Ontario 2018: Dramatic polling shift and an anomaly watch

With just over a week to go till the provincial assembly election of 7 June, polls in Ontario have shifted quite dramatically.

Here is what it looked like, according to the CBC Poll Tracker, on 18 May:

The Progressive Conservatives (PC) were well ahead in votes, and strongly favored to win a manufactured majority of seats with 41% of the vote. It’s good to be a 40-percent party under FPTP, especially when you are in a highly non-Duvergerian party system with two other large parties splitting most of the remaining three fifths of the vote. The New Democrats (NDP) were far behind, at not quite 30%, and the incumbent Liberals not even polling a quarter of the votes.

Ten days later, here is how things have shifted:

Well, it is a little more “Duvergerian” in that it looks like a close race between two parties, the PCs and the NDP. But not anything like your supposed lawlike “two-party system”, with a third party at over 20% and the fourth just below 5%.

As to what has has led to this shift, and the possible echoes of the 1990 election (which resulted in the only NDP government in the province’s history, to date), see Eric Grenier’s explanation at CBC.

This being a FPTP system, even with a polling lead as of now that is almost two percentage points, it is not as simple as the party with the most votes being assured of governing (whether with a majority, minority, or as head of a coalition). Note how in today’s projection the NDP is favored to win fewer seats than the PCs and the latter party is still quite likely to win a majority of seats.

Thus I hereby declare Ontario 2018 to be on anomaly watch.


Malaysia election 2018

Malaysia’s election counting is underway, and reports abound that the opposition alliance has won. (Opposition, but led by an aging former prime minister who defected from the long-ruling party.)

Malaysia uses plurality in single-seat districts (FPTP), and is (in)famous for its severe malapportionment. It will be interesting to see how big the vote swing is, but the seats outcome apparently will be close. The BBC report linked above says the opposition has 115 seats out of 222.

Sierra Leone 2018

[See caveat in comments about the electoral rules of the earlier elections. For now, I am not changing the post, even though I should re-do it with averages only from the FPTP elections.]

On Sunday, Sierra Leone held its presidential runoff. Sierra Leone is one of those examples of a relatively rare combination: presidentialism with an assembly elected by plurality in single-seat districts. Some of the other examples of this combo are also found in West Africa, including Ghana and Liberia. In this entry, I will consider the effects of Sierra Leone’s institutions on the party system, applying some of the logical models of Votes from Seats.

The runoff rule used for the presidency is even rarer (unique?). A second round is required if the leading candidate in the first round does not reach 55% of the valid votes (Art. 42.2.e of the constitution of 1991).

Julius Maada Bio of the Sierra Leone People’s Party (SLPP) won 43.3% in the first round on 7 March. The runner up was Samura Kamara of the All People’s Congress (APC), with 42.7%. This was the country’s closest contest thus far since the current democratic institutions were inaugurated in 1996.

Sierra Leone has had one president during this time period who was elected with less than 55%. In 2007, Ernest Bai Koroma of the APC won with just 54.62%. However, this was in the runoff. He had 44.3% (to 38.3% for the runner up) in the first round. And herein lies the real oddity: One might wonder why it is OK to elect a president with just half of the votes, plus one, in a two-candidate runoff, but a total falling between 50% (plus one) and (one vote under) 55% would not be sufficient to win in a single round.

So far Sierra Leone has not had an election in which the first-round leader was in that 50-55% grey zone. Dating to 1996, first-round leaders’ vote percentages have been 35.8, 70.1, 44.3, 58.7, and 43.3

Sunday’s runoff (results for which will not be known for about a week) is to replace outgoing President Koroma, who was elected in 2007 and reelected in 2012.

In the assembly elections, concurrent with the first round of the presidential election, only 90 of the 132 constituencies have been declared so far. (There are also 12 seats reserved for tribal chiefs.) The SLPP has won 47 seats to the APS’s 32. The Coalition for Change has eight, despite its presidential candidate having placed fourth with only 3.5% of the vote. Obviously the Coalition for Change has a regional base, and parties with regional strength can win under FPTP despite having a low nationwide vote total. (National vote totals for assembly are not yet available.) The party of the third-place presidential candidate, who won 6.9%, is called the National Grand Coalition, but evidently it is not. On the other hand, it also is apparently not regional, having won no assembly seats (at least among those declared).

The assembly has been increased in size from the last election, when there were 112 elected seats. This remains slightly undersized for a country with a population around seven million. The Cube Root Law would imply an assembly of around 192.

As for the assembly party system, the current assembly size, S=132 (ignoring the indirectly elected chiefs), and the use of FPTP (M=1) implies an effective number of seat-winning parties, NS=(MS)1/6=2.26. On currently declared seats, we have NS=2.45 (counting each of three independents elected thus far as a “party”). That is only a very minor deviation from expectation.

The combination of FPTP for assembly and a two-round presidential election might be expected to inflate NS due to the expected (and observed) proliferation of presidential candidates seeking votes in the first round. At least it would be so expected if one believes in coattail effects. There were sixteen presidential candidates contesting the first round, and seventeen parties with assembly candidates in at least some districts.

While the effect of the first-round threshold of 55% is not clear, we might expect it to enhance fragmenting effects, relative to a standard majority runoff. Candidates who are unlikely to win might enter anyway, hoping to deny even a strong leading candidate an outright win. Given that an outright win is more difficult in Sierra Leone than in other two-round systems, the effect might be to enhance first-round fragmentation. Under a “coattails” expectation, that fragmentation would carry over into the assembly elections, even with the use of FPTP for those elections, held concurrent with the first round of the presidential contest.

In Votes from Seats, Taagepera and I express some skepticism about coattail effects, at least in terms of their impact on the effective number of parties. In fact, we go so far as to claim that one can deduce the effective number of presidential candidates (NP) from the assembly electoral system. A more direct logical expectation, developed in the book, goes from the assembly voting party system to NP; to the extent that the voting fragmentation (measured by the effective number of vote-earning parties, NV) is over-fragmented, relative to the electoral system expectation, then NP will be inflated as well.

Sierra Leone is thus a good test case for the logical models of Votes from Seats. First of all, it has changed its assembly size twice now, while retaining FPTP. Second, as noted already, it combines the FPTP assembly electoral system with a two-round presidential formula that might tend to increase fragmentation of the presidential contest. If it does so, it may also tend to increase NS and NV, if coattails explain assembly party-system fragmentation. In a table below are the results, showing all three actually observed effective numbers (NSNVNP), where available, and the expected values. The expectations are derived from the seat product (MS) in the case of NS, but for NV, we should use the derivation from observed NS, because if the latter is over expectation, for sure NV will be, too. For NP, the table reports the expectation from NV, which is the more direct route. Again, if NV, is higher than expected (perhaps because so is NS), then NP will be, as well. However, we can also compare the institutionally grounded expectation, derived from MS only.

What we see is that NV was far “too high” in the initial election under the current constitution, given the quite low assembly size. So was NP, and thus it looks like a “win” for the coattails expectation, perhaps because as an initial election before the civil war (starting 1991) was fully settled, many candidates may have entered unsure of who would be viable. The 2002 election, following the settlement of the war, also looks like a case of coattails, as the winner easily dominated the field, leading to very low values of all three effective numbers.

Nonetheless, on average, the institutionally derived expectations perform well. Even with the first election being well off the expectation (and the second, too, albeit less so and in the opposite direction), overall, the ratio of observed NS to actual has been only a little above 1.00; the ratio of expected to observed is 1.153, shown in the bottom line. (If we ignore the anomalously fragmented 1996 election, the mean NS is 2.175, or slightly below the expectation from the assembly sizes used in 2002-2018.)

Given actual NS, the observed NV has been almost exactly as expected, on average, with a ratio of 1.025. And while the slight over-fragmentation of the average assembly election result in Sierra Leone gets magnified when we look at expected NP from MS (i.e., from the assembly electoral system only, for which the ratio is 1.225), the expected NP from observed NV is not too far off, with a ratio of 1.16. Note that the ratio for NP from observed NV is almost the same as the ratio for NS from the assembly seat product.

Thus, even with a presidential electoral formula (super-majority runoff) that theoretically promotes more fragmentation than the assembly electoral system (FPTP), there is scant evidence–beyond 1996–that we are unable to predict the assembly party system from the assembly electoral system. There is also scant evidence that we can’t predict voting fragmentation for both assembly and presidency from the assembly party system. The small over-fragmentation of the assembly party system, on average, gets carried through to the other measures. This over-fragmentation might be due to the fragmenting incentives of the presidential electoral formula, but only in 1996 is the evidence for such an explanation, based on candidate entry and their coattails, compelling. Otherwise, it seems the assembly seat product allows us to get a pretty good handle on the output indices of Sierra Leone’s elections.

The seat product model, based on the assembly electoral system, performs well, even in a new post-war democracy like Sierra Leone, and even given the country’s somewhat unusual combination of institutions.

The US Supreme Court gerrymandering case

I do not have time to dissect the arguments before the US Supreme Court in the case concerning the permissibility of the partisan gerrymander in Wisconsin. It clearly is a case of great importance to issues we care about at this blog. So, feel free to discuss here.

I highly recommend two pieces by Michael Latner:

Sociological Gobbledygook or Scientific Standard? Why Judging Gerrymandering is Hard (4 OCt.)

Can Science (and The Supreme Court) End Partisan Gerrymandering and Save the Republic? Three Scenarios (2 Oct.)



The UK 2017 result–Comparative data forays

Well, the election that I thought would be just a boring “typical” snap election in which the incumbent takes advantage of the unprepared opposition… did not quite turn out that way.

Some things happened that are not supposed to happen. And some things about the result are glaringly off the mark of what we should expect from the Seat Product Model (which, of course, is meant to predict average trends, not individual elections).

Top two dominance but no majority

A party is not supposed to gain votes, but lose seats. It is hard to exaggerate how extraordinary this is. The top two parties combined for 82.4% of the votes, the highest in the UK in a long time. The last time it was over 80% was in 1979. The last time over 75% was 1992, and in the three elections immediately before this one, the figure had been around two thirds.

Yet, despite the recovery of the top-two vote shares, there is no majority party. Parliamentary majorities have been won on far less in the past, and one would not expect such dominance of the two leading parties (42.4% and 40.0%) under FPTP to fail to produce majority government. But here we are.

I was curious to know just how common it was for both parties in a FPTP parliamentary system to have at least 40% of the vote, but there to be no parliamentary majority. In my dataset of FPTP elections, consisting of 210 observations, I find one case: Trinidad and Tobago 1995 (two top parties on 48.8% and 47.2%, tied in seats with 17/36). (I have not kept this updated in recent years, and perhaps I am failing to remember one that would be included if I had.)

If I drop my threshold a little lower, to the top two parties both being at at least 38% (but no seat majority), I get one more case: Canada 1957. Of course, the main reason why a leading party with 40% or even 38% of the votes so often gets a majority under FPTP is that it tends to have a more substantial lead over the runner-up, implying many districts are competitive.

Thus it is not only the top two absolute sizes that matter for getting a majority, but also their ratios. How common is it for the top two parties to have votes so similar? First of all, let’s define a ratio of the top two in votes; the mean of this ratio in the data sample is 1.67 (median 1.26). In this UK election, it was 1.06. Approximately 15% of the elections are this close. However, only around 3% of all the elections are both this close and result in no majority party, including UK 1974 (Feb.).

Thus the UK17 combination of two-party dominant, close, and no seat majority is pretty unusual!

Campaigns and leaders

Campaigns and leaders matter. That is not in itself surprising, but many political scientists (sometimes including me) consider them less important than “fundamentals”–whatever those might be. But May did not look like someone who could provide “strong and stable” government. And indeed, she may not get to provide any government at all, if she can’t survive a seemingly inevitable challenge to her position from within.

On the other hand, does Labour’s success relative to low expectations suggest leaders do matter? Did voters actually come to like Corbyn? I am aware of no evidence that such was the case. I suspect he was still a drag on the party, but will leave it to other analysts to try to sort this out. It seems to me that any reasonably competent Labour leader could have won this election, which in turn would never have happened, because May would not have called it had the main opposition had a reasonably competent leader.

The numbers compared Seat Product expectations

On the quantitative indictors, the effective number of vote-earning parties (NV) was, by my calculations from data at BBC, 2.88. The last time it was that low in the UK was 1987, when the leading party (Conservative) won a vote share about the same as this time (42.3%), but it won 57.8% of the seats.

The effective number of seat-winning parties (NS) was 2.47. This is not so unusual, by UK standards, as the figure was 2.53 in the 2015 election and 2.57 in 2010, the last time no party won a majority. In fact, the UK has tended to have a less fragmented parliamentary party system than expected from the Seat Product Model, which would be NS=2.94. The maximum observed since 1945 was the just-reported 2.57 in 2010.

For NV, the Seat Product Model says to expect 3.32, based solely on the large assembly size. Although the post-WWII mean is much lower than that, the electoral party system was finally behaving in the 1992-2015 period, with all those elections seeing NV>3, and the last three (2005, 2010, 2015) all being at 3.6 or higher. Then came 2017, and the party system stopped behaving properly!

It should be emphasized that the Seat Product Model does not expect a majority party; with this large an assembly, even FPTP “should have” a largest party size of 44.5%. At 48.9%, the Conservatives are only a little higher than where they should be. But, of course, actual UK experience usually returns a majority in parliament, and this election was certainly expected to do so–where those expectations are based on political factors and the opinion polls, not the humble Seat Product Model.

Governance and policy

As for government-formation, clearly it is a Tory minority government. Claims by a few pundits that Corbyn could somehow assemble parliamentary support are pure fantasy. And there almost certainly won’t be a coalition. The most likely formula is backing from the Democratic Unionist Party (DUP), of Northern Ireland. The DUP’s 10 seats plus the Conservatives’ 318 combine for just over half the seats.

What will it mean for policy, especially Brexit? I can’t claim to know! But the DUP does not want a “hard border” with the Republic of Ireland, and that implies a “softer” Brexit. On the other hand, if the main motivation May had in calling the election was to boost her standing against restive members of her own caucus who want a harder Brexit, she failed. It will not be easy governance or policy-making for May or an intraparty successor.

Funny how elections don’t always turn out how we expect them to. Democracy! FPTP!

Appendix: Effective Number of Parties and the Seat Product Model

The effective number of parties is a size-weighted count, where each party’s share (of votes or seats) is weighted by itself through squaring. The squares are summed, and you take the reciprocal. See Michael Gallagher’s excellent website for details.

I am not going to explain here the logic behind the Seat Product Model. For that, see Taagepera (2007) or Li and Shugart (2016), or the forthcoming Shugart and Taagepera book, Votes from Seats (2017, due out in October). But the equations are as follows, where M is the mean magnitude (1, in the case of FPTP) and S is the assembly size (650 in recent UK elections).



Seat share of the largest party: s1=(MS)-1/8.

The important thing to understand about these equations is that they are not post-hoc regression fits. They are logical models, derived without reference to the data. When tested against the data from hundreds of democratic elections under various electoral systems, they are astonishingly accurate.

Related earlier posts and comment threads:

UK 2017: Green Party won’t stand in Ealing constituency

So much for fixed terms

UK 2015 and Diverter’s Law

Does UK 2015 mean the death knell for Duverger’s Law?

UK 2017: Green Party won’t stand in Ealing constituency

Here is something we do not see in First-Past-the-Post elections* as much as the Duvergerianists seem to think we should: one party agreeing not to have a candidate in order to avoid vote-splitting in a district.

The Green Party has pulled out of a crucial election seat in a bid to help the Labour Party beat the Tories – the first tactical withdrawal of its kind ahead of the general election.

The decision is expected to allow more votes to go to Labour MP Rupa Huq, who beat the Conservatives with a majority of just 274 votes in 2015, when no other party managed to attract more than seven per cent of the vote.

Green Party members in Ealing — where the party won 1,841 votes in the 2015 election — voted not to field a candidate last week, after Ms Huq promised to campaign for voting reform and the environment.

* Except in India!