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federal election 2015

Progressive Conservative leader Stephen Harper, left, greets Liberal leader Justin Trudeau, right, prior to the beginning of the Globe and Mail Leaders Debate in Calgary, Alberta Sept.17, 2015.MIKE STURK/Reuters

The Conservatives and Liberals could receive the same number of total votes across the country on election night, but the Tories would still end up with more seats in Parliament. This is often attributed to a greater vote efficiency of the Conservatives compared with the Liberals. This efficient vote isn't a virtue of Stephen Harper's campaign machine, but a consequence of how voters are distributed into constituencies.

If we go back to 2011, we can see how this plays out. Let's say the national popular vote was a three-way tie and rebalance the 2011 election results applied to the new constituencies using the assumption of a uniform national swing in every riding. In that scenario, the Conservatives would win 139 seats, the NDP would win 106 and the Liberals would win just 88. Doing the same calculation, but making the national numbers line up with the polls, shows that the Conservatives could still end up with a few dozen more seats.

While this assumption of uniform national swing is too simplistic to model real voting dynamics and should not be seen as a prediction, it is a useful reminder that even when parties receive the same number of votes, they might not win even a similar number of seats.

Imagine a party with 5 per cent of the vote nationally. The most inefficient way for this vote to be spread out would be to have 5 per cent of the vote in each constituency as it would result in zero seats. A much better distribution would be to concentrate this vote in one or two dozen ridings, enough to win them, and have no votes in any other constituency.

This second example would be called an efficient vote because the individual votes would be easily converted into seats, while the first example would be called an inefficient vote because the votes would lead to nothing.

Not every vote in a first-past-the-post system is equally efficient. It's clearer at the extreme ends. A smaller party like the Greens could increase its 4 per cent vote share in 2011 to 10 per cent without picking up all that many seats. At the other end of the scale, a considerable upswing in Conservative support in Alberta compared with the 2011 results could at best net the party the sole seat the party failed to win in the last election.

A classic example of this is in Quebec. Of the two main provincial parties, the Parti Québécois has historically had a much more efficient vote than the Liberals, needing fewer votes than the Liberals to win the most seats. This is largely because the Liberals are particularly popular on the west island of Montreal. While this might not sound like a bad thing, they end up winning by such huge margins there that they "waste" additional votes that do not turn into new seats.

The riding of Jacques-Cartier, the only provincial constituency with an anglophone majority, was won by the Liberals by a margin of more than 75 percentage points in the 1998 provincial election in Quebec. They won 32,924 votes there, compared with the second-place PQ, which won just 3,315. The margin was 29,609, which were votes that did not add a single seat to the Liberal count, and could have been better placed in other ridings. Distributed among 10 ridings, for instance, these voters could have overturned many seats won by the PQ.

This PQ vote efficiency resulted in the party getting a huge majority, winning 76 of the 125 seats up for grabs despite the Liberals winning the most votes. In fact, they won 27,618 more than the PQ. Perfectly performed polls would have shown a close race between the PQ and Liberals, but knowledge of the province's vote efficiency would have suggested that this was bad news for Jean Charest's party.

Vote efficiency can be increased by focusing on specific ridings at the expense of others. (This was the Green Party's successful strategy that got Elizabeth May elected in 2011.) Yet this generally goes only so far as most people still vote based on national issues. Political science research suggests that local campaigns have an important, but still small, effect, influencing 3 to 10 per cent of the eventual vote in most ridings.

Knowing about the differing vote efficiencies of the parties is key to interpreting national poll numbers correctly. In the case of Quebec in 1998, Liberals knowing that their party was tied with the Parti Québécois might have been confident of victory and subsequently disappointed on election night.

Similarly, a tied national vote between the Liberals and Conservatives looks as though it will result in the Conservatives winning the most seats, though far short of a majority. Those looking for a Liberal victory should become more confident of also winning the most seats only when their vote margin lead looks larger than three or four percentage points.

Paul Fairie is a political scientist in Calgary who designed The Globe and Mail's Election Forecast.