The Obama-Clinton alliance, formalized with Bill Clinton's blockbuster speech at the Democratic convention, confirms what has often been played down: President Barack Obama has chosen to build on Clinton's legacy rather than abandon it.

This is why the 2012 election matters not only to Americans but also to supporters of the moderate left across the world. What's at stake is whether the progressive turn that global politics took in the 1990s will make a comeback over the next decade, and also how much progressives who embraced markets during the heyday of the Third Way sponsored by Clinton and British Prime Minister Tony Blair will adjust their views to a breakdown in the financial system they did not anticipate.

Polls reflecting an Obama upturn since the conventions suggest the Obama-Clinton politics of balance is far more popular than ideological conservatism. The two conclaves plainly shifted the campaign's focus to the views of Mitt Romney and Paul Ryan – and the more swing voters think about what the Republican ticket would do, the less they seem inclined to support it.

Many conservative commentators attribute Obama's bounce to Romney's failure to be specific enough. They don't want to acknowledge that on core issues, the electorate is far closer to Obama's moderate progressivism than to Romney and Ryan's conservatism.

Voters favor tax increases on the wealthy to balance the budget, have little interest in less regulation of capitalism and widely accept that Obama inherited an economic mess caused by conservative policies. The electorate is even starting to notice what it likes about Obamacare, a reason why Romney, earlier this month, listed all the new law's benefits that he would preserve.

The often-disparaged high command of the Romney campaign seems to know all this. Romney thus keeps trying to change the subject – to false attacks on Obama's welfare changes, to misleading assaults on the health care law's impact on Medicare, and, disastrously, to Romney's reckless criticisms of the president after the killings of Americans in Libya. Romney is scrambling because he knows the dynamics of the campaign are shifting against him.

The movement in the presidential race reflects a broader trend visible in many nations. In the immediate wake of the financial crisis, electorates moved not toward parties of the left, which is what one might expect during a crisis of capitalism, but toward the right. Conservative-leaning parties won a long list of national elections in 2009 and 2010, including the Republicans' midterm triumph here.

But since then, the center-left has mounted a comeback, reflected in the victory this year of Socialist Francois Hollande in France and a sharp poll swing against Britain's Conservative-led coalition government.

Yet the center-left's resurgence comes with asterisks. Last week's elections in the Netherlands, for example, produced a mixed verdict: The center-left Dutch Labor Party made impressive gains, but these were more than matched by the advances of the governing center-right VVD, which came out narrowly ahead. The Dutch election was, to a significant degree, a victory of the center and a defeat especially for the extreme right.

This search for moderation, argues David Miliband, the former British foreign minister who is close to Blair and an architect of Third Way policies, is why it's important that Obama is not leaving aside Clinton's market-friendly, socially conscious approach but revising it.

In an interview with my Washington Post colleague Dan Balz and me in Charlotte, Miliband argued that voters in the wealthy democracies are looking not for radical departures but for the new and better balance between government and the market that Third Wayers were trying to achieve. At the same time, he acknowledged that advocates of this approach needed to recognize the urgency of more effective oversight of the financial markets, one area where Obama has needed to move beyond Clinton's policies.

At the election night gathering of the Dutch Labor Party in Amsterdam, I heard almost exactly the same argument from Godelieve van Heteren, a former Labor member of parliament. "There is now a new debate over what kind of regulation there should be of the market" – regulation, she said, aimed at being effective without "killing entrepreneurship." Voters, she added, primarily yearn for "reasonableness."

American conservatism's glorification of the unfettered economy is thus out of step with the balanced approach that voters here and across the capitalist democracies are looking for. Obama and Clinton know this. It's the central problem Romney faces, which is why he is flailing around.

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