The Brexit cycle

EDIT: the pollster has corrected an error. May’s deal is a Condorcet winner after all (i.e., it would beat either of the other options in one-on-one competition.) The Delta Poll blog post about the poll has been corrected, without any indication of the previous error, although its author did note the error on Twitter. The first pie diagram in the image has the numbers reversed.

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Sometimes it just really is awesome to be a political scientist. You see, we have a large literature on the theoretical problem of preference cycles. But they don’t ever happen in real life, right?

Or we could depict it the following way, which makes clearer why it is called a “cycle”:

What could we expect from electoral reform in BC?

This week is the beginning of the mail voting period for the referendum on whether to reform the electoral system for provincial assembly elections in British Columbia. The ballot asks two questions: (1) Do you want to keep the current FPTP system or “a proportional representation voting system”: (2) If BC adopts PR, which of three types of PR do you prefer?

The second question offers three choices, which voter may rank: Mixed-Member Proportional (MMP); Dual-Member Proportional (DMP); Rural-Urban Proportional (RUP).

I have reviewed before what these options entails, and will not repeat in detail here. Besides, the official BC Elections site explains them better than I could. What I want to try to get it here is how we might expect BC’s provincial party system to change, were any of these options adopted. To answer that question, I turn, of course, to the Seat Product Model, including the extended form for two-tier systems developed in Votes from Seats.

The punch line is that the various scenarios I ran on the options all suggest the effective number of parties in the legislative assembly would be, on average, somewhere in the 2.46 to 2.94 range, the effective number of vote-earning parties would tend to be in the 2.83 to 3.32 range, and the size of the largest party would be somewhere between 45% and 51% of the seats. Again, these are all on average. The ranges just provided do not mean elections would not produce a largest party smaller than 45% or larger than 51%. Actual elections will vary around whatever is the point prediction of the Seat Product Model for any given design that is adopted. And fine, yet important, details of whichever system is adopted (if FPTP is not retained) will remain to be fleshed out later.

The ranges I am giving are formula-predicted averages, given the inputs implied by the various scenarios. I explain more below how I arrived at these values. The key point is that all proposals on the ballot are quite moderate forms of PR, and thus the party system would not be expected to inflate dramatically. However, coalition governments, or minority governments with support from other parties, would become common; nonetheless, single-party majority governments would not likely disappear from the province’s future election outcomes. As we shall see, one of the proposals would make single-party governments reman as the default mean expectation.

Before going to the scenarios, it is important to see whether the real BC has been in “compliance” with the Seat Product Model (SPM). If it has tended to deviate from expectations under its actual FPTP system, we might expect it to continue to deviate under a new, proportional one.

Fortunately, deviations have been miniscule. For all elections since 1960, the actual effective number of vote-earning parties has averaged 1.117 times greater than predicted. That is really minor. More important is whether it captures the actual size of the largest party well. This, after all, is what determines whether a single-party majority government can form after any given election. For all elections since 1960, the average ratio of actual largest-party seat share to the SPM prediction is 1.068. So it is even closer. For an assembly the size of BC’s in recent years (mean 80.7 since 1991), the SPM predicts the largest party will have around 57.8% of seats. The mean in actual elections since 1991 has been 62.7%. That is a mean error on the order of 4 seats. So, the SPM captures something real about the current BC electoral system.

Going a little deeper, and looking only at the period starting in 1996, when something like the current party system became established (due to the emergence of the Liberals and the collapse of Social Credit), we find ratios of actual to predicted as follows: 1.07 for effective number of vote-earning parties; 1.07 for largest parliamentary party seat share; 0.905 for effective number of seat-winning parties. If we omit the highly unusual 2001 election, which had an effective number of parties in the assembly of only 1.05 and largest party with 96.2%, we get ratios of 0.98 for effective number of seat-winning party and 0.954 for largest party size. The 2017 election was the first one since some time before 1960 not to result in a majority party, and it is this balanced parliament that is responsible for the current electoral reform process.

As for the proposed new systems, all options call for the assembly to have between 87 seats (its current size) and 95 seats. So I used 91, the mean; such small changes will not matter much to the estimates.

The MMP proposal calls for 60% of seats to remain in single-seat districts (ridings) and the rest to be in the compensatory tier (which would be itself be regionally based; more on that later). So my scenarios involved a basic tier consisting of 55 seats and a resulting 36 seats for compensation. Those 36/91 seats mean a “tier ratio” of 0.395 (and I used the rounded 0.4). The formula for expected effective number of seat-winning parties (Ns) is:

Ns=2.5^t(MS)^0.167.

With t=.4, M=1 (in the basic tier) and S=91, this results in Ns=2.81. I will show the results for other outputs below.

For the DMP proposal, the calculations depend on how many districts we assume will continue to elect only one member of the legislative assembly (MLA). The proposal says “rural” districts will have just one, to avoid making them too large geographically, while all others will have two seats by combining existing adjacent districts (if the assembly size stays the same; as noted, the proposals all allow for a modest increase). In any case, the first seat in any district goes to the party with the plurality in the district, and the second is assigned based on province-wide proportionality. For my purposes, this is a two-tier PR system, in which the compensatory tier consists of a number of seats equivalent to the total number of districts that elect a second MLA to comprise this compensatory pool. Here is where the scenarios come in.

I did two scenarios, one with minimal districts classified as “rural” and one with more. The minimal scenario has 5 such districts–basically just the existing really large territorial ridings (see map). The other has 11 such districts, encompassing much more of the interior and north coast (including riding #72, which includes most of the northern part of Vancouver Island). I will demonstrate the effect with the minimal-rural scenario, because it turned out to the most substantial move to a more “permissive” (small-party-favoring) system of any that I looked at.

Of our 91 seats, we take out five for “rural” districts, leaving us with 86. These 86 seats are thus split into 43 “dual-member” districts. The same formula as above applies. (Votes from Seats develops it for two-tier PR, of which MMP is a subset.) The total number of basic-tier seats is 48 (the five rural seats plus the 43 DM seats). There are 43 compensation seats, which gives us a tier ratio, t=43/91=0.473. Ah ha! That is why this is the most permissive system of the group: more compensation seats! Anyway, the result is Ns=2.94.

If we do the 11-rural seat scenario, we are down to 80 seats in the DM portion of the system and thus 40+11 basic-tier seats. The tier ratio (40/91) drops to 0.44. The resulting prediction is Ns=2.61. This does not sound like much, and it really is not. But these results imply a difference for largest seat size between the first scenario (45%) and the second (49%) that makes a difference for how close the resulting system would be to making majority parties likely.

Finally, we have RUP. This one is a little complex to calculate because it is really two different systems for different parts of the province: MMP for “rural” areas and STV for the rest. I am going to go with my 11 seats from my second DMP scenario as my “rural” area. Moreover, I understand the spirit of this proposal to be one that avoids making the districts in rural areas larger than they currently are. Yet we need compensation seats for rural areas, and like the full MMP proposal, RUP says that that “No more than 40% of the total seats in an MMP region may be List PR seats”, so this region needs about 18 seats (the 11 districts, plus 7 list seats, allowing 11/18=0.61, thereby keeping the list seats just under 40%.) That leaves us with 91-18=73 seats for the STV districts. The proposal says these will have magnitudes in the 2-7 range. I will take the geometric mean and assume 3.7 seats per district, on average. This gives us a seat product for the STV area of 3.7*73=270.

In Votes from Seats, we show that at least for Ireland, STV has functioned just like any “simple” PR system, and thus the SPM works fine. We expect Ns=(MS)^.167=2.54. However, this is only part of the RUP system. We have to do the MMP part of the province separately. With just 11 basic-tier seats and a tier ratio of 0.39, this region is expected to have Ns=2.13. A weighted average (based on the STV region comprising 80.2% of all seats) yields Ns=2.46.

The key point from the above exercise is that RUP could result in single-party majority governments remaining the norm. Above I focused mainly on Ns expectations. However, all of the predictive formulas link together, such that if we know what we expect Ns to be, we can determine the likely seat-share of the largest party (s1) will be, as well as the effective number of vote-earning parties (Nv). While that means lots of assumptions built in, we already saw that the expectations work pretty well on the existing FPTP system.

Here are the results of the scenarios for all three output variables:

System Expected Ns Expected Nv Expected s1
MMP 2.81 3.19 0.46
DMP1 2.94 3.32 0.45
DMP2 2.61 3.01 0.49
RUP 2.46 2.87 0.51

“DMP1” refers to the minimal (5) seats considered “rural” and DMP2 to the one with 11 such seats. If we went with more such seats, a “DMP3” would have lower Ns and Nv and larger s1 than DMP2, and the same effect would be felt in RUP. I did a further scenario for RUP with the MMP region being 20 districts, and wound up with Ns=2.415, Nv=2.83, s1=.52; obviously these minor tweaks do not matter a lot, but it is clear which way the trend goes.And whether any given election is under or over s1=0.50 obviously makes a very large difference for how the province is governed for the following four years!

I would not really try to offer the above as a voter guide, because the differences across systems in the predicted outputs are not very large. However, if I wanted to maximize the chances that the leading party would need partners to govern the province, I’d probably be inclined to rank MMP first and RUP third. The latter proposal simply makes it harder to fit all the parameters together in a more than very marginally proportional system.

By the way, we might want to compare to the BC-STV proposal that was approved by 57% of voters in 2005 (but needed 60%, and came up for a second referendum in 2009, when no prevailed). That proposal could have been expected to yield averages of Ns=2.61, Nv=3.0, and s1=.49. By total coincidence, exactly the same as my DMP2 scenario.

Edit: The following paragraph is based on my own misreading of the proposal, which contrary to what I say here, calls for province-wide proportionality if MMP is chosen. What it says about Scotland still applies, so I will leave it here. [Then again, maybe not?]

A final note concerns the regional compensation in the MMP proposal vs. province-wide in DMP. In an on-line appendix to Votes from Seats, I explored whether regional compensation in the case of Scotland produces a less permissive system than if compensation were across all of Scotland. I concluded it made no difference to Ns or s1. (It did, however, result in lower proportionality.) Of course, if it made a difference, province-wide would have to be more favorable to small parties. Thus if this were a BC voter’s most important criterion, DMP might pull ahead of MMP. However, the benefit on this score of DMP is greater under a “low-rural” design. The benefit of DMP vanishes, relative to MMP, if the system adopted were to be one with a higher share of seats marked as rural. I certainly am unable to predict how the design details would play out, as this will be left up to Elections BC.

The bottom line is that all proposals are for very moderately proportional systems, with MMP likely the most permissive/proportional on offer.

Turkey referendum: Latin Americanization on the road to autocracy

Turkey will go to the polls on April 16th, to vote on a set of constitutional amendments which would change the country’s system of government to presidentialism. Though it seems that in Turkey, the current system is generally referred to as ‘parliamentary’, Turkey has actually been semi-presidential (specifically, premier-presidential) since the country’s first direct presidential election was held in 2014.

The amendments passed the three-fifths legislative majority necessary to put them to referendum with support from the Nationalist Movement Party (MHP). Introducing presidentialism has long been president Erdogan’s express wish. The idea has apparently been around in Turkish politics for a while before it was adopted by the Erdogan and his party, AKP. Full presidentialism seems to have been ‘plan A’, so introducing semi-presidentialism (passed in 2007, entering operation in 2014) was perhaps only ever meant as a way-station toward this goal.

The main details of the amendments are as follows:

  1. Establishing presidentialism:

As stated above the president is already elected directly, specifically using a two-round system. The president is to become both head of state and head of government, with the power to appoint and fire ministers and the vice president. There is no requirement for the Grand National Assembly to confirm appointments. Executive office is incompatible with assembly membership. Interpolation of ministers is to be removed from the constitution, leaving MPs with written questions.

  1. Legislative powers:

The president is to have veto power over legislation, subject to absolute majority override in the assembly. He is to have the power to issue decrees in “matters concerning the executive power” and regulations “to provide for the enforcement of the laws, provided they are not contrary to them”. These cannot affect fundamental rights, except under a state of emergency; an emergency can be declared by the president without confirmation by the assembly, but the latter must be notified immediately and can shorten or end it at any time. These decree powers are essentially the same as those currently held by the cabinet. The president would also dominate the budgetary process: the complete budget is to be proposed by the president and put to a straight up-or-down vote in the assembly without possibility of amendment, with failure to adopt a budget within a timeframe leading to continuation of previous arrangements.

  1. Term lengths and dissolution power:

The assembly’s term in extended to five years (from the current four) and legislative and presidential elections are to be held concurrently. If the presidency becomes vacant, fresh presidential elections must be held. If parliamentary elections are due within less than a year, then they too are held on the same day as early presidential elections; if the parliament has over a year left before its term expires, the newly elected president serves until the end of the parliamentary term, after which presidential and parliamentary election cycles are held concurrently again.

The president is to be limited to being elected twice, but there are some exceptions, the first of which is that a mid-term vacancy-filling election doesn’t count towards the total. The current presidential power to dissolve the assembly is retained, in addition to a new clause which enables the assembly to dissolve itself, by three-fifths majority vote – in either case, fresh elections are held for both president and assembly, who serve new five-year terms. Early concurrent elections triggered by the assembly can always be contested by the president.

  1. Impeachment

The president or any member of the executive is indicted by two-thirds majority in the assembly (upon which many powers, including dissolution, are suspended), which takes the decision on removal to the Supreme Court. A president which has thus been removed is ineligible for re-election.

  1. Judiciary

The acts of the president, previously protected, are now to be subject to judicial review. The structure of the judiciary will not change much – with the role of the president in appointments remaining quite strong. Of the Council of Judges and Prosecutors, the president is to appoint 6 and the assembly is to appoint 7 (4 of whom must be judges from the highest courts) – for renewable four-year terms. The Council appoints most (two-thirds to three-quarters) of the judges of each of the highest courts, with the rest being appointed by the president directly.

According to the BBC, Erdogan claims that the new system will ‘resemble those in France and the US’. There is clearly little truth to this. First of all, France is semi-presidential, specifically the premier-presidential variant. This means that the prime minister, while appointed by the president, can formally only be removed by the assembly – in other words, what Turkey has now. These amendments would outright abolish the prime ministership and parliamentary responsibility, granting the president (already in a position to play a dominant role in the country’s government) absolute control over the executive branch.

Does that mean that the new system will essentially be the same as the US? Not really. Presidential or not, the proposed system includes numerous features bearing little resemblance the American model of checks and balances. The amendments would invest the Turkish president with extensive constitutional decree powers, allow him to all but dictate the budget, but on the other hand leave him with a substantially weaker veto than the US. The absence of assembly confirmation vote for ministers, not to mention presidential dissolution power, are also alien to the US constitution. Overall, the proposed institutional framework is to bear far greater resemblance to past and present constitutions of Latin America, where assembly confirmation is non-existent, emergency and decree powers are common, while some of the other institutions in question have featured occasionally, e.g. presidential dissolution power (Ecuador, formerly Chile and Argentina) and weaker veto (Brazil, formerly Venezuela).

In any case, the proposed amendments represent an immense consolidation of power in the hands of president Erdogan. It would probably allow him to serve beyond the supposed limit of two five-year terms. Judicial appointments involve a somewhat greater degree of presidential influence over a judiciary that has already lost a great deal of independence in recent years. Judicial review, needless to say, will not amount to much. Furthermore, the requirement for judicial ratification may leave impeachment ultimately toothless even in the unlikely event that the requisite majority were achieved in the assembly. Meanwhile, the weak veto and the assembly’s own (weaker) power to call early elections is unlikely to provide much balance in practice. Though dissolution would entail new elections for both president and assembly, a president armed with the power to dissolve the assembly still seems more likely to have the upper hand in the exceptional situation his party ever lacks a majority there – exceptional because of the country’s majoritarian system, and because the president’s very power of calling early elections enables him to do so opportunistically, as Erdogan did in 2015[1].

The Venice Commission’s report characterises the proposed changes as “a dangerous step backwards” for democracy in Turkey. It certainly feels hard to disagree.


[1] One might add (as the Venice Commission does) the fact that elections will be concurrent, which is certainly true, though, as we have recently seen, it’s certainly possible (though still uncommon) for countries to elect a president in the second round that was not of the legislative majority elected concurrently with the first round (e.g. Argentina, Peru), while more generally, two-round systems cause vote fragmentation in the first round. If elections in Turkey remain competitive, it may be that the two round system will, in the long run, cause fragmentation which will spread to the assembly. Perhaps more likely is that once in a while, the concurrent elections could result in divided government as in the first scenario I mention here. A situation like that might provoke Linzian scenarios, but is probably most likely to simply result in early elections at some point, whose outcome would most likely be a reversion to the regular unified control.

Canadian electoral reform process: NDP now says there could be a referendum

Canada’s New Democrats are now willing to support a referendum on electoral-system change, “if it means consensus among parties” on the parliamentary committee, which is to report on Dec. 1.

Previously, the NDP and the Liberals and other advocates of reform have been opposed to a referendum, either because they consider the Liberals’ platform pledge (and that of the NDP and Greens) a sufficient mandate for change, or because they fear a referendum can’t be won . Or both. The Conservatives, on the other hand, have consistently said such a big change must not happen without a referendum. Presumably they think they can defeat it.

The above-linked National Post story refers to this as not “the first time the NDP appeared to have out-maneuvered the Liberals on the electoral reform file.” This remark refers to the NDP having successfully forced the Liberals to make the composition of the committee reflect the parties’ shares of the popular vote instead of their shares of seats. The Liberals have a (manufactured) majority of seats, and the norm for committees is generally proportional representation according to seats.

At the time, I thought the Liberals’ concession to their not having a majority was a clear case of “act-contingency”–not wanting to appear opposed to a potentially popular concept of reform, whatever their sincere preferences on their platform commitment once they (surprisingly) won a majority of seats.

However, in recent weeks, I have thought that the non-majority on the committee was opening up a “perfect” opportunity for the Liberals to declare, “sorry, we tried, but could not get cross-party consensus”, and let the status quo remain. The NDP move may be an effort to head off that outcome and take their chances with a referendum. They might need to get a deal with the Conservatives to make it work.

That may not be quite as far-fetched as it seems. Both parties actually could benefit from a moderate PR system. For the NDP, usually the third-largest party nationally, the appeal of PR is obvious. For the Conservatives, the benefit would be from allowing the party’s disparate wings to appeal separately, either as factions competing within small multi-seat districts* or eventually as separate parties, as they were not so long ago.

The next several weeks may determine whether electoral reform can advance, at least to a referendum, against what remain pretty formidable hurdles.

 

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* I am assuming it would have to be STV or open lists. Closed lists are probably out of the question, even as part of an MMP system. And while the NDP and Greens logically prefer MMP (more highly proportional, even with only province-level compensation), the Conservatives and Liberals would like small-magnitude PR, if keeping the status quo looks uncertain. (And if, for the Liberals, AV is not achievable.)

PEI 2016: Referendum favors MMP

The Canadian province of Prince Edward Island (PEI) held a referendum (“plebiscite”) on electoral reform. The voting, which could be done online or by phone, took place from 27 October to 7 November, Results have now been announced, and the majority preference is mixed-member proportional (MMP).

Interestingly, it was a vote among multiple options, conducted by alternative vote (instant runoff). The initial plurality choice was the status quo, first past the post (FPTP). But this was the first choice of only 31.2%. The runner up in first preferences was MMP, with 29%.

Through elimination of lower-ranking choices and transfer of preferences, MMP came out with a majority on the fourth round of counting, 55% to 45% over FPTP (leaving out exhausted ballots, which were just under 5%).

Other options were “FPTP with leaders” (status quo, except that party leaders who did not win a riding would get a seat if the party cleared 10%), “Preferential Voting” (i.e., alternative vote), and something new called “Dual-Member Proportional“.

Perhaps it is not at all surprising that the transfer patterns reveal a “change as little as possible if we must change” coalition and a “more change” coalition. FPTP took a bigger lead on the count following elimination of FPTP+, by far more timid of the reform proposals. After the elimination of AV, which would be the next most-similar proposal to the status quo, MMP actually got more of these voters (43.9% to 36.7% for FPTP). Given that DMPR got 19.5%, the pro-AV voters had a clear majority for some sort of PR over keeping majoritarianism. On the final count, MMP got 82.6% of the eliminated votes for DMPR. This adds up to quite a clear consensus for a move away from the majoritarian model. (Note that STV was not an option.)

PEI had a referendum on an official proposal for MMP in 2005, which went down to a big defeat. Since that time, the province has continued to have some of the odd results (e.g. 2007) that are inherent to FPTP, especially given such a small assembly. In the most recent provincial election (2015) there was another large manufactured majority, although the Green Party managed to win a seat despite just 11% of the provincewide vote.

The timing of the vote is interesting, given that the federal parliamentary committee studying electoral reform is due to report in just a few weeks.

The PEI referendum result is non-binding.