At the Pamplona bull run, once they unsnick the latch on the corral, no matter how smartly dressed you are, or how athletic, you are always going to look like a frightened person running away from bulls.

So it is in Pamplona, so it was in Madrid on Saturday for deposed socialist leader Pedro Sánchez. He picked his moment carefully to take on the raging bulls of his party oligarchy. But they still managed to trample him, and mercilessly.

Sánchez’s mistake was to challenge the tradition of “turnism” – whereby the socialists and conservatives simply alternate in power, enriching their friends while 20% of Spaniards lack jobs.

After two indecisive elections, Sánchez continued to block a rightwing government and to hold out the possibility of the socialist PSOE governing, with the support of the radical left party Podemos. For this, he was summarily ejected in a chaotic coup led by the party’s powerful regional government bosses.

Sánchez’s fate is one more signal of the crisis facing European social democracy. It was shaped for three decades around the certainties of neoliberalism. Now the free-market model has failed, social democracy seems stripped of the intellectual resource to renew itself.

And that, in turn, is the product of a deeper incoherence. Parliamentary socialism was born across Europe in the 1890s from multiple sources – moderate Marxism, trade unions, co-ops, splits from liberalism.

In 1945, social democracy had to be reinvented across continental Europe, this time as both an overt and covert bulwark against Soviet influence. And, in the 1970s, as the remaining dictatorships collapsed in Spain, Portugal and Greece, there was once again a moment of reinvention.

Throughout the century, it is remarkable how little emerged by way of a cross-border intellectual culture of the centre-left. If you wanted to choose a globally influential thinker for the centre-left after the second world war, you would have to go for the Hungarian-American historian Karl Polanyi. Polanyi argued that capitalism consists of a “double movement” – the push for free markets and the pushback against them, to regulate them in the interests of society.

The beauty of Polanyi’s big idea was that it allowed the centre-left in the 1980s to find a justification for its work that could survive the demise of the working class. Instead of “protecting the working class”, the aim of social democracy became understood as “regulating capitalism for its own good”.

The root cause of all social democracy’s problems since 2008 is that it is no longer clear how this can be done. There was a rightwing version of neoliberalism, red in tooth and claw; and a progressive version – with its financial inclusion agenda, gay marriage, and meritocratic ethos in education, healthcare and social policy.

But the central tenets of the economic system were set in stone in the Lisbon treaty, mandating austerity and forbidding the protection of key industries against the global market.

Now the economic mainsprings of neoliberalism are broken, social democracy’s task is to speed the invention of something else. But as Pedro Sánchez’s fate suggests, it is ill-equipped for doing that. Most socialist elites and bureaucracies in Europe – including Britain, as the backlash against Jeremy Corbyn shows – are attuned to running a capitalism that does not work, and seem incapable of imagining any other future.

The radical left – in the form of Podemos in Spain, Syriza in Greece, Bernie Sanders in the US and Corbyn in Britain – stands foursquare for the replacement of neoliberalism. But with what?

At its best, the new left radicalism is municipal, inclusive, audaciously anti-racist and promotes horizontal democracy. At its worst, it becomes an expression of revolt only; a list of demands; a celebration of resistance techniques; a rehearsal of leftwing tropes from yesteryear. In the one country where the radical left took power, Greece, it was forced into submission by north European social democrats.

But now there is a series of alarm calls. The near victory of the far right in the Austrian presidential election in May prompted an inner-party coup, putting left-leaning centrist Christian Kern into the chancellorship.

Kern, though a lifelong technocrat, is surrounded by thinkers from the left. Last month, he issued an open call for Europe to break with austerity, to double its proposed fiscal stimulus and – in a thinly veiled attack on Angela Merkel – to stop gaming the crisis for national advantage.

French socialism, meanwhile, is staring at moral collapse. It is impossible for any of its candidates in next year’s election to beat the far-right Marine Le Pen, and its supporters go into that crunch battle knowing they will have to vote for a conservative to stop her. And in Italy, premier Matteo Renzi has staked the centre-left’s future on a constitutional referendum he looks likely to lose.

All this explains why Corbyn’s victory has raised an alarm flag inside European social democracy. It shows you can move a traditional socialist party to the left. The defeat of Sánchez, exactly one week later, is meant to show that you cannot.

The Spanish socialist elite is reconciled now to four years of conservative government as the price for keeping the new, vibrant and radical left away from power. But Spain is about to teach the whole of Europe’s centre-left a lesson: if you cling to neoliberalism, you die. If Podemos, the radical left party, can open itself up to those among the socialists disgusted at Sánchez’s overthrow, the path is open for its emergence as a Syriza-style hegemonic left party.

The question, then, is the one posed by Austrian chancellor Christian Kern. Is Europe’s social democracy going to impose austerity for ever or, even if only for the selfish purposes of survival, actually begin to fight it?