Crunching the numbers of the 2015 Election

In October 2015 the liberals won 184 seats in the Canadian Parliament of 338 seats. The CBC called it a “decisive majority” (link). The National Post wrote that the Liberals “steamrolled to a stunning majority victory” (link). From my perspective, those conclusions seem hyperbolic.

The numbers that the media used as a basis of discussion are in the following table.

  Lib Con NDP BQ Green
# Seats 184 99 44 10 1
# votes 6,940,000 5,610,000 3,470,000 830,000 88,000
% of vote 39.6 32.0 19.8 4.7 3.5

While I wouldn’t call it a stunning majority victory, it seems that Canadians were clear in their choice of a governing party. However, there were some questions that weren’t asked during the campaign or in the analysis afterwards that may have provided a different view.

Spoiler #1: Of the 17.7 million votes cast in the last election, only 5.26 million had any bearing on the results.

Spoiler #2: Of these 5.26 million ‘necessary’ votes, only 14,622 (in sixteen ridings) were needed to give the Liberals a majority government.

Firstly, did each party’s seats have the same support from the electorate? In the following table I have divided the popular support of a party by the number of seats won by a that party.

  Lib Con NDP BQ Green
# Seats 184 99 44 10 1
# votes 6,940,000 5,610,000 3,470,000 830,000 88,000
% of vote 39.6 32.0 19.8 4.7 3.5
# votes/seat 37,700 56,700 78,800 82,600 610,000

There is quite a variation. Each Liberal seat is supported by only 37,000 voters. That is slightly less than half of the support of the NDP seats, and only a sixteenth of the support of the Green seat. One could argue that this is a misleading statistic. Our system doesn’t allow votes to be transferred from one riding to another, so a division of number of seats by number of votes is simplistic. On the other hand, it is a natural consequence of focusing on the big picture. Digressing slightly, this provides an argument for my proposal of Direct Representation in a previous blog post (link).

Secondly, how many of the total votes were cast for successful candidates? Consider the subset of votes that were cast for a successful candidate and ignore those that were cast for the losing candidates. After all, votes for losing candidates had zero impact on the election; all the Conservative/NDP/BQ/Green/Other voters in a riding that was won by the Liberal candidate could have stayed home and the electoral result would have been the same. The following table shows those totals.

  Lib Con NDP BQ Green
# Seats 184 99 44 10 1
# votes 6,940,000 5,610,000 3,470,000 830,000 88,000
# ‘successful’ votes 4,620,000 2,750,000 890,000 190,000 37,000

Of the 17.7 million votes cast in the election, only 8.5 million, slightly less than half, are ‘successful’ votes; there were 25.9 million eligible voters and less than a third of them played any role in the result. It is amazing that only a quarter of the votes for the BQ or the NDP actually resulted in a seat. This is an argument against the legitimacy of the election and the fairness of our current electoral system. These numbers summarize the main argument of people advocating for proportional representation. Many votes are wasted, and this wastage is not evenly distributed across the parties.

Thirdly, how many of the votes cast for a successful candidate were actually needed? The margin of Liberal victory in Liberal ridings in the 2015 election ranged from over 29,000 votes (in Lac-Saint-Louis) to 92 (in Edmonton Mill Woods).  Those extra votes didn’t change the result. Those voters (aside from the single voter in each riding that put the Liberals ahead of the second-place candidate) could have stayed home and the result wouldn’t have changed. The following table shows the ‘necessary’ votes.

  Lib Con NDP BQ Green
# Seats 184 99 44 10 1
# votes 6,940,000 5,610,000 3,470,000 830,000 88,000
# ‘successful’ votes 4,620,000 2,750,000 890,000 190,000 37,000
# ‘necessary’ votes 2,830,000 1,570,000 690,000 160,000 13,000

Of the 17.7 million votes cast in the 2015 election, only 5.26 million were ‘necessary’. None of the other votes would have changed the result.

Finally, how many votes were needed for the Liberals to form a majority government? The Liberal candidate was successful in 184 ridings, each with a different margin of victory. If 16 of those ridings had gone to another candidate, the Liberals would have had 168 seats, and would have formed a minority government. The following chart shows the margin of victory for all 184 liberal victories, with an inset showing the 16 smallest margins (which totalled 14,622 votes).

LiberalMargins3

These 14,622 Liberal voters were key to the liberal majority. If they had voted another way, or stayed home, the Liberals would not have “steamrolled to a stunning victory”.

Conclusion

Statistics are dangerous and can be misleading. It is for good reason that there are “lies, damned lies, and statistics”. On the other hand, they can highlight areas that warrant further consideration. From the analysis of this post, it seems clear that the distribution of seats that resulted from the 2015 election did not particularly reflect the actual voting. The number of seats that each party is a consequence of less than a third of the actual votes. Technology is available to allow us to do better.  See my blog post on Direct Representation (link).

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