How will historians remember 2011, the year which, according to the satirists at the Onion, has already used up the next decade's entire supply of news? Some wonder if the Arab revolutions put 2011 on a par with 1917, when the Ottoman Empire broke up. Perhaps it will stand alongside the great European upheavals of 1848 or 1989. Or there might be a mixed story to tell, with 2011 remembered as the year when democracy was demanded in one part of the world just as it was exposed as paralysed and impotent in the face of economic crisis almost everywhere else.

Democracy's humbling has been most dramatically visible in Greece and Italy, where elected leaders have been pushed aside in favour of technocrats and fixers, elevated without so much as shaking a single voter's hand. Their mission will include the surrender of much economic sovereignty, putting those decisions further out of the reach of their own citizens. What Greeks and Italians endure today, other eurozone nations might well face tomorrow as they are told to make similar sacrifices of autonomy to save their economic skin.

Whether in Europe or beyond, democratic leaders have seemed powerless to beat back the engulfing global crisis, the failure of the G20 at Cannes exposing their weakness for all to see. And yet, according to one who was there, the leaders of the world's authoritarian states – China, Russia, Singapore, Saudi Arabia – had a spring in their step in Cannes, confident that they could face down whatever the economic meltdown threw at them.

Why is the democratic world faring so much worse than its non-democratic rivals in the current storm? Start with austerity. It may not be the best solution for a worldwide crisis of anaemic growth and falling demand – indeed it is surely making the problem worse – but it is what the markets demand in return for manageably low rates of interest on the money they lend to governments. That it is these men, not those we elect, who are all-powerful is not new: Bill Clinton discovered as much nearly two decades ago when, in a spitting rage, he shot back at advisers who warned he had to trim his economic plans: "You mean to tell me that the success of my program and my re-election hinges on the Federal Reserve and a bunch of fucking bond traders?"

Given that it is the markets who call the tune, the question then becomes one's ability to dance to it most nimbly – and in that endeavour democracy is an impediment. Leaders who have to face the voters simply cannot impose austerity on an unwilling population without paying a price, whether in riots on the streets of Athens, protests in Madrid or Occupy camps in London and New York. In the immediate postwar era, people might have been readier to endure rationing and hardship in, say, Britain because there was a sharper sense of collective identity and solidarity, a belief that their sacrifice was the consequence of a worthy cause and that good times would come eventually. But now society is less cohesive: austerity is seen as the result not of defeating foreign tyranny in a just war but of bankers' reckless greed; and few believe, as they once did, that they are guaranteed to be better off than their parents.

None of these headaches press the same way on the masters of Beijing or Moscow. "Vladimir Putin is the most powerful human being in the world," says the political scientist and head of the Eurasia Group, Ian Bremmer. "He can change his country on a dime" – unrestrained by the rule of law or by any meaningful democratic checks.

Similarly China's rulers can switch national budgetary priorities in a heartbeat, spending trillions on stimulus with a stroke of a pen. If China's banks show the same unwillingness to lend as they have in Europe or the US then the politburo in Beijing simply issues an order for them to do so. No wonder that, contemplating the paralysed decision-making of Washington DC, the New York Times columnist Tom Friedman has fantasised about America becoming "China for a day". For democracies, saddled with the creaking machinery of checks and balances, slow, incremental change is possible – but firefighting in a crisis is much harder.

Indeed, it is democracy itself that the markets seem to despise. They don't mind when it delivers stability and predictability. The gridlock implicit in the US system was once appealing to the markets, with their conservative belief that the government that governs least, governs best. But now that same tendency tries their patience. When Standard & Poor's downgraded the US credit rating in August, it stated baldly that this was its verdict on the weakness of "American policymaking and political institutions" and their inability to cope with the economic hurricane.

Mark Leonard, who leads the European Council on Foreign Relations, calls this the "democratic penalty" that western nations are paying, a judgment that "there is a real crisis of governability," with both the EU in a mess and the US paralysed by partisanship, the latter trend towards dysfunctionality exacerbated by the retreat into a dogmatic, rightwing laager by the Republican party.

It's amusing, especially for outsiders, to laugh at the parlous state of the Republican presidential field, whether at Rick Perry's inability to remember his own proposals or Herman Cain's struggle to recall what exactly it was the US did in Libya recently. But what does it say when the highest office of the most powerful democratic nation on earth is sought by a group of such low quality? Some say it means no more than that the talented Republicans – the likes of Jeb Bush, Chris Christie and Mitch Daniels – have calculated that Barack Obama is too formidable a campaigner and fundraiser to beat, and that it makes more sense to run in 2016. But it's hard not to view a foreign policy debate as bad as the one the Republican candidates staged last Saturday as evidence of a fundamental lack of seriousness, a flight from the world from one of the two main parties.

The larger problem of democracies' weakness has not been caused by the economic crisis, so much as revealed by it. The growth statistics for the pre-crash decade tell a revealing story. The EU, US and Japan did OK, clustered together in the low single digits. But China and Russia enjoyed figures nearly twice as high. The best performing economies were the most authoritarian states.

This is hard for westerners to take. Our post-1945 story is that democracy is the best possible system, delivering the best possible outcomes for peace and prosperity. We long believed that authoritarian systems were always bound to fail, because they could not adapt or innovate, that they were fated to be clumsy and out of touch with their citizens, like the old Soviet Union. But China, for one, is challenging that received and comforting wisdom. It uses some of the techniques of democracy – including ceaseless polling – to ensure it avoids steps that might trigger social unrest, an approach Leonard calls "deliberative dictatorship".

In the end, democracy will surely prove its innate strength. Putin's tsarist rule – which, like that of the Saudi royal family, is reliant on extracting resources from the ground – cannot last for ever. But 2011 has punctured the sense of easy supremacy democratic societies used to enjoy. To reassert themselves they might have to break from the rules now choking them, and insist that it is people, not markets, that are sovereign.