Jeremy Corbyn’s candidacy is about as improbable as his ideas. He didn’t even ask to be on the ballot for leader of Britain’s Labor Party, yet he’s ahead in the polls – and part of his appeal is his unapologetically old-fashioned economic thinking.

Imagine Bernie Sanders winning the Democratic Party’s nomination for president in the U.S. Like Sanders, Corbyn is a longtime activist and campaigner, guided by personal hard-left conviction rather than party loyalty or strategic calculation. For both men’s supporters, that’s the appeal – and, for their parties, that’s the danger.

Labor has been through this before: After losing to Margaret Thatcher’s Tories in 1979, it had a long and passionate affair with socialism before finally putting centrist Tony Blair in charge in 1994. Something similar could happen again. Many Labor supporters blame their crushing defeat in May on Blair’s New Labor legacy and a deficit of vigorous leftism. Many socialist radicals, in any case, would rather lose with honor than win with moderation. Corbyn is such a throwback that he’s even open to revisiting one of Blair’s first and most notable triumphs: striking “Clause Four” from the party constitution, which supported “common ownership of the means of production, distribution and exchange.” Apparently, in 2015, Corbyn doesn’t regard that issue as closed.

For now, though, this isn’t just, or even mainly, about policy. Corbyn, like Sanders in the U.S., speaks to the prevailing disenchantment with the insincerity of ordinary politics. Many voters – not just those on the left – want a change from all that.

Whether they’ll want the policies that Corbyn will eventually have to spell out, supposing he wins, is much more questionable. In 1983, a leading member of the Labor Party called its election program “the longest suicide note in history.” That’s something for Corbyn and his supporters to think about