As expected, Canadians yesterday voted, albeit narrowly, for a centre-left government. But they’re not going to get one.

According to the latest figures, the Liberals, New Democrats and Greens received 51.2% of the vote between them. But they have won only 113 out of the 308 seats — 76 to the Liberals, 37 to the NDP, none at all to the Greens.

Under a fair electoral system — for example, the Sainte-Laguë form of proportional representation that New Zealand uses — the Liberals would have won 81 seats, the NDP 56 and Greens 21. That would be a narrow but workable majority as against 117 Conservatives and 31 from the Quebec Bloc — who instead won 143 and 50 respectively. (Two independents make up the total.)

Anyone with a spreadsheet can do a Sainte-Laguë calculation in 30 seconds. It’s not rocket science. So why do so many so-called democracies put up with such patently undemocratic outcomes? (Australia does better, but not by much.)

The result means Conservative prime minister Stephen Harper is back in office with another minority government, having picked up 1.4% and 19 seats from 2006. Not much of a return for an election held a year early that was supposed to deliver a Conservative majority.

But things are worse for the Liberals. At 26.2%, they scored their lowest vote since 1867, and Stephane Dion looks like being the first Canadian Liberal leader in more than a century never to be prime minister.

The moral for other countries is somewhat obscure. The global financial crisis doesn’t seem to have had any decisive effect; it may have helped drive the swing away from the Conservatives in the middle of the campaign, but it may also have made voters ultimately reluctant to gamble on a change of government.

The Liberals’ key promise of a carbon tax and aggressive action on climate change is getting a lot of blame, but since more than half the drop in the Liberal vote went to the Greens it’s not clear that the electorate is really anti-environment. Dion’s apparent difficulty with the English language may have been just as important.

Most of all, Canada shows that electoral systems matter. In a winner-take-all system, division is a recipe for disaster. The Conservatives learned that lesson in the 1990s; now the left-of-centre parties need to do the same.