**Update:** In a comment (#7), I compare the result to the seat-vote equation estimate.

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Three Canadian provinces have elections this week. Voting has already been completed in Prince Edward Island (PEI) and Manitoba, and is taking place today in Ontario, the largest province. Each elections shows–or is likely to show–the vagaries of FPTP.

(Newfoundland & Labrador votes next week, 11 October)

First, the election in **PEI** produced a lopsided majority–again. The incumbent Liberal party returned to office with 22 of the 27 seats, on a slightly reduced vote percentage (51.4% compared to 52.9% in 2007). This was a loss of one seat, with the Conservatives winning 5 (+1). For the second straight election, the Greens supplanted the NDP as the (distant) third party, with 4.3% (up from 3%).

The province has a history of lopsided results (as I have shown in graphs); the 2003 Liberal victory marked an alternation from a Conservative government, which itself had 23 seats. In the election before that, the Conservatives had 26 of the 27 seats. In 1996, the last time no party won a majority of the vote, the Conservatives, with 47.4% could manage “only” 18 seats (a 2/3 majority).

The seat-vote equation, which estimates seats under FPTP systems, based on jurisdiction-wide votes for the top three parties, the size of the assembly, and the number of voters, says that a party with around 51% of the votes, where the second party has around 40%, “should” be expected to win around 65% of the seats, rather than the 85% it won in this election. ((Four seats in PEI were decided by fewer than 100 votes, and some of these might swing on recounts. Each major party has won two of these seats, based on current results.))

One key reason why PEI has such lopsided results is that its assembly is about half the size that the cube root rule says it “should be,” for its electorate. With around 80,000 voters turning out in recent elections, an assembly of 55 seats would be more appropriate than 27. The undersized assembly is why the seat-vote equation sees as “normal” for FPTP even a a party with just over 50% of the votes potentially getting almost two thirds of the seats. The geographic distribution of the vote in PEI, and its tendency towards big island-wide vote swings, only exacerbate an inherent tendency for big seat bonuses for the largest party.

Of course, the Island could also get less distorted results with even a modestly proportional mixed-member system, such as the one resoundingly turned down in a referendum in 2005.

In **Manitoba**‘s election, the incumbent NDP was returned to office with 37 of the 57 seats (64.9%) on just 46% of the votes. The NDP had won 36 seats in 2007 on 48% of the votes. So the party’s votes declined, but it seats increased. The second-place Conservatives substantially increased their votes, from 37.9% to 43.7%, yet saw their seats remain steady on 19. Such are the vagaries of FPTP. Liberals saw their votes fall from 12.4% to 7.5%, and dropped from 2 seats to 1.

The seat-vote equation would expect such a close race between the top two parties to have resulted in a seat split of about 30-27, instead of the actual 37-19. ((Given the greater gap in votes between the top two, we would expect the 2007 election to have split the seats 37-20; in other words that election turned out almost exactly as expected.))

Manitoba has no record of particularly odd results, although in both 1990 and 1995 the second largest party won many more seats than it “should have” won. This is a pattern that can result in a plurality reversal (higher seat total for the second largest party in votes), if the election is close enough. In both of those elections, the Conservatives won narrow seat majorities on less than 43% of the votes, while the second-place NDP in 1995 had 40% of the seats despite only 33% of the votes. ((In 1990, it had only 28.8% of the votes, yet 35% of the seats.)) Evidently, in several recent elections the NDP’s geographic distribution of its votes has been such that it can translate them into many more seats than expected, whether it is the largest or runner-up party. I point this out simply because this week’s election was quite close in votes (46%-44%) yet produced an unexpectedly large seat bonus for the NDP. A plurality reversal may have been barely more than a couple of percentage points of the provincial vote from happening.

In today’s **Ontario** election, we see real three-party competition, with the third largest party, the NDP, polling at around a quarter of the votes. The incumbent Liberal party won 71 seats in the 2007 election, or 66.4% on just 42.2% of the vote. For most of this year, it was expected to lose, possibly by a wide margin, to the Conservatives. Yet as the official campaign got underway, the Liberals and NDP made gains in polls. For a while the Liberals and Conservatives looked headed for a near tie in seats, with neither winning a majority, and a potential plurality reversal. Now the Liberals could retain a majority of seats, depending on how some key ridings (districts) turn out.

The ThreeHundredEight final projection sees the Liberals winning 58 seats (54.2%) on 36.6% of the vote (to 33.3% for Conservatives). No party in Ontario ((at least since 1967, which is the first year in my data.)) has won a majority of seats on less than 40% of the votes since the NDP won 74 of a then 130-seat parliament on 37.6% of the vote in 1990–the only time the NDP has been the governing party. For the record, the seat-vote equation agrees that this projected vote split would produce a majority (about 56 seats); what it does not expect is the mere 29 seats the Liberals are expected to win, according to the ThreeHundredEight projection. The seat-vote equation expects such a close second place to be good for 44 or 45 seats, which would leave only 7 for the NDP. That the NDP could be projected to win 20 seats by ThreeHundredEight–which takes into account district-level information unlike the seat-vote equation ((As I often point out, the seat-vote equation is not a projection tool. It is only meant to see how close an actual result deviates from what a “typical” FPTP election would produce, for a given jurisdiction-wide votes breakdown, and number of voters and seats)) –only shows how much the existing FPTP electoral system favors the NDP. Their huge manufactured majority in 1990 shows this pro-NDP bias is not new. ((Of course, potentially winning in this election nearly three times the number of seats as could be expected in a “normal” FPTP system offers minimal benefit when some other party has won a manufactured majority. Clearly the NDP today–although not back in 1990!–would benefit from a proportional system that would promote minority or coalition governments in which such a strong (in votes) third party could have real policy influence.))

Ontario’s three-party competition suggests it would be well served by a proportional system, such as the mixed-member system proposed by a citizens assembly, but turned down in a referendum the same day as the provincial parliamentary election in 2007.

Finally, both Manitoba and Ontario, like PEI, have undersized assemblies. For their population sizes, the cube root rule expects around 100 seats in Manitoba (instead of 57) and 200 in Ontario (instead of 107). Small assembly sizes only exacerbate the chances of anomalous results, although if one wanted seats distributions more reflective of votes distributions, a proportional electoral system would do the trick without needing to increase assembly size.

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For more on the seat-vote equation and estimating the seats in first-past-the-post systems, see:

Matthew S. Shugart, “Inherent and Contingent Factors in Reform Initiation in Plurality Systems,” in To Keep or Change First Past the Post, ed. By André Blais. Oxford: Oxford University Press, 2008.

Past election data and estimates of seats come from the data set originally prepared in conjunction with the chapter, and updated since.

Error on year of NDP majority in original entry corrected.

Notes: