down in its results, where users hardly venture.

This would not be a problem if there were several big search engines. But Google’s market share in most European countries exceeds 90%. When the firm introduced the changes, traffic to rival websites, such as Britain’s Foundem, plunged. This denied other firms the chance to compete and reduced consumer choice, said Ms Vestager. Google has 90 days to find a way to treat its own comparison-shopping service and those of rivals equally.

Predictably, Google wants none of this. It says its search service is far less dominant than it appears: consumers look up products on many other sites, including Amazon and eBay (the commission did not count these as search engines). Google also notes that the changes made in 2008 benefited consumers. “People usually prefer links that take them directly to the products they want,” Kent Walker, the firm’s general counsel, wrote in a blog post. Here, Google appears to have a point. Why would consumers want to click on a link which leads them to another site if they can see products and prices neatly lined up above Google’s search results?

The European Court of Justice, the EU’s highest court, will have to weigh the merits of its argument. Google will appeal, and there are weaknesses in the commission’s case, such as the difficulty of proving real consumer harm from the treatment of other price-comparison sites. Yet the commission deserves credit for tackling a question, which is increasingly important but which American trustbusting agencies have avoided: what is the responsibility of dominant online firms, including Amazon and Facebook, when direct competitors, large and small, offer products and services on their platforms?

The prevailing wisdom, particularly in America, used to be that “super-platforms”, despite their size, do not unfairly use their market power and thrive because of their unceasing innovation. The competition is always just one click away, argues Herbert Hovenkamp of the University of Pennsylvania. If Google were to degrade its search results by demoting links to better services, users would just switch to a rival service, such as Bing or DuckDuckGo.

But as digital platforms have grown ever bigger, that thinking has started to change, even in America. A growing number of antitrust experts now accept the commission’s view, that network effects create high barriers to entry in online markets. This means that Google, for instance, can in fact degrade its search results selectively (and disadvantageously to its direct competitors) without having to fear that its users will defect, says Maurice Stucke of the University of Tennessee. “We need these super-platforms to adhere to a principle of neutrality,” he says.

How can such a principle be enforced? In the case at hand Google could just feed all search queries through one algorithm and do away with the second one that produces the Google Shopping results. But what if this one algorithm still ends up putting Google’s links on top? Will the commission then force the firm to reveal its inner workings and even rewrite it? If search algorithms become more personalised, as is expected to be the case with digital assistants such as Amazon’s Alexa, it will be even more difficult to detect bias.

Ms Vestager can put such questions aside for the moment. But this week’s decision sets a precedent. Her team will now examine other offerings from Google, including travel information and reviews of local businesses. It may well push for scrupulously equal treatment in these fields, too—which would limit how the search giant can combine and link its services, at least in Europe.

Queen Margrethe

Ms Vestager has let it be known, too, that Google is likely to be found guilty in the two other cases she has launched against it. One deals with Android, its mobile operating system, and whether the firm has used it to protect and expand its position in online search. The other examines whether Google has hurt competition in online advertising. Brussels insiders say that decisions (and further hefty fines) may come as soon as July.

Fair competition is essential in an industry that is reshaping society rapidly, Ms Vestager argues. As the cases, and the fines, pile on, there is sure to be resistance from across the Atlantic—and perhaps even sympathy for Google. Even her fans wonder whether Ms Vestager is too zealous. But it may require someone as forceful as the Dane to take on the biggest platforms.