POLLING stations in Chile’s presidential election closed at 6pm on Sunday. By 6.45pm, and with barely a third of the votes counted, the centre-right’s candidate Evelyn Matthei had acknowledged defeat. That was how emphatic her opponent’s victory was. In the end Michelle Bachelet, who also held the presidency from 2006 to 2010, won with 62% of the vote to Ms Matthei’s 38%. That was by far the widest margin of victory in any of the past four presidential elections, all of which have gone to a second round. In the previous three, no one got above 54%.

The only downside for Ms Bachelet (and indeed for the entire Chilean political elite) was a turnout of just 42%, well down on the 49% recorded in the first round last month. Just 5.7m people voted, out of an electorate of 13.5m. The low turnout was as much to do with a change in the rules as with voter apathy: this was the first presidential election in Chile in which voting was voluntary.

“Today, a lot of Chileans didn’t go out and vote,” Mrs Bachelet said in her victory speech on the Alameda, Santiago’s main thoroughfare. “We have to persuade them to believe again, not in me, not in a party, not in a political group. We have to make them believe again in democracy.”

Ms Bachelet has nonetheless been gifted something that no Chilean president has enjoyed for a decade—a healthy parliamentary majority. Her New Majority coalition will have 68 seats in the 120-seat lower house and 21 seats in the 38-seat Senate.

That should be enough for her to get much of her ambitious programme—a confection of tax reform, education reform and electoral change—approved. For the centre-right, meanwhile, a period of reflection and regeneration beckons. Sebastián Piñera, the outgoing president, delivered healthy economic growth but could not satisfy demands for a fairer society. Managing that balancing-act will now be Ms Bachelet’s challenge.

Update: This blog was updated on December 17th. The original version said that Ms Bachelet's programme included tax cuts. Although she has promised a cut in income tax, she also campaigned on a pledge to raise corporate tax.