Using math to explain how Doug Ford won

One of the interesting wrinkles in the Ontario Progressive Conservative Party’s Decision Day That Would Not End was the disclosure that on the last ballot of the leadership contest, Christine Elliott got more individual votes than Doug Ford and also led in more provincial ridings than he did. Despite this, she lost the race under the weighted counting system being used to pick a leader, which assigned a maximum of 100 points to each riding, distributed those points proportionally, and added up the total for the whole province.

It is something like an “electoral college” system, only with 100 electors for each state instead of just one. (The only wrinkle is that in three northern ridings where fewer than 100 PC members voted, the individual ballots were counted as only one point each, giving those ridings a weight of less than 100 points. But this detail didn’t change the overall result.) As my colleague Andrew Coyne pointed out grumpily on the Day That Would Not End, the Ontario PC’s slightly paradoxical outcome is a bit like if someone running for U.S. president had won the popular vote and the Electoral College, but somehow lost anyway.

It’s not a lot like that, because candidates have to win according to the rules they are given, even if they are given in great haste after the leader those candidates intend to replace was set on fire and thrown out a window. (Moreover, U.S. states are theoretically allowed to split up their Electoral College delegations, and Maine and Nebraska, being run by freakazoids, actually do it.) But for Elliott to win more votes and more ridings and lose the contest is so counterintuitive that one’s first instinct is to wonder how the heck that is possible.

It’s easy to whip up a toy example to convince yourself it is. Imagine a very small universe of five ridings. Candidate Belliott beats Candidate Bord in three of them, 6 votes to 5; Bord wins the other two 2-1. If these ridings were all weighted equally, Bord’s twothirds shares in the ridings with fewer votes would be decisive.

Something like this, on a larger scale, is what happened in the real Ontario PC contest — it is what must have happened, in principle: Elliott’s vote had to have been less efficient overall. CBC News and its election analyst Eric Grenier obtained the details of the last PC ballot, and it is easy to see Doug Ford’s relative dominance in the ridings where individual votes had more weight.

The combined efforts of the Elliott and Mulroney campaigns delivered crushingly large margins in the Toronto ridings of St. Paul’s, University-Rosedale, Don Valley West, and EglintonLawrence: Elliott won these on the last ballot by more than 70-30. Ford, with most of Tanya Granic Allen’s votes appended to his, did almost as well in the Fordland-ish parts of Toronto, but individual votes there were weighted almost as lightly.

His deciding advantage came in what I can only describe as the metallic/smoky parts of Ontario (Sudbury and Nickel Belt, Timiskaming-Cochrane, AlgomaManitoulin, Hamilton Centre and Hamilton Mountain) and in Windsor, where he typically led 55-45 or 65-35. In these areas, most of them currently held by the New Democrats in the legislature, each individual vote of a Conservative member ended up being worth perhaps four or five times as much as a downtown Toronto vote.

Some of you are probably pumping your fists and saying “Take that, cocooned metropolitan elites!” And I don’t suppose the Ontario Conservatives mind very much if you do. Their electoral system was “designed,” if that is the word, to mirror the Ontario general-election map: that is practically axiomatic, if your paramount goal is to win the general. If the hinterland is given a little extra power over Rosedale, as it is in the legislature, many PCs will probably regard that as a cultural feature rather than a bug, too.

And if the PCs had a general desire to reward provincewide strength at getting out the vote, they accomplished that, too, though probably without anticipating that it would tilt the field in a decisive way. Ford and Elliott had a nearly equal number of last-ballot votes (in the end she led by fewer than 2,000 of the 62,000+ cast; given that the party apparently spent so many hours trying to assign ballots of uncertain geographic provenance at the end of the accounting crisis, it would probably be unwise to state things more specifically than that). But the Ford (plus inherited Granic Allen) raw vote count, if the CBC figures are right, was much more uniform across the province: the standard deviation of Ford’s actual lastballot counts was only twothirds of what Elliott’s was.

So on several levels, the PCs’ weighted voting system met the theoretical goals it was presumably intended to, and should not be instinctively castigated as stupid. The only question is whether it was really appropriate to inadvertently privilege votes in NDP ridings so much, seeing as the New Democrats are not what the Soviets used to call the “Main Adversary” in the forthcoming election.