Vitruvius's Experimental Election Predictor
By Marcus Vitruvius, The Sagacious Iconoclast
Recension 3.3.7, 2011-05-02
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The 2011 Election ~ Final Results
For the first time since confederation, the Liberal Party of Canada is neither Her Majesty's Government nor Her Loyal Opposition. The Bloc Québécois have been nearly wiped out. The leaders of both those parties lost their seats. The New Democratic Party is for the first time Her Majesty's Loyal Opposition, but with more than half the NDP seats in Quebec, and 77% of Quebec's seats NDP, the NDP & Quebec are now stuck with each other.
Clearly it's been an unusual election; that is also reflected in Ve: The Right Honourable Stephen Harper, Prime Minister and leader of Her Majesty's Government, has achieved a majority of 167 seats with a Ve of 6.3, one point below (sic) his 2008 minority of 143 seats with a Ve of 7.3. The projected seat range for Ve = 6.3 was 136 to 164, Mr. Harper bettered that by three, so next time that boundary will have to move slightly.
The pollsters final results came in at ΣVe/n = 4.81, ca. 1½ points below the final election value (but they would have been worse if not for the COMPAS result). They were ca. two points low in 2008, yet ca. two points high in 2004 and 2006. The following text & images have been updated to reflect these excellent results.
(All images can be picked for larger views.)
Introduction to Ve
For the last seven years I've been experimenting with a Canadian Federal election results predictor, known as Vitruvius's Experimental Election Predictor, which is defined as follows:
where C is the percentage of voters who poll for the Conservative Party (of the day, which since 1962 has included the Progressive Conservatives, the Reform Party, the Canadian Alliance, and the Conservative Party), and L is the percentage of voters who poll for the party in first place on the left of the aisle (which has traditionally been the Liberal Party but was the NDP in the last week of the 2011 election), as measured by various pollsters, or as counted on election day.
For example, if we take the 2008-09-19 polling results from Nanos Research, we have C = 39 and L = 28, giving Ve = 7.37. Or, if we take the 2005-04-12 polling results from Environics, we have C = 30 and L = 36, giving Ve = -3.96.
The idea behind Ve is straightforward. If there were only two parties, C and L, then the ( C + L ) ÷ 100 term is equal to 1.0, and Ve simplifies to: ( C - L ). That's a pretty obvious measure of who's going to win (there are no minority governments if there are only two parties), as long as Ve isn't too close to zero (in which case per-riding splits become dominant).
With more than two parties, the certainty of Ve decreases, so the ( C + L ) ÷ 100 term reduces the value of Ve toward zero, according to the percentage of votes not going to C or L, in which case the "close to zero" argument in the previous paragraph kicks in.
The real value in reducing the per-party poll results into a single Ve value is that then allows us to plot the Ve values, against time, for multiple pollsters, and still have the graph come out simple enough to parse. It's the gross trends that Ve exposes best, and those are best studied across multiple pollsters.
The interesting thing about Ve in Canadian federal elections is that if we look at the actual election results since 1962 (as shown in the graphs and tables later in this essay), then, at least historically speaking, if Ve is less than -8 we have a Liberal majority, between -8 and -4 we have a Liberal minority, between -4 and 1 it's indeterminate (one Conservative minority, one Liberal minority), between 1 and 6 we have a Conservative minority, between 6 and 8 we have had one Conservative majority & one Conservative minority, and when greater than 8 we have Conservative majorities.
Seven Year Ve Polling History
The following graph shows the value of Ve, according to a number of different pollsters, over the last seven years. The Ve breakpoints of 8, 1, -4, and -8, as described above, are shown in dark and light blue, and light and dark red horizontal lines. Significant temporal events are shown as gray vertical lines.
As we can see from that graph, the Liberals were in strong minority territory, under Mr. Martin, coming into the 2004 election. Mr. Harper, leading Her Majesty's new Conservative Party of Canada official opposition, surged briefly prior to the election, but the Liberals won a final minority of 136 seats with a final election result of Ve = -4.7.
During AdScam, the Conservatives surged to minority territory, but the furor died down back to a Liberal minority. The Conservatives surged again in the run-up to the 2006 election, and this time it held, with the Conservatives winning a minority of 124 seats with a final election result of Ve = 4.1.
During the 2008 election, the Conservatives surged to majority territory. However, in the election, the final result was Ve = 7.3, resulting in the Conservatives winning a minority of 143 seats.
The 2004 Election
The following graph shows the run-up to the 2004 election. That was Mr. Harper's first election as leader of the new Conservative Party of Canada, and though advances were made during the campaign into weak minority territory, by the time of the election the trend was declining and the Liberals won a final minority of 136 seats, with a final election result of Ve = -4.7, a couple points below the closing opinion polling values.
The 2006 Election
The following graph shows the run-up to the 2006 election. In this case Mr. Harper's Conservatives progressed steadily against Mr. Martin's Liberals over the course of the campaign, and captured a minority of 124 seats with a final election result of Ve = 4.1, again a couple points below the closing opinion polling values.
The 2008 Election
The following graph shows the run-up to the 2008 election. In this case Mr. Harper's Conservatives moved into majority territory against Mr. Dion's Liberals over the course of the campaign. In the final election results, the Conservatives captured a minority of 143 seats with Ve = 7.3, this time a few points above the closing opinion polling values.
History of Ve since 1962
The following table shows the actual final values of Ve, according to Elections Canada results, for all the elections since 1962. As in the above graphs, dark and light blue and red are used to show Conservative and Liberal majorities and minorities. One of the interesting things this table shows is that since the Progressive Conservatives melted down in 1993 and the Reform Party garnered 52 seats, the number of seats held by the "new right" has monotonically increased in every election.
The following table shows the same data as the previous table, but this time sorted by the value of Ve, so high values of Ve and Conservative majorities appear near the top, and low values of Ve and Liberal majorities appear near the bottom. It is from the examination of this table that the Ve breakpoints of 8, 6, 1, -4, and -8, as described above, were derived.
Seat Projections
Based on the previous table we can determine upper and lower boundaries on historic seats-won data trends. Then, given a value of Ve, we can project the range of seats to be won (as long as historic data continues to delimit the boundaries). The following chart shows such data since 1962, with such boundaries, and with the 2011 election result shown as the larger blue dot.
Data Sources
Opinion poll data since 2005-04-09 has been obtained from the 2006, 2008, and 2011 Canadian Federal Election Polling pages at Wikipedia. Earlier 2004 and 2005 data was collected from multiple sources by hand. Final election results since 1962 were obtained from the Canadian Federal Elections page at Wikipedia, and from Elections Canada's 2011 election results.
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