LONDON'S mayoral race is too close to call, but one thing is clear: the contest rests on voters' second choices. The pink ballot that Londoners will fill in on May 1st has two columns: one to mark their favourite candidate, and another to name their grudging second preference. Ken Livingstone, the Labour incumbent, and Boris Johnson, his Conservative rival, are expected to finish neck-and-neck in the top two spots, neither with a majority. The second choices of those who backed losing candidates will be added to their totals, to produce a winner.

The “supplementary vote” has never mattered much before in London, where Mr Livingstone has won the past two elections comfortably. (By contrast, three of England's 12 other elected mayors have at one point taken office only thanks to second preferences.) Now, it could swing things. The biggest prize is the votes cast off by the Liberal Democrats, Britain's third-largest party, which may account for nearly half the total. At London's last mayoral election Lib Dems backed Labour over the Tories. Their current candidate, Brian Paddick, has refused to say which of his rivals he dislikes least, but some polls show Lib Dems leaning towards Mr Johnson.

That may be misleading. For one thing, the polling samples are tiny (sometimes fewer than 100) at that level of detail. And it is tricky to get at true intentions, admits Nick Sparrow of ICM, a polling company. “We have a long history of casting one vote rather than two. The pollster may be asking about something that the poor old respondent has not previously thought about,” he says.

The London Assembly is also hard to predict, again owing to the way it is elected. In a system introduced in 2000 that no other English council uses, 11 of its 25 seats are allocated by proportional representation to any party that polls above about 5%. Small parties benefit: at the last election seats were won by the Greens and the right-wing UK Independence Party (UKIP), which have never elected an MP. The worry this year is that the British National Party (BNP), a thuggish far-right outfit, could win a seat, as it came close to doing last time.

In the past the far right was kept at bay by the electoral system. Tony Travers of the London School of Economics points out that in 1977 the National Front polled 5.3% in elections for the Greater London Council, but failed to win a seat because London then used a first-past-the-post system. If the BNP managed that share this year, it would win a seat. Their chances have been improved by the implosion of UKIP, whose supporters they hope to attract. Maybe—but only one in five UKIPers chose the BNP when casting their second-preference votes in the last mayoral election.

Much rests on turnout, which in past years has been little more than a third. Higher turnout will make it harder for the BNP to reach the 5% threshold, and may benefit Mr Livingstone, whose supporters are more reluctant to vote than Mr Johnson's. Turnout might be boosted by the candidates' larger-than-life personalities and intense rivalry. Which makes it all the odder that the outcome may be determined by people who don't much like either of them.