SHE ended her presidency in 2010 with a sky-high approval rating of 84%. Barring an upset, Michelle Bachelet looks set to return for a second term next year with her popularity undiminished. On June 30th she comfortably won a primary election in the Concertación, Chile’s centre-left coalition, taking 73% of the vote. Little seems to stand between her and victory in November’s election. She would be the first president in 81 years to win a second term (consecutive terms are not allowed).

Her opponent in that race will be Pablo Longueira, a combative former economy minister and stalwart of the conservative Independent Democratic Union. Mr Longueira narrowly won the centre-right primary, staged on the same day. He has a lot of ground to make up: of the 3m votes cast in the two primaries, Ms Bachelet took over 1.5m, nearly twice as many as the two centre-right candidates combined.

The rhetoric of the primary campaign suggests that a second Bachelet government would be a good deal more left-wing than the first. She has proposed an overhaul of higher education, promising to abolish tuition fees and make the heavily privatised sector not-for-profit within six years. That policy is aimed at the students who have staged large-scale protests against the centre-right government of Sebastián Piñera since 2011. It would cost the equivalent of between 1.5% and 2% of GDP, Ms Bachelet says. She plans to pay for it by raising corporation tax from 20% to 25% over four years, and doubling a stamp tax on borrowing operations to 0.8%. She also wants to scrap a programme that allows firms to defer indefinitely the payment of tax on their reinvested profits. Businessmen squeal that cutting the tax break will stifle investment.

Ms Bachelet also promises a more liberal approach to social affairs. She says she wants to legalise gay marriage and allow abortion in some limited circumstances (Chile is among the handful of Latin American countries that ban abortion outright, even when the mother’s life is in danger). Her other proposals are more vague. She says, for example, that the country needs a new constitution, but has offered few details. She wants a new electoral system, but has not said what sort.

Her opponents are preparing to throw everything they have at Ms Bachelet. They have accused her of a clumsy response to the earthquake that hit Chile in 2010, at the end of her presidency. But the allegations do not seem to have stuck. Her support in Maule and Bío Bío, the regions worst affected, is as strong as it is elsewhere.

Two things could yet threaten her seemingly unstoppable campaign. The first is that a number of left-leaning independent politicians have said they will run for the presidency. One of them, Marco Enríquez-Ominami, took 20% of the vote in the first round in 2009. Although he is unlikely to repeat that showing, he could eat into Ms Bachelet’s support.

Second, many voters have yet to lend their support to any candidate. Until last year voting was compulsory. Now that Chileans may choose to stay at home, getting out the vote will become a crucial part of campaigning. Turnout at the primaries was 23%—higher than expected, but an indication that most votes are still to play for. Both Ms Bachelet and Mr Longueira, who represents the most conservative wing of the centre-right, are likely to tack to the centre as the election approaches.

Even if she wins the presidential race, Ms Bachelet must hope that her allies do well in parliamentary elections due on the same day. During much of her presidency she was hamstrung by the lack of a parliamentary majority, just as Mr Piñera has been during his. Nonetheless, if the primaries are a guide, Chileans seem poised to give their country’s first female president a second term, perhaps with a congressional majority to boot.