Some thoughts on Peru’s midterm election

After the Constitutional Tribunal ruled them legal, Peru held extraordinary legislative elections on 26 January. President Vizcarra dissolved Congress on the grounds that Congress had voted no-confidence in his cabinet (although not directly) twice. This was the first use of this provision since Peru’s 1992 constitution was promulgated, and as such it was the first time when legislative and presidential elections were not held concurrently.

However, the election did not merely lack a presidential contest. Almost uniquely, President Vizcarra, despite having been elected as part of former President Pedro Pablo Kuczynski’s party (previously Peruanos por el Kambio, now Contigo), chose not to endorse any party for the elections, merely advising voters to inform themselves. This reluctance was seemingly not due to any concern that Vizcarra’s endorsement would be a weakness for any party: at the time of the election, his approval rating stood at 58%.

Peru’s unicameral Congress is elected using open party-list proportional representation in 26 regions, with a 5% threshold applied at the nationwide level. The average district magnitude of 5 makes this a relatively moderate form of proportional representation, which explains why Keiko Fujimori’s Fuerza Popular was able to win a comfortable majority of 56% of the seats in Congress at the 2016 election despite only winning 36% of the vote.

The results of this election, however, were extraordinarily fragmented. The largest party, Accion Popular, got only 10% of the vote, and nine parties made it above the 5% threshold to enter Congress. More than a quarter of votes went to parties below the threshold, and in four provinces the leading party will receive no representation in Congress.

I will leave it to Peruvian experts, which I most certainly am not, to discuss what this result means for Vizcarra’s ability to pass his agenda. However, the results are interesting for other reasons.

Since the promulgation of the 1992 Constitution, Peru’s party system has remained quite stable (at least in terms of numbers, the identity of the parties has changed quite a lot). It has also remained quite close to the number of parties that the Seat Product Model (Shugart and Taagepera, 2017) would predict.

These elections are thus extremely unusual, and are perhaps indicative of the high importance of presidential elections and presidential endorsements in imposing structure on legislative elections in presidential countries. A fact particularly suggestive of this is the disastrous result for the two leading parties in 2016, both of which were affiliated to presidential candidates. Keiko Fujimori’s Fuerza Popular fell from 36% of the vote and 78 seats to 7% and 15 seats, while Peruvanos por el Kambio/Contigo fell from 16% and 18 seats to 1% and no seats.

Jamaica 2011: As good as PR–or not (updated)

Final results show the PNP won with 53.3% of the votes, to the JLP’s 46.6%. However, even as the final vote total was much closer than the preliminary result upon which this entry was based, the PNP picked up an additional seat. (Note that this gives it exactly two thirds of the seats.)

Thus the result was far from proportional, after all. In fact, it was even more majoritarian than a “typical” FPTP result would be with the given input parameters. The PNP’s Advantage Ratio is 1.25, whereas the Seat-Vote Equation would predict it to have been 1.14.

I am leaving the rest of this as originally crafted. The analysis of other elections stands, but that of 2011 would be altered by this new information. Thanks to Jon, in a comment, for the tip.
Jamaica held its general election on 29 December. Like the other former British territories in the Caribbean, Jamaica elects its parliament by first past the post (plurality) in single-seat districts. Also like other English-speaking Caribbean islands, Jamaica has a parliament that is significantly undersized, given its population. So this makes Jamaica a perfect opportunity to break out our old favorites, the Cube Root Rule of Assembly Size, and the Seat-Vote Equation.

The election result itself saw an alternation in power from the Jamaican Labour Party (JLP) to the Peoples National Party (PNP). Various news reports before the election had said the election was expected to be close. But it was not. The PNP won 41 seats to the JLP’s 22. Thus the JLP was defeated after a single term, which had been its first time in power since its defeat in 1989. (That was a two-term government, although its second term then was tainted by the PNP’s election boycott in 1983.)

The Jamaican case is of some interest to comparative elections specialists because it has an almost perfect two-party system. The two main parties combined for 99.87% of the vote in this election. The PNP won 61.3%.

Only once since 1959 has the third party in a Jamaican election won more than 1% of the vote (NDM, 5.2%, 1997). That makes Jamaica arguably a more “pure” two-party system than its very large neighbor to the north, and probably the biggest country to have a strict two-party system other than that really big one.

So, how did the system perform, in terms of the proportionality of translating votes into seats? We might expect a party winning over 60% of the vote in a first-past-the-post system to be significantly over-represented. The expectation is all the greater given the small size of the parliament, for the country’s population. With a population of around 2.7 million (just over a million voters), the Cube Root Rule would lead us to expect an assembly of more than double its actual size of 63. ((To be fair, they did increase their assembly size. It was only 60 seats from 1976 to 2007!)) Smaller assemblies mean less proportionality, other things constant. They tend to produce very high disproportionality under FPTP.

Yet the PNP’s 41 seats represent 65.1% of the total, hardly at all greater than its 61.3% of the vote.

The Seat-Vote Equation suggests that a “normal” case of about one million voters, 63 seats, and the top two parties at 61% and 38% of the votes would result in a leading party winning 84% of the seats. That would have been 53 seats, to 10 for the JLP.

In the 2011 election, then, Jamaica’s electoral system produced an almost completely proportional result.

This is not a systemic tendency, or if it is, it is a very new one. In fact, the Advantage Ratio (percent votes divided by percent seats) for the largest party in Jamaica had never been below 1.10 before this election (when it dropped to 1.06). Something has been going on in Jamaican elections recently: Every election that was contested by both major parties since 1959 had seen an Advantage Ratio of at least 1.16. Every contested election from 1976 through 1997 saw this ratio be at least 1.33, peaking at 1.50 in 1997, when the PNP won a third consecutive term. Then suddenly it dropped to 1.12 in 2002, when the PNP won a fourth term, in a very close election (50.14% to 49.77%). ((And, in case you are wondering, as I was, I checked: there is only a small relationship in FPTP systems between the top two parties’ difference in votes and the largest party’s advantage ratio. The effect is statistically significant, but the coefficient is around only .007. In any case, the falling ratio in close elections in 2002 and 2007 is consistent with the modeled relationship, but the greater fall in 2011 is most certainly not.))

From looking at the data on seat allocation, I can’t tell what has changed. But I can certainly tell that something has. For the third time in a row, the result has been unusually proportional for a FPTP system–and, in 2011, quite proportional for any electoral system.

The election was called early, as one was not due until the fall of 2012. The Prime Minister, Andrew Holness, in September replaced Bruce Golding (yes, another case of inter-electoral change of PM through “intra-party” mechanisms). Apparently, Holness felt he needed to go to the people for a new mandate. Apparently, it did not work out so well.

As an aside, how often do countries (especially in the Western world) hold elections in the final week of December? I imagine it must be very unusual.

As a further aside, in how many other countries is the more right-wing of the major parties called “Labour”? Or does the more left-wing party have “National” in its name? ((Yes, of course, it also has “People’s”, which is pretty much the only way I can remember which is which.))

Data cited in this entry are from my own research files.

Canadian provincial elections this week

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

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.

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.


Really, the Conservatives are under-represented, the Liberals over

What if we had a FPTP parliamentary system in which there were three national parties, and their vote percentages in any given election were:


We would have to call that fairly typical FPTP stuff. Not your ideal Duvergerian pattern, to be sure, but nothing remarkable in the real world of FPTP elections. Now let’s suppose their seat percentages were:


Pretty unremarkable, too, right?

Yes and no. On the one hand, this is what we should expect with FPTP: the two biggest parties with higher percentages of seats than votes, and the third party with significantly lower seats than votes.

Of the 211 FPTP elections in my database, there are 23 in which the largest party won from 38% to 42% of the vote (regardless of other parties’ percentages and excluding four plurality reversals). Of those 23 elections,* what’s the average seat percentage for the largest party? 54.35%. (The median is 52.63%, and the range is 36.15% to 69.09%.) So a large party winning around 40% of the votes and 54% of the seats is totally unremarkable.

Yet in another sense, the largest party in this Canadian election, the Conservatives, is under-represented–relative to a norm of FPTP expectations. Here I am speaking of the expectation set by the seat-vote equation,** which takes a distribution of the top three parties (plus “others”) and computes a “normal” output of seats for a given voting population and assembly size. Here is what the seat-vote equation thinks the seat distribution should look like, given the actual vote percentages:

    185 (60.1)
    100 (32.5)
    22 (7.1)

We’ll call that 1 “other” seat the Green winner, given that the Greens indeed did win their first elected seat. The seat-vote equation does not do well with regional parties. Fortunately for the equation, the regional party in this election almost disappeared (4 seats for the BQ, down from 50).

So the Liberals did quite a bit better than can be expected for the national third party. As a result, the Conservatives are under-represented, relative to FPTP “norm,” with 18 fewer seats than the equation’s estimate.

For all those who think the Liberals’ run as a viable party is over, be cautious. The British experience tells us that a Liberal party can survive for a good long time between the big parties of left and right. The party’s over-shooting of the seat-vote equation estimate underscores the extent to which it retains an efficient regional distribution on which it could build to win back seats in the future. In percentage terms, it is about where the British Liberal Democrats are in seats. This is a big shift, to be sure, but it is premature to write the party off, or to assume it will merge with the NDP.

Perhaps the bigger question is whether the NDP can survive as a major national left-wing party; first it will have to reconcile its now dominant Quebec wing with the NDP constituencies in the rest of the country. If it can’t, the Liberals will resume relevance, whether or not they surge back to “major party” status again anytime soon.

For all those advocates of proportional representation in Canada, this election is bad news. The first past the post system functioned about as expected, notwithstanding the under-inflation of the governing party’s plurality.

* The elections are: BC 1963, BC 1972, BC 1991, CA 1963, CA 1965, CA 1972, CA 1993, CA 1997, CA 2000 (the last majority government in Canada before this election), MB 1986, MB 1988, NS 1999, NS 2006, ON 1977, QC 1976, SK 1975, UK 1975, UK 1992, UK 2001, IN 1967, IN 1977, IN 1989.

** For details, click the words, seat-vote equation in the “Planted in” line above. There was an entry on election day applying the equation to the EKOS final projection, and many previous entries applying it to various past elections.

The seat-vote equation and Canada 2011

I have hesitated until now to run the seat-vote equation on the polls for Canada’s current election, because the campaign has been so unpredictable and regional and riding-level factors are likely to be decisive. Then again, maybe this is Canada’s most nationalized election in two decades or so…

So I ran it, based on the EKOS final numbers:

    CPC 34.0
    NDP 31.6
    LPC 20.8
    BQ 6.4
    GP 5.9

(Most other vote projections do not differ much from this.)

Disclaimer and background: The seat-vote equation is NOT a seat predictor. This is not a “projection”; you can find those elsewhere. The seat-vote equation simply tells us what the main parties’ seat totals “should have been” for a given votes distribution, based on “mechanical” features of the electoral system–how many districts there are in relation to the number of voters. It offers no insight into district-level factors. It has missed some past Canadian elections badly; in fact, I assembled the database specifically to see which elections were so out of line with how FPTP works that electoral reform might be put on the agenda. There have been many of those over the years in Canadian provinces, although at the national level Canada’s FPTP has not been prone to “anomalous” results, but rather has tended to be relatively proportional compared to other FPTP systems. (The seat-vote equation performed either admirably or terribly in the UK 2010, depending on your criteria.)*

With that disclaimer and background out of the way, what does it say the seats “should be” if we use the above votes?

    CPC 146
    NDP 123
    LPC 38
    others 1

Of course, the BQ is not going to win only one seat, and the Greens just might won one, as well. I said it was not a projection!

The seat-vote equation does not like parties that win seats despite having quite small national vote shares. It is right about the Greens getting 0 or 1 seat on their ~6%, but not about the BQ, despite the latter also being on only 6%. Regional concentration, or its absence, matters in FPTP.

Nonetheless, and for whatever it might be worth, the estimates for the Conservatives, NDP, and Liberals are well within the range of the EKOS seat projections. To be precise, the CPC and NDP numbers are near the upper end of the EKOS projections, and at least one of them will need to be nearer the lower end (130, 103, and 36, respectively, at EKOS) to make room for 10-20 BQ seats.

But, yes, a third straight Conservative plurality–possibly reduced from what it was in the dissolved parliament–and an NDP total around 100-125 really could happen. And if those were the top two parties’ seat totals, it would mean that Canada 2011, far from being any sort of anomalous FPTP election, would be in line with what the seat-vote equation says “should be” the outcome, given these expected votes.

* For more on the seat-vote equation, just click those words in the “Planted in” line above. I have been writing about the equation and various elections, especially Canadian federal and provincial elections, since 2006. The first entry in the series provides the most detail about the equation’s application. If you want the full explanation, please 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.

Anomaly Watch: Trinidad and Tobago votes

Campaigning is in the final stages in advance of the Trinidad and Tobago general election of Monday, 24 May. The race is expected to be tight. This is a “snap” election called by PM Patrick Manning, leader of the Peoples National Party (PNM). Will he be sorry for having called it early?

In my work on “systemic failure” and reform in FPTP systems,* I concluded by drawing up a “watch list” of jurisdictions where recent results suggested the electoral system was inherently prone to producing anomalies, based on deviations of actual outcomes from what the Seat-Vote Equation would expect. T&T was on my Watch List. In the case of T&T, the inherent tendency towards unexpected outcomes derives from a frequent over-representation of the second-largest party, relative to expectations based on “normal” performance of FPTP systems.

For instance, in 1995 and 2001, the top two parties tied in seats due to the second party performing considerably better in seats that would be normally expected. In 1995 the PNM was the largest party but it won a lower percentage of seats (47.2%) than of votes (48.8%); in 2001 the United National Congress (UNC) was first in votes by a respectable margin (49.9% to 46.5%) yet each party won half the seats. Either of these elections could have resulted in a spurious majority (or “wrong winner”).

This will be the country’s fifth election since 2000. The 2001 election had been called very early: in 2000 the UNC had won a very narrow majority of both votes and seats (51.7% and 52.7%, respectively). It fell to 49.9% of votes and half the seats in 2001, and then another election was called in 2002. This one produced alternation to the PNM, with majorities of both seats and votes (55.6% 50.9%, respectively). The party was reelected in 2007, and despite a fall in its votes (to 45.9%) its seats increased (to 63.4%). A third party, the Congress of the People (COP), won over 22% of the vote but no seats.

The underlying problem in T&T stems from two common sources of poor FPTP performance: small assembly size and regionalism. The assembly size was stuck on 36 for many elections (at least as far back as 1966). That is very small for a country with now over 650,000 votes cast in the last two elections (and around a million eligible). By the Cube Root Rule, a country this size should have an assembly of 100-125 members. This problem was “addressed” in 2007 when the assembly was finally increased–all the way to 41.

The nature of regionalism can be seen by looking at the maps from recent elections at Psephos. As is common under FPTP, each party has strongholds and only a few seats change hands at any given election. The UNC dominates most of the center and southeast of Trinidad, whereas the PNM wins nearly every seat in Port of Spain and on Tobago. The partisan division mirrors the division between citizens of Indian or African descent, with the governing PNM relying on the latter group.

In this election, the UNC and COP have joined forces as the core components of a five-party pre-election coalition known as the People’s Partnership. It might seem that such a coalescence of the opposition would make a dramatic difference in the votes-seats conversion to the opposition’s advantage, but it may not. A quick and not-very-systematic perusal of the district-by-district results in 2007 shows only a few districts where the PNM won with less than 50% and where the combined UNC-COP vote would have meant PNM defeat. Most PNM districts were in fact won with majorities, whereas it was the UNC that often won with less than 50%. Still, if the race really is close, even a relative few seats could tip the result. A few seats could result in an over-representation of the Peoples Partnership even if it second in votes–and could even contribute to a spurious majority.

About the campaign, the Jamaica Observer (second link above) notes:

Music in the nation famed for calypso has played a key role in campaigning.

One PNM video shows red-clad crowds dancing at rallies in front of a smiling Manning, with slogans such as “free education” sliding across the screen to a catchy tune.

On the other side, a People’s Partnership campaign song contains the lyrics: “Allegations here, allegations there,” and shows pictures of flashy high-rise buildings alongside hospitals without beds.

“I can’t vote for that!” rings out the chorus.

Trinidad and Tobago would be better served by some form of proportional representation and has earned its place on the Watch List.

* “Inherent and Contingent Factors in Reform Initiation in Plurality Systems,” in the edited volume by Andre Blais, To Keep or Change First Past the Post.

How far off the seat-vote equation was the UK 2010 result?

How under-represented was the Conservative Party on 6 May? Oh sure, I know that the party was over-represented, relative to its vote share. But that’s what FPTP is supposed to do. In fact, it is supposed to do so sufficiently to give a “decisive” result. At least that’s what David Cameron said throughout the campaign in defense of the current electoral system. So, relative to the expectation of a substantial boost from FPTP, how under-represented was the largest party in the recent UK election?

By running the seat-vote equation on the actual voting result, we can get an idea of the answer to this question. The Conservatives won 307 seats, for 47.2%, on 36.1% of the vote. Labour came second with 258 seats, for 39.7%, on 29% of the vote. For these top two vote percentages, the seat-vote equation says the largest party “should have won” 51.4% of the seats and the second “should have won” 31.5%. (The Liberal Democrats presumably “should have” won the greater part of the remaining 17%, rather than the mere 9% that they have to show for their 23% of the vote.*)

For the largest party, obviously the deviation between an expectation of 51.4% and an actual result of 47.2% is minor, aside from the rather important detail of these percentages straddling the magic 50% (plus 1) marker.

The outcome of the election continues in a striking way the over-representation of Labour. Note that their 29% of the vote could have been expected to result in just over 30% of the seats, but instead they are close to 40%. The bias of the system in favor of Labour, whereby that party wins more seats than the Tories for any given vote share, is well known. It is likely not, however, a product solely of the current district boundaries, as Cameron and other Conservatives are fond of saying. Districting plans come and go, but this bias has been in place for some time.

We can see the differential treatment of the parties by looking at the advantage ratios (%seats/%votes). In this election, Labour had A=1.37, which is the best result for a second-place party in the UK in my data-set (which goes back to 1959). For the Conservatives, A=1.31. While this is a relatively low A for the largest party, in the UK context it is not low–for a first party branded as “Conservative.” Even when the Conservatives were winning substantial seat majorities from 1979 through 1992, their A surpassed 1.25 only in 1983 (1.44) and 1987 (1.37), while in the “Thatcher landslide” of 1979 it was only 1.22. (In 1992 it was 1.23.) Labour, on the other hand, enjoyed advantage ratios of 1.47 or greater in each of the three recent elections when it was the largest party.

These figures suggest that the Conservatives might have a hard time finding a FPTP districting plan** that would really work for them, unless they can again be confident of surpassing 38% or so of the vote. Meanwhile, Labour is benefiting rather handsomely from FPTP, though the 2010 outcome in particular suggests that the bulk of that advantage is coming at the expense of Britain’s rather large third party instead of the Conservatives.

* Various fourth and lower-ranked parties won around 4% of the seats, owing to concentration of the relative few votes won by any one of them, despite combining for 11.9% of the vote. We can discount them for present purposes and just call them “others.” (Which is not to say that some of them might not prove relevant in the coming parliament, of course.)

** That is, without major gerrymandering on a scale not practiced in the UK, unlike the USA.

Ontario’s election and the failure of the MMP proposal

As has been discussed extensively already in the previous thread (the comments to which have been very interesting), the voters of Ontario rejected a proposal to change their provincial electoral system to MMP. It was not even a close call; a change to MMP would have required the support of 60% of voters (and majorities in 60% of the districts). It received the support of only 36.6%.

The support MMP achieved was somewhat less than what the incumbent Liberal party obtained in the parliamentary elections, which was 42%. Yet that 42% has translated into 71 of 107 seats, or more than 66% (one seat less than a two-thirds majority). This represents a four percentage-points decline in popular support for the Liberals. In 2003 the party also won 71 seats, though out of a total then of 103.

The Conservative party also lost votes, going from 34.6% in 2003 to 31.7% now. It will have 26 of the 107 seats (compared to 25 of 103 in 2003). Its leader, John Tory, was defeated in his own district.

The big vote winners in this election were the New Democrats and Greens, especially the latter. The Green party won 8% in this election, about double what it had before. And, while the NDP would be the closest party to the Greens on many programmatic questions, the party’s vote surge did not come at the NDP’s expense, as the NDP votes went from 14.7% to 16.8%. The NDP also gained seats (from 7 to 10).

The Greens, of course, won no seats. They came closest in the district of Bruce-Grey-Owen Sound, where their candidate won 35% of the vote, but was defeated easily by a Conservative with 46%. (Do any of my readers know anything about this district? I am intrigued by the sort of place where a Green could get more than a third of the vote! Update: We now have such information in the comments!)

As far as the trusty seat-vote equation is concerned, this is a somewhat unremarkable result. Supporters of MMP will point to the huge manufactured majority, or to the Greens vote gain with no seats, and say, see, we told you so! But it is ho hum. Given this number of voters in the province, this number of seats in the legislature, and these vote totals for the various parties, we would expect a party with 42% of the votes to have won around 69 seats. So it won 71. Yawn. We would expect the Conservatives to have won around 34. So, they were a bit under-represented, relative to expectations, but 8 seats not won out of 107 is hardly enough to prevent the main opposition from functioning.

The NDP is, of course, considerably over-represented. Oh sure, it got only 9.3% of the seats on nearly 17% of the vote. But a third party with just over half the votes of the second party “should” win no more than 4 seats. Luckily for the NDP, it is adapted to FPTP in Ontario. It is sufficiently concentrated to win several seats. In fact, the 7% of seats it won in 2003 was its worst showing in many years. It won as many as 14% of the seats as recently as 1995, ((I am using seat percentages here, rather than actual numbers, because the size of Ontario’s parliament has been something of a moving target in recent years.)) and actually had a majority in 1990, on a mere 37.6% of the votes–talk about being adapted to FPTP! It is the Greens, on the other hand, who are the maladapted party, with a voter base far too dispersed to win any seats. ((Ontario has a very small parliament, for its population size. By the cube-root law, it “should have” around 200, or double the current size. But even such a big increase would have made little difference in the expected seat balance in this election. Of course, in the real world, it might have made one Green seat possible and might have put the Conservatives closer to their expected share. I would guess that a doubling of the size of the parliament would be an even tougher sell than MMP–which was to include a 20% increase in the size of parliament (or to about where it was as recently as 1995). ))

Ontario was never a case I considered ripe for electoral reform of the PR variety. In fact, in my paper on the topic of reform in FPTP systems (forthcoming in an Oxford volume edited by André Blais), I state that Ontario is a surprising case of an electoral reform process. Unlike British Columbia (where an STV proposal won 58% in 2005, though it likewise needed 60%) and New Zealand (where voters adopted MMP in a 1993 referendum)–or even PEI ((in P.E.I., a proposal for MMP was defeated in a referendum. Click the link on the province name for discussion.)) and New Brunswick ((In New Brunswick, a planned referendum on a proposal for MMP has been called off. Click the link on the province name for discussion.)) –Ontario had no record of significant anomalies to put electoral reform on the policy agenda in the first place. There is none of the “inherently” bad performance that we can expect from FPTP systems, whereby they may seriously under-represent the party that gets the second most votes such that the opposition is decimated, or over-represent it such that it, rather than the leading vote-winner, gets to form the government.

The only “contingent” factor, among those I identify in my academic work on reform in FPTP systems, that was present in Ontario was the coming to power of a party that had long been out of power. Before 2003, the Liberals had spent decades out of power, aside from 1985-90. In 1985 they formed a minority government despite having the second highest seat total, which in turn they had despite having the most votes (in the only somewhat anomalous election in the province). In 1987 they won a very large majority, only to be voted out after one full term. So, it is not surprising that such a party might come to power (as it did in 2003) with a program of “Democratic Renewal” and that it might even want to open up the question of whether to change an electoral system that, if not systematically biased, had not let the party exercise even a share of power (aside from 1985-90) despite its being a party that regularly won 30% or more of the vote.

In other words, the systemic factors predicting a reform process in Ontario were always weak. But there was some partisan-interest factor at work for the Liberals. The problems with partisan-interest factors, of course, are that they (1) may make it harder to convince voters who favor other parties to think reform is also good for them, and (2) the very interest-based factors may shift if the party starts doing better. This is clearly a good time to be a Liberal in Ontario. It is an even better time to be a Liberal under FPTP. And, apparently it is a good time to be an Ontarian: In the absence of systemic factors (whether the electoral system itself, or perceived policy failures and government mandate violations, as during New Zealand’s reform process), there was no general ill feeling towards politics-as-usual to impel voters to vote for reform simply because there is “something wrong.”

The result for the MMP referendum was by no means foreordained. The province has a multiparty system, for which some form of PR would make a lot of sense. Its Citizens Assembly was a model of civic participation, and its 103 members crafted a really sound proposal. But they faced an uphill battle. The result is not a surprise. However, the proposal is out there, and isn’t going to be totally forgotten. If the Greens’ success was not a blip, or if the Liberals are reelected again in 2011 despite losing the party vote (which would be very much within the realm of the possible), or the Conservatives come to power and are perceived to have done so only because of a divided center-left, the supporters of MMP will have their “we told you so!” moment. Maybe somehow the proposal, or something similar, would be dusted off and be put to another vote.

I do not think electoral reform is dead in Ontario. But it is certainly dormant.

Newfoundland: A lopsided majority (but it could have been even worse!)

Tuesday’s provincial parliamentary election in Newfoundland and Labrador produced a lopsided majority. The main opposition party, the Liberal Party, was reduced to just three seats, while the NDP held its one seat. The incumbent Conservatives won 43 seats. They also did rather well in the votes: 69.6%, up from 58.7% in 2003. The Liberals won just 22%, down from 33.2% four years earlier. (47 of the 48 seats were at stake; the other race has been delayed due to the death of a candidate.)

Before the election result was in, I noted that the electoral system in the province is actually biased against the Conservative party. In most recent elections, it has won fewer seats, whether in opposition or in government, than the seat-vote equation would predict for the parties’ vote totals (and the size of parliament and total votes cast).

Believe it or not, even this result is no exception. The Conservatives “should have” won more than 98% of the seats–perhaps 100%, given that the Liberals’ expectation works out to less than half a seat. In the actual election, all the poor Conservatives could muster was 91.5% of the seats.

Some systemic factors just can’t be beaten down no matter how well you do!

I suspect the Conservatives are not complaining too much, however, about the “bias” against them. Nor the Liberals too pleased with their being “over-represented.”

Ontario election and referendum on MMP

MMP was defeated resoundingly, getting less than 37%.

And, oh, by the way, the Liberals won nearly two thirds of the seats on only 42% of the vote.

More later. Meanwhile, this thread continues to grow. Thanks for the comments. (I have weighed in there a few times, too.)

On 10 October, voters in Ontario will vote in a general provincial election. They will also vote in a very important referendum on whether to change the electoral system for future provincial parliamentary elections from the current FPTP to MMP.

The proposed MMP–mixed-member proportional–electoral system was recommended by a Citizens Assembly, made up of ordinary citizens selected (mostly) at random from the voter rolls (sort of like a grand jury). The assembly was given the task, under law, of deliberating about how elections actually work in Ontario and whether there might be a superior model. If it recommended an alternative, it was legally guaranteed that its proposal would be put up against the current system in a provincewide referendum. That time is now, and Ontario voters can decide whether to keep or change FPTP. Or, rather, a super-majority of Ontario voters can decide to change, as the proposal must obtain 60% provincewide, and majorities in at least 60% of the 107 provincial ridings (electoral districts).

Under the proposal, voters would have two votes–one for a candidate in their local riding (as now), and a second vote for a party list. There would be 90 (instead of the current 107) districts in which a single legislator would continue to be elected by plurality of votes cast. There would be 39 compensatory seats, from closed party lists, allocated to “top up” the seats of any party that had won more than 3% of the provincial party vote, but whose number of districts won was a proportional share (of the full 129 seats) that was less than its party vote share.

There is video debate on CBC that you can watch (about 6.5 minutes long), and CBC also has a list of some of the key arguments for and against.

Meanwhile, in the provincial election, it will be business as usual for FPTP. One party–and it will be the incumbent Liberal party, unless there is a very big surprise–will get “reelected” with around 42% or so of the vote, and is projected to win more than three fifths of the seats. The Conservatives–led by, and I kid you not, John Tory–will win around a third of the votes, but probably under 30% of the seats. The New Democratic Party (NDP) may win around 17% of the votes, but only around 11 seats (10%). The Greens may win five or six percent–and one poll says 11%–of the vote, but almost certainly no seats.

Obviously, Ontario has a multiparty system, and would be well served by a more proportional electoral system, which would raise the prospect of Liberals cooperating with one or more parties. If MMP were being used in this election, perhaps the Liberals would cooperate, after the election, in forming a government and passing policy with the NDP. Or they might strike a deal with the Greens, who would win anywhere from 7 to 14 seats, depending on their vote total, rather than zero. Under the current system, the Liberals will rule alone in spite of their having only 43% (or so) of the vote. Nonetheless, the referendum’s chance are considered a long shot.

The MMP proposal may not even make it over 50%. To get to 60% is hard. After all, one former FPTP jurisdiction, New Zealand, has MMP today because a vote of more than half the voters was sufficient in its 1993 referendum. The MMP proposal would have been considered defeated if 60% had been required; the change was endorsed by “only” 54% of the voters. In British Columbia in 2005 a referendum on a different electoral reform, also proposed by a Citizens Assembly, obtained around 58%, where, as in Ontario, 60% was required. (In BC, a second referendum is scheduled on the proposal.) Meanwhile, most governments in New Zealand under FPTP, as well as in Ontario and BC have been single-party majorities based on well under half of the vote–and sometimes on less than 40%.

It is perhaps surprising that a jurisdiction such as Ontario in which the ruling party usually is endorsed by well under half the voters, and where there are important parties other than the top two, would not be “ripe” for some form of proportional representation, such as MMP. However, Ontario is not exactly the most likely case for an electoral reform process to have emerged in the first place. It has had none of the serious anomalies–such as a party with the second most votes winning a majority of seats–as New Zealand had for two elections in a row (1978 and 1981), or as British Columbia had (1996).

With its multiparty politics, it has had some erratic results under FPTP, but nothing out of the ordinary. The graph below shows the patterns over recent decades.


This graph–as with others I have shown here in the block on the “seat-vote equation”–shows, in the lower segment, the deviation of the second largest party (in seats) from what it would be expected to have won, for the given votes for the parties and the size of the assembly and the number of total votes cast. On that lower (dark green) trend line, we see the identity of the second largest party. The trend line in the upper part of the graph shows how close elections have been.

The one really noteworthy–and perhaps “anomalous” election–was over twenty years ago. In 1985, the party with the most votes was the Liberals, with 37.9%, but the Conservatives, who had 37.0%, won the most seats. The Conservatives did not, however, win a majority. They won 52 of 125 seats, and the Liberals were actually able to form a minority government, with the support in parliament of the third party, the New Democrats. Then, in 1987, the Liberals called an early election and won a very large majority: 95 of 130 seats, on 47.3% of the vote.

As can be seen by the trend line in the lower portion of the graph, the electoral system has been somewhat biased against the second largest party–except in 1987, when that party was the NDP. In most elections before 2003, the second largest party was the Liberals, and they have won fewer seats than the second party would have been expected to have won (given the vote shares of the parties, the number of seats at stake, and the number of votes cast).

However, the bias has not been great, and the anomaly (if it was one) of 1985 was a long time ago. It is somewhat surprising that the Liberals actually promised prior to the 2003 election to convene a Citizens Assembly, and that they then went ahead with it. Now we are at the decision point. Will Ontario voters agree that MMP would be an improvement, or do they like the status quo electoral system in which they will most likely reelect their current government on 43% of the vote?


The Globe and Mail has a rather odd editorial.
It almost seems to think the electoral reform is a good idea, but says to vote against it, partly because it claims the idea has been given short shrift in the general-election campaign. It suggests, rather strangely, that MMM would be better. And it wishes the threshold were at 5% instead of 3%.

Newfoundland and Labrador election today

Votes are being cast today in a general election in the province of Newfoundland and Labrador. The incumbent Conservative party is expected to be reelected. The current standing of parliament is 34 Conservatives, 11 Liberals, and 1 NDP (and two vacancies).

The Conservatives won the last election, in 2003, handily. Those 34 seats represent more than 70% of the seats, which were won on a solid majority of the votes: 58.7%.

Despite the 2003 outcome, the electoral system (FPTP, of course) is actually biased against them. How can an electoral system be “biased” against a party that has more than two thirds of the seats? Consider that in a “normal” FPTP system, with such a small assembly, and two leading parties at almost 59% and only 33% of the votes, respectively, we might expect the leading party to have around 86% of the seats. That would be 41 seats, or seven more than the party actually won. If we value strong oppositions, we might consider the actual, biased, outcome a lot better than the “expected” one. The twelve seats the Liberals won in 2003 almost gives the opposition something resembling a caucus, whereas the seven they would have been expected to win would hardly deserve to be called opposition caucus (though it actually would not be close to the most decimated opposition in even recent Canadian provincial electoral history).

Obviously, with one party so dominant and the other party retaining significant representation in parliament, the electoral system would not be expected to be a political issue in the province. And indeed it is not, as far as I know. Nonetheless, as the graph below shows, the bias against the Conservative party–or in favor of the Liberals–is systemic and ongoing.

Click the image to open a larger version in a new window.

This graph, as with others I have shown here in the block on the “seat-vote equation” shows, in the lower segment, the deviation of the second largest party (in seats) from what it would be expected to have won, for the given votes for the parties and the size of the assembly and the number of total votes cast. On that lower (dark green) trend line, we see the identity of the second largest party. Since at least 1989, every time the Conservative party has come in second in votes, its seat share has fallen below expectation (the horizontal line at zero). When the Liberals fell to second place in 2003, the party was significantly over-represented (as discussed above).

Why this has not been a political issue–that is, why Newfoundland and Labrador does not have a significant electoral-reform movement–is apparent in the upper part of the graph. This portion indicates how close the election is, in votes. The 1989 election actually shows the vote differential as negative, because it is indicating the vote difference between the party with the most seats and the party that came in second in seats. In other words, the 1989 election was a plurality reversal: The Conservatives were second in seats despite having the most votes. The votes split in 1989 was 47.50% to 47.05%, but the Liberals won 31 seats to only 21 for the Conservatives.

So, while the bias against the Conservative party is not currently politically significant–the party is enjoying a large majority in spite of it, and will probably continue to do so after today’s election–it has significant political consequences in 1989. A plurality of voters that year actually voted to retain the Conservative government then in power, but the electoral system produced a “spurious alternation” to the Liberals. It may not have seemed spurious at the time (at least to those who are not Conservative partisans), as the Conservatives were actually big vote gainers, compared to 1985 (when they had only 36.6%, compared to the Liberals’ 48.4%). Nonetheless, the opposition failed to win the plurality that one presumably expects in order for an incumbent government to be voted out of office.

After the 1989 anomaly, the Liberals were returned to power in the next three elections, and, as the graph above shows, there was not a close election among the three.

The bias in the Newfoundland and Labrador electoral system is not an issue now, but if it continues in future elections, and if one of those is very close, this province’s electoral system is a good candidate for producing another anomaly.

Jamaica: Updated count

In an updated count, the Jamaica Labour Party’s lead has widened by two seats. It now appears to have won 33 to the People’s National Party’s 27. One of the seats that changed hands as a result of a recount now shows a JLP lead of 9 votes!

The interactive map of the outcome is interesting, inasmuch as it shows there is not a really stark regional divide. My quick perusal shows only four districts that are not bordered by at least one district won by the other party. Three of those are on the far western tip of the island (all PNP) and the other (also PNP) is on the edge of Kingston. Even in the capital area, of the 13 districts in the most densely populated area, the PNP won just 7.

The nationwide votes percentages have not changed, even out to two decimal places, as more votes have been added to the count and individual districts have been recounted: 50.14 to 49.77.

The revised count means that the second-place PNP is under-represented, relative to the seat-vote equation’s estimate, by 4.4 percentage points (3 seats, or 2.6 if you want the decimal-point estimate). Not much, in other words, but technically enough to make the difference between a tied parliament and one with a majority that, while narrow, is enough that a single absence from its caucus on any given day won’t threaten the government’s business.

It’s a very close result, but a majority voted for the alternation that will now occur. If all FPTP elections worked like this, it could actually be considered a reasonably representative democratic electoral system.

Jamaica: A razor-thin result

Jamaicans voted in general elections Sunday. According to BBC, the result was expected to be close.

A more recent update than that below has the JLP at 32 seats. ((More recent still: 33; see the link at the bottom.)) PM Simpson “accepts” the results, yet may still challenge them once the final count is in. The three closes seats, mentionend below, are already in the PNP column, so recounts there have no chance of reversing the overall result.

Result: Yes, yet another cliffhanger! JLP won the votes, 50.14% to the PNP’s 49.77% (a margin of 2,940 votes), and the seats split 31-29 in favor of the JLP. So, Jamaica will have a change of government, by the thinnest of margins. These results are preliminary, and, obviously, if there are even minor problems that result in some recounts, they don’t have to change much to produce a big change in the overall outcome.

BBC reports that three constituencies were decided by fewer than 100 votes. The PNP has not conceded defeat, and may challenge the results once they are official in a few days.

By the seat-vote equation, the JLP would be expected to have won almost exactly 30 seats ((In an earlier version, I said 35. I mis-read my data lines! The point estimate would be 50.6%.)) ; in other words, as in 2002, pretty much right on target to the actual result. When we are dealing with such slight margins, even a small degree of over- or under-representation can be consequential. Both a hung parliament and a plurality reversal (which would have been a spurious “reelection”) were narrowly averted (assuming these results hold), and the new majority can’t afford anyone to be sick on the day of an important vote!

The remainder below is unchanged from the original Sunday evening planting.

While we wait on the results, let’s look at our old friend the seat-vote equation and what it tells us about the performance of Jamaica’s first-past-the-post (plurality) system in recent elections.


The upper part of the graph (the dashed line) shows the gap in vote share between the two largest parties in each election. When there is a solid square symbol, it indicates an election in which there was alternation from one party to the other. (The 1983 election, boycotted by the Peoples National Party, is not shown.)

The lower portion, with the solid green line, indicates deviation from the expected seat total of the second largest party, based on the seat-vote equation. The second-largest party in parliament following each election is indicated (PNP=Peoples National Party; JLP=Jamaica Labour Party; in the world of Jamaican politics, the “labour” party is the right-wing party).

The seat-vote equation takes into effect the vote shares of the major parties, the number of votes cast, and the size of the legislature (60 seats since 1976) and gives an estimate of what each party would have in a “typical” FPTP election with those input parameters. (Click on “seat-vote equation” above and scroll for more detailed explanations related to other elections.) This method allows a quick assessment of whether the electoral system is performing as FPTP is expected to perform.

The verdict on Jamaica is that there is some tendency to under-represent the second party in recent elections, except in 2002, which was one of those ho-hum elections–the sort that, were it typical of FPTP, no one would talk about electoral reform! In that election, the PNP won its fourth straight with 52.2% of the vote and the JLP won 47.2%. The two parties split the seats, 35 to 25 (58.3% to 41.7%, or almost exactly what we should expect.

As the top portion of the graph shows. elections have been getting closer each time since the PNP resoundingly won its first reelection attempt after taking power back from the JLP in 1989.

Late polls, according to the BBC link above, put the JLP, led by Bruce Golding, slightly ahead of the PNP, which currently holds 35 seats, and its leader and Prime Minister Portia Simpson.

Both Ms Simpson Miller and Mr Golding are contesting their first general election as party leaders.

During the campaign the PNP has argued that it has improved health care and reduced unemployment to below 10%.

Mr Golding’s JLP has complained that Jamaica’s unemployment rate of 9% remains too high.

The party has also criticised the government’s handling of the economy and the island’s high crime rate.

Ms Simpson Miller became prime minister 18 months ago, but her popularity has since been declining steadily, our correspondent says, adding that the JLP now has its best chance for some time of ending its 18-year absence from office.

The vote had been planned for 27 August but was postponed after Hurricane Dean ravaged the Caribbean island.

It is, of course, in close elections that the performance of an electoral system–especially one based on single-seat constituencies–is really put to the test. Back in 1962 and 1967, the last really close elections in Jamaica, the graph shows us that the second party was significantly under-represented. (In those years the JLP won 57% and then 62% of the seats when the votes were split almost in half.) However, Jamaican politics has changed a lot in those forty years, so those elections offer little guidance as to what we can expect once results are in from today’s contest. Assuming the election is indeed close in votes, will the two parties have almost the same number of seats (perhaps even a hung parliament ((As in Jamaica’s one-time West Indies Federation partner Trinidad and Tobago in 2001)) or a plurality reversal ((As in Belize in 1993.)) ), as the 2002 seat-vote allocation would suggest? Or will the leading party be significantly over-represented, as has been the case in most Jamaican elections?

You can follow results at The Jamaica Gleaner‘s Elections site or their blog.

Update: Yes, it is close! As of 7:00 PDT, JLP with a very small lead in votes (around 4,000 about 800,000) and 24 seats to the PNP’s 23, with 3 seats not yet determined. (These results are very preliminary, of course, and from the links given in the last paragraph before this one.)

Quebec’s results and the performance of FPTP

The results of the Quebec provincial election were stunning enough, as we have been discussing in the previous planting. No one saw the strong showing of the ADQ coming. The fall of the ruling PLQ to minority status was expected, but there was quite a late swing away from the PQ. A few days before the election, it looked as if a PQ minority government was possible, but the party wound up in third place.

In this entry, I want to look not at the shifts in voter sentiment, but rather at how the electoral system took those actual votes and turned them into seats. This is a politically relevant question for Quebec given that the province: (1) has never before had an election result in a minority situation, and (2) has had a recent electoral-system review process. The minority government might be seen as a sign of the “failure” of the FPTP system just at a time when there has been discussion of replacing FPTP with some form of PR.

The seat-vote result is striking in being almost proportional:

    PLQ, 33.1% votes, 38.4% seats
    ADQ, 30.8% votes, 32.8% seats
    PQ, 28.3% votes, 28.8% seats

We certainly do not normally expect such close correspondence of votes and seats percentages in FPTP systems.

To get an idea of whether this aspect of the election is a “surprise” or not, I turned to one of my favorite tools, the seat-vote equation (originally devised by Rein Taagepera). If you are unfamiliar with the seat-vote equation, I suggest clicking on those words at the top of this planting and scrolling back in time–especially to the first planting in that orchard block (an estimation of seats in the then-upcoming Canadian federal election). But the short version is that the seat-vote equation allows us to estimate a “normal” seats distribution based on the following inputs (and only these inputs):

    The votes shares of the leading parties
    The total number of votes cast
    The number of seats in the legislature
    The number of electoral districts

Naturally, in FPTP systems, those last two are the same quantity.

The s-v equation does not incorporate any information about the geographic distribution of the parties’ supporters, notwithstanding the obvious importance of such distribution to the actual outcome. Parties win seats in FPTP systems solely based on where their votes are–no district-level plurality, no seat–rather than as a function of their jurisdiction-wide votes shares.

So, how did the equation perform in this election? Asking this question is really another way of asking a more politically relevant question: How did the electoral system perform? The latter question assumes that there is some “expected” relationship between jurisdiction-wide party support and their legislative support. Deviations from the s-v equation estimates would suggest that the electoral system is not translating votes into seats in a predictable manner. Again, we should not necessarily expect such a predictable translation when the system is FPTP, because of the dependence of parties on local pluralities rather than on jurisdiction-wide support in order to win seats.

Following are the (rounded) predictions of the seat-vote equation, based on the known values of the input variables indicated above:

    PLQ, 51
    ADQ, 42
    PQ, 32

These hardly differ from the actual result (48, 41, 36). The s-v equation expects the largest party to get a bigger bonus than it actually got and the third party to get slightly more punished than it actually was. But it tells us that, in a jurisdiction with FPTP and the number of seats and voters that Quebec has, an election so close among the top three parties in votes should produce a fairly close correspondence of seats and votes. The predicted advantage ratio for the PLQ was 1.23; its actual ratio was 1.16. Even FPTP with three-way competition can produce moderate deviations from proportionality and Quebec’s 2007 result was one where moderate deviations were both expected and actually materialized.

As for the impact of this outcome on the electoral system review, I am not in a position to predict the political consequences of this outcome on that review, but I would conclude that the outcome has not made the objective case for PR stronger. None of the formal review processes in FPTP jurisdictions in the last four decades stemmed from a minority situation, and Quebec’s result was not even disproportional. The existing electoral system gave Quebec voters pretty much what they voted for.


Paul Wells and his readers have been having fun figuring out the smallest shifts of votes that could have produced a very different seats result–a reminder that s-v correspondence in FPTP systems does sometimes rest on knife’s edge results.

Mr Wells also offers a great video link on the PQ, 1976. Ah, those were the days…

FPTP in Malaysia: Would MMP be better?

In a publication called Sun2Surf, which describes itself as the “Malaysian source for news and lifestyle,” an article on 22 January noted that a Ph.D. candidate at Essex who is doing research on Malaysian elections has argued that MMP would be preferable to Malaysia’s current FPTP system. (Can you imagine an American “news and lifestyle” publication devoting an article to electoral reform? Alas, you can only imagine it.)

Wong Chin Huat said Malaysia’s FPTP electoral system was not democratic because worldwide, FPTP notoriously produced seat-vote disproportionality, made much worse in Malaysia because of partisan constituency delineation.

He said the mal-apportionment of the FPTP system, coupled with gerrymandering (unfair electoral advantage by redelineating constituency boundaries), produced a scenario in the 2004 elections where Barisan Nasional (BN) won 91% of seats in Parliament with only 64% of votes.

Meanwhile, PAS only secured 2.7% of seats despite having 15% of voter support, DAP 5.5% of seats with its 10% voter support, and Parti Keadilan Rakyat 0.5% of seats with 9% voter support.

I am certainly not about to disagree that MMP would be a vast improvement over FPTP for just about any jurisdiction. However, it is worth exploring his claims about the specific impact of the existing FPTP system in Malaysia.

I have insufficient knowledge of Malaysian elections and political geography to know the the extent to which either malapportionment (districts having unequal voter populations) or gerrymandering (districts having lines drawn in such a way as to make one party or demographic group likely to win the plurality) would be the primary explanation for the leading alliance having won more than 90% of the seats on 64% of the vote, rather than the FPTP system’s inherent disproportionality.

Each factor could be a parameter in a model connecting the vote to the seat outcome, such that we would know how much bonus the leading party/alliance would have in hypothetical equally populated districts with unbiased boundaries.

From a quick look at the votes and seats, and an application of the seat-vote equation, it appears that any gerrymandering (and perhaps malapportionment) has been done to bias in favor of minorities, not against them. If that is the case, the way that the ruling alliance has managed FPTP has contributed to minority representation and has dampened the normal plurality-bonus effect of this electoral system. Continue reading