It is "always difficult to distil the many and varied messages that electorates send politicians into a single story", saysThe Times; even more so when the electorate is spread across 28 nations. Whichever way you look at the result of last week's European elections, they were "terrible" for integration.
From The National Front in France to Syriza in Greece, far-right nationalist and hard-left parties, who won a third of the seats in the EU parliament, delivered the same verdict: they do not like the direction the EU is taking.
The response will be informed by the "distinct and incompatible" visions of the future of Europe that leaders hold. Some, including David Cameron, see "the drift towards federal power as the source of the EU's lack of legitimacy" (decisions are taken at EU level, with no real say from Europe's citizens).
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Others believe that what is needed is greater integration and federalism so that the EU "functions in a more effective and streamlined way".
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The real danger is that nothing will happen, says Gideon Rachman in the FT. The main business at this week's EU summit is likely to be which insider gets to be head of the European Commission. Serious adjustments to policy are "just too hard" to agree on.
But this "cannot be allowed to happen". The anti-establishment parties may be very divided, but they "do share a common theme: the strong belief that the EU has become too powerful at the expense of the nation state".
To say that the vote was actually about immigration or the economy and not about Europe is to "miss the point". Controlling borders and national finances are two of the "basic functions" of the nation state, and both have been "largely ceded to the EU".
The challenge for EU leaders now is to see if they can restore some national democratic control over these areas without actually dismantling the union itself. The results will help Cameron to win the argument for change, says The Times.
If re-elected next year, he has pledged to renegotiate Britain's relationship with Europe. "We need an approach that recognises that Brussels has got too big, too bossy, too interfering," Cameron said. "It should be nation states wherever possible and Europe only where necessary."
