Among the electoral system types to be considered by Canada’s upcoming reform-proposal process is the mixed-member proportional system (MMP). What might we expect Canada’s effective number of seat-winning parties (Ns) to be under MMP?

As noted in the previous post on comparing the Alternative Vote to FPTP, Canada has had almost exactly the Ns, on average, that we should expect it to have, given its assembly size (around 2.6). Thus I will start from the premise here that Canada would continue to have about what we expect if it had MMP staring in 2019 (or whenever). That is, recent elections the country are neither surprisingly under- or over-fragmented, so there is no reason to think the country would over-shoot the expectation under a new system. (It might be more realistic that it would under-shoot, but that depends on how much we believe there is pent-up demand for new parties or for growth of existing smaller ones. I will leave that aside here.)

The answer to this “what if” depends on the precise MMP model. What Li and Shugart (2016) have shown is that a minor addition to the Seat Product Model (of Taagepera, 2007) captures two-tier compensatory systems well. MMP is a type of two-tier compensatory system, so let’s apply that model to a hypothetical Canadian MMP. The formula is:

Ns=2.5t(MSB)1/6.

In this formula, MSB is the “basic-tier seat product”, defined as the mean magnitude of the basic tier, times the total number of seats in that tier. For a typical MMP system, we retain M=1 in the basic tier, so the basic-tier seat product is simply the number of seats elected in that tier. The t in the formula stands for “tier ratio”, which is the share of the total assembly that is elected in the compensatory tier. This is an exponent on a constant term that is empirically determined to be 2.5. (Determined from the broader set of cases on which this is tested.*)

If a country’s electoral system is “simple”, meaning there is just a single tier, as with FPTP, then the above formula reduces to Taagepera’s (2007) seat product model:

Ns=(MS)1/6.

(In a system with no upper tier, t=0, and MSB=MS.)

For purposes of estimating, I am going to assume the assembly size will remain the same, currently S=338. I will further assume that it would be politically difficult to reduce the number of districts (ridings) in the basic tier of an MMP system too much below the current number (which is, of course, 338). I will adopt two thirds of the current number as my estimate of “not too much”. In such a scenario, we get a basic tier of 225 seats, giving us t=.33:

Ns=2.5.33(225)1/6=1.35(2.47)=3.33.

I did not plan my scenario to get to three-and-a-third, but it has a nice ring to it. And seems pretty reasonable. For comparison purposes, this is not much different form what Canada had in 2006 (3.22) or Germany, an actual MMP system, had in 1998 (3.31).

Based on another formula in Taagepera (2007), which is empirically very accurate, we can also derive an expectation for the seat share of the largest party (s1):

s1 = Ns-.75.

For our hypothetical MMP system in Canada, this implies the largest party with just over 40% of the seats.

We can tinker with the scenarios. For instance, suppose the assembly size were increased to 400, with half the seats in the basic tier. Then we get:

Ns=2.5.5(200)1/6=1.58(2.42)=3.82.

As would be expected intuitively, the fragmentation of the House goes up due to the larger compensation tier, and in spite of the basic-tier seat product being correspondingly lower. This scenario would have an expected s1=.366.

Note that I have ignored thresholds here. My ongoing research with Taagepera suggests that thresholds matter, but unless the threshold is very high (more than 5%) or the seat product, MS, is extremely high, the value of the threshold has much less impact than the parameters discussed here.

In conclusion, under common Mixed-Member Proportional (MMP) designs, Canada could expect its House to have an effective number of parties ranging from 3.33 to 3.8, compared to a recent average of around 2.6 under FPTP. Its largest party could be expected to have around 36% to 40% of the seats, on average, compared to majorities or nearly so in recent elections.

* Note that this parameter’s empirical derivation raises the risk that it could be an artifact of the particular sample we have, and thus not reliable for determining an expectation value, as I am doing here. Fortunately, unless it is off by a wide amount, it does not make a large difference. For instance, 2.33 =1.26, whereas 3.33 =1.44. This variance in our prediction is much less than “normal” fluctuation from election to election in many countries.

1. Alan says:

I am deeply concerned for how remote areas would suffer under MMP because of the immense districts that MMP requires.

Assume an electorate of 1000 and an assembly of 100. The electoral ratio is 10 under FPTP.

If the new MMP assembly has 50 list MPs and 50 district MPs, then it follows that MMP districts must have twice the electoral ratio of the FPTP district at 20.

It is occasionally argued that STV requires huge districts that do not work in remote areas, On the same electorate and assembly size, the STV district would indeed have a population of 30 (assuming that magnitude cannot be less than 3) but it would have an electoral ratio of 10, exactly the same as the FPTP district and half the electoral ratio of the MMP district. And that is assuming that districts of magnitude 1 are not allowed in remote areas…

• Dave Hutcheon says:

At present there are 2 ridings in northern Alberta with population density close to 1 person per square kilometer. All the rest of the ridings have distinctly lower density (10 other northern provincial ridings plus 3 territories) or distinctly higher density (the remaining 323).

If all of these 15 ridings were kept as single-member constituencies, the remaining MMP ridings would be of geographical sizes within a traditionally accepted range, assuming a second tier to have 1/3 of the seats.

While it is not esthetically pleasing to have a hybrid SMC + MMP, this seems to me an acceptable way to recognize the realities of Canadian geography without seriously compromising the goals of MMP.

• Alan says:

The Federal Division of Farrer, where I live, has a population density of approximately 0.75 er square kilometre. A clerk at the AEC once invited me to ‘pop in’ to the divisional office, unaware that would be a round trip of more than 1400 kilometres.

It is a traditional claim on this blog that only MMP is viable where you have remote areas with small populations because STV multimember districts are too large. I am merely noting that MMP districts would be larger than FPTP districts, and would have a larger electoral ratio than their STV equivalent.

When the state of New South Wales applied STVPR to the election of the legislative assembly the rule was magnitude 5 in urban areas and magnitude 3 in rural areas. There is no reason not to add a third category of magnitude 1 seats in remote areas. In that case the big STV districts in remote areas argument would collapse entirely.

• Naomi says:

Alternatively, the sizes of the FPTP districts under MMP could be allowed to vary from area to area. You could have relatively few people in rural ridings and a few times as many in urban ones. The compensation tier would then make sure the overall partisan balance came out right despite the intentional mal-apportionment

• Anne says:

More generally, polls consistently find about 2/3 of Canadians are either very satisfied or satisfied with our current government. How might one expect this level of satisfaction to change under MMP?

Canada has so many great, hard-working talented local representatives that make a real effort to connect with their constituents. I’m concerned that in Germany’s MMP, votes for local reps are not seen as having the same importance as votes for party which determines the makeup of government.

Would Canada lose much of what is good about our local rep system in MMP?

• Alan says:

MMP would be a better system for Canada than FPTP. It is not the system of proportional representation that I would prefer, but it would have significant advantages over the present system. FPTP promotes a divisive winner-takes-all politics that is completely unlike what I know of the Canadian character. It frequently generates reverse majorities*, as in Australia in 1996 and possibly in 2016. (We are still counting) The experience in New Zealand, Scotland and Wales has been that local MPs tend to be overvalued compared wth list MPs.

*I managed to save MMS from having to read about the ‘reverse majorettes’ produced by predictive spell-checking.

• In response to Anne, I would say that the New Zealand experience is probably more relevant than Germany’s, given that the former also started out with FPTP. Of course, NZ adopted MMP at a time when public approval of the government was low, so MMP probably helped. I don’t see it is too likely to cause Canadians to be less satisfied if it were adopted, but it depends (at least in part) on how well voters and elected representatives adapt to the change. Having said that, if voters like the outcome of the recent FPTP election in Canada, it may undermine the argument for change to some extent. (I do not mean my argument for change; I mean the public opinion around the issue.)

As for the relative importance of MPs under the two modes of election, Germans seem not to care. New Zealanders do, but this is an asset, not a bug. MMP in New Zealand has been associated with probably more attention to local needs than under the old system, by disconnecting (mostly) the local vote from the government outcome.

In response to Naomi, I agree that MMP can allow greater tolerance of malapportionment, due to the compensation mechanism. I have never attempted to model how much is “tolerable”, however.

• Rob says:

Canada wouldn’t lose much with Australian optional preferential voting. Assuming the Liberals think that they would benefit from this system, they might not, and the NDP could benefit from Liberal transfers, and the same could be said for the Conservatives as they too could get transfers from Liberals as well. They need not be a referendum, but perhaps the Greek method of changing the electoral system is a good idea with a simple majority to propose, and then an election in-between the next parliament ratifies the changes for the 2023 election. Justin Trudeau is being too ambitious in changing an electoral system, NZ Royal Commission proposed MMP in 1986, but the electoral system proposed change was done by referendum in 1993, and did not go into affect until 1996. It took 10 years to make the change happen. Changing an electoral system method is very similar to amending a Constitution, the way votes translate into seats is the most important consideration any democracy has to make, it can’t be done hastily, it is odd the most countries treat the electoral method as an ordinary law.

2. No one proposes 50/50 MMP for Canada. Some have suggested the ratio should run as high as 40% top-up MPs, others speak of 33% (although since Wales has kept showing how badly such a low ratio works, they are fewer than they were in 2004 when the Law Commission of Canada reported.) Even the Law Commission’s demonstration model ended up with 35.2%, which is still a bit low. My current simulation uses 37.6%, which would make local districts an average of 60% larger. But in Northern Ontario, Northern Manitoba and Northern BC they would be 50% larger. (Northern Quebec will likely need special provisions.)

As to the number of effective parties, one should really do two calculations, one for Quebec’s MPs, one for the ROC’s (Rest Of Canada). In the ROC, if the Green Party’s vote doubles as they expect it would under PR (and I agree), even the moderate MMP model most recently discussed by Prof. Henry Milner (8-MP regions) would likely give the Green Party, on the votes cast in 2015, 14 of the 19 MPs that perfect proportionality would give them in the ROC. Therefore, the simulation’s result in the 260 ROC seats would be 113 Liberals, 90 Conservatives, 43 New Democrats, and 14 Greens. How many “effective parties” is that? In Canada, most people would just say we would have four parties (five in Quebec).

Although the 2015 votes are increasingly irrelevant. On virtually every poll since the election, Justin Trudeau’s Liberals would receive an absolute majority under any PR system.

3. It’s worth noting that Canada’s notoriously opaque and complicated constitution would seem to preclude a nationwide MMP tier, as seats are required to be distributed between provinces and territories. Exactly how this would be amended is somewhat unclear, though the most obvious procedure involves consent of two-thirds of provinces with half the population.

• No one is proposing a nation-wide tier. It would be by province or, like Scotland and Wales, by region within a province.

• Alan says:

Is anyone aware of an inclusive electoral reform process that included a referendum apart from New Zealand and the ACT in 1992?

• Wilf, I know that. I was simply wondering what impact the difference between one nationwide PR tier with 115 seats and ten (not including the territories) province-wide PR tiers with an average magnitude of eleven would have on MSS’s calculation of the likely number of parties. To the best of my knowledge, the seat product model does not account for such a difference, though I assume it would have some impact on the number of parties (though that would be muted with a nationwide threshold).

• Yes, that will be fun in a province like PEI, with four seats (which is about twice as many as it should have anyway, but nevermind that). In a district that small, you basically end up needing to have 3 of the 4 seats as top-up seats otherwise proportionality is highly unlikely to be satisfied. Seven-seat Newfoundland poses its own problems due again to the small overall size but also due to the issue of how to deal with Labrador, already the least populous riding in the country. For PEI at least, and probably Newfoundland, it might actually be better to have the entire province act as a 4-seat (and 7-seat for Nfld) STV district and scrap the entire MMP idea in those provinces. Better yet, scrap the idea of MMP altogether because in every province it is going to create an issue whereby the low density ridings either get further enlarged in extent and/or the population imbalance between urban and ‘wilderness’ ridings is further exacerbated.

• Rob says:

Why does Canada have such a strange amending formula for it’s Constitution? One would that Canada would have embraced a Scandinavian style amending formula or an Australian legislative proposal, but ratification by referendum, or maybe a combination of both?

• dbailie says:

Lack of agreement between the federal and provincial governments on a constitutional amending formula meant that the British Parliament retained responsibility for the British North America Act long after Canada gained legislative independence in 1931. The convoluted journey towards the adoption of the Constitution Act, 1982 and the current amending formula can be found here https://en.wikipedia.org/wiki/Patriation.

4. As to a referendum, the Canadian province that came closest to implementing PR was Quebec in 2004-5, getting to the stage of a draft bill and many public hearings by a Select Committee sitting jointly with a Citizens Committee — a lovely consultation model — which resulted in a report from each calling for the model to be given improved proportionality. No one called for a referendum. Quebec uses those for bigger issues. More recently, the leader of the Quebec counterpart of the Conservatives, then named the ADQ, Gérard Deltell, made a lovely speech in the National Assembly on Sept. 27, 2011 which will come back to haunt him now that he is one of the three Conservative MPs on the Special Committee on Electoral Reform. He called for MMP, and said “that this has been put off for too long. The Parti Quebecois, since its founding, had in its election manifesto the issue of changing the voting system and was in power for 18 years and did not do it. The current government had it in its election platform in 2003. In 2004 it even undertook to do it, and has still not done it. . . We have almost 30 months before the next election. We have time to do what all the parties have always urged, that is, a proportional system. ” No mention of a referendum.

• Correction: back in 2006, after Quebec’s public hearings, the official opposition PQ called for a referendum, while the Liberals and ADQ said a parliamentary consensus on an electoral reform package would make a referendum unnecessary. The PQ position was considered as an excuse to delay the project, since proportional representation would have hurt the PQ, so their position was always “yes, but not yet.”

5. Would nationwide calculation of the proportionality, but provincial lists (similar to Germany) be acceptable, or is the only plausible model one with compensation calculated only province-by-province?

Even if it were province-by-province, I don’t think I’d want to complicate the model by introducing a parameter for sub-national compensation. I recognize that reality will be more complicated than the model–by definition of what a model aims to do.

Note that I used 33% compensation tier in my first scenario because I agree that 50:50 is not reasonable for Canada, and the large rural ridings are partly why. I do agree that MMP can allow a greater tolerance of regional disparity in riding (single-seat district) populations, without sacrificing proportionality. Surely this could be modeled, but again, it would be complicated to do so.

Any complexity added to the system–including regional compensation and greater malapportionment in the basic tier–makes it harder to say with confidence what the effects would be. This is a problem for those of us asked to give “what if” advice, but the actual designers sometimes have to make such compromises against the principle of simplicity.

• Alan says:

You’d have to expect the Supreme Court to take the view that if the constitution requires list MPs to represent provinces and territories then they have to be elected on the basis of votes local to each province and territory.

The law commission report recommended consultation with indigenous Canadians about the creation of indigenous MPs. I’d guess that would take a section 41 unanimous consent amendment.

• The answer really lies in the name of the founding process that created Canada: Confederation. It’ll be proportionality by province because Confederation was a coming together of separate colonial provinces, not the division of a single entity into provinces. Only with respect to the three territories could you “pool” them.

If we were discussing introducing elective proportionality into the Senate, however, the answer might be slightly different because the concept of multi-province “regions” exists in the Senate, so you might be able to get away with proportionality-by-region with your German-style provincial lists. Of course for Ontario and Quebec it makes no difference as those provinces are regarded as regions in their own right.

But in neither case would I see it as plausible for a nationwide calculation of proportionality to be implemented by jigging the provincial top-up lists.

• The German nation-wide calculation was ruled out by the Law Commission of Canada. It would mean provincial seats would be determined by votes from another province, and it is possible that the weight of the results from outside of a small province would be greater than results from inside the province. And regardless of the weight, can you picture votes from Alberta being given any weight in electing an MP from Quebec? The question answers itself.

• Yes, as I suspected. I had forgotten that the Law Commission explicitly addressed this, but I should have known.

• Wouldn’t German-style national calculation but provincial lists require potential extra compensation to avoid negative vote weight?

6. As for Wilf’s suggestion of calculating effective number of parties for Quebec and rest of Canada, it could be done, although the assumptions of the model may not be valid. (Impossible to say, actually.) I have done something similar in the past when trying to model votes-seats conversion in advance of Canadian elections (you can find the posts on this blog; I think I last did it for the 2011 election).

As an aside–please note that it is the number that is “effective”, not (necessarily) the parties!

7. The reduction of SMC representation in sparsely-populated areas was also a sticking point in New Zealand when it switched from FPTP to MMP two decades ago. Specifically, the South Island had its 25 general electorates (i.e. regular constituencies) reduced to 16, and not surprisingly that part of the country was almost evenly divided in the 1993 referendum, with MMP prevailing there by a razor-thin margin. That said, by the time the issue was revisited in 2011 the original controversy appeared to have subsided: the South Island delivered a clear majority against scrapping MMP (albeit by a smaller percentage margin than the rest of the country).

As for having PR top-up seats at a sub-national level, I should note that when Senate elections in Italy switched in 1993 from de facto PR to a sui generis mixed system (by scrapping the impossibly high 65% threshold required to win a single-member seat), the general rule was that in each region at least a quarter of the seats would be PR, and the rest FPTP. As a result, except for a couple of very small regions which were not assigned PR seats as they only elected one or two senators, and a third region where treaty obligations required equal representation for both of its provinces, the proportion of PR seats varied from one-quarter to one-third of the seats; apparently, the rule was to multiply the total number of seats assigned to a region by 0.75, and then discard any resulting fractions to obtain the number of single-member constituencies, with the remaining seats becoming PR mandates, allocated at the regional level. However, the 1993-2005 Italian Senate system did not strive for full proportionality; rather, the idea was to compensate in a limited fashion minority parties faring poorly in the SMC races. Perhaps not surprisingly, the main beneficiary of the PR compensation element – “recupero proporzionale” in Italian, literally “proportional recovery” – was usually the second-largest party; among third parties, the only instance where proportional compensation had a distinct impact was in the 1994 general election, in which the centrist Pact for Italy (basically what remained of the once-mighty Christian Democratic Party) polled 16.7% of the vote but won only three SMC seats of 232 (1.3%); however, once the PR “recovery” seats were allocated, the seat figure rose to a more respectable 31 of 315 (9.8%) – not quite proportional to the ticket’s share of the vote, but a definitive improvement over a dreadful (if predictable) FPTP showing.

At any rate, Canada is going to face similar issues with the smaller provinces if it ends up adopting MMP with PR top-up on a sub-national level (and just so we be absolutely clear, I don’t think a nationwide PR tier is practical in a country as vast and diverse as Canada, or for that matter achievable). Some have suggested doing without single-member districts in problematic cases like Prince Edward Island, but that strikes me as highly unlikely in a country where FPTP appears to be so deeply ingrained in the political culture (at least as far as the ruling classes are concerned). On the contrary, it would seem to me far more likely that such problem cases could be manipulated to further dilute the top-up component.

Finally, I should note that a reduction of SMC seats to 225 under MMP (with the remaining 113 set aside for PR top-up) would mean Canada would have roughly the same number of ridings as it did just over a hundred years ago. Whether that’s a good thing or not (or could be construed as such either way) I do not know.

• Dave Hutcheon says:

If we accept as a given the “opaque and complicated” formula for allocated HOC seats among the provinces, what is the impact of applying MMP to each of the four Atlantic provinces separately? In the 2015 general election the region’s 32 seats all were taken by the Liberals, though the Liberals’ share of popular vote would have entitled them to just 19 seats.

The 32 seats were distributed as 7 to NL, 4 to PE, 11 to NS and 10 to NB. If MMP picked the number of top-up seats to be the number closest to 1/3 of the provincial total, there would have been 2+1+4+3 = 10 top-up seats. All would have gone to other parties, leaving the Liberals with 22 seats, an excess of 3 over the result of treating Atlantic Canada as a single unit. A top-up fraction of, say, 37% could have reduced the discrepancy to 1 seat.

A 3-seat discrepancy pales in comparison to the 51 “excess” seats that the Liberals won nation-wide thanks to the FPTP system. In weighing MMP against FPTP or other systems, the “PEI problem” is rather small factor.

8. Ed says:

To echo some of the other commentators, Canada has two particular problems with its House of Commons representation, that combined almost mandate single member districts. One is geographical and not unique to Canada, though its worse in Canada than in other countries. The second is constitutional and unique to Canada.

The geographical problem is the existence or remote, sparsely populated regions. Elections Canada in fact has already created about half a dozen single member ridings that have much lower populations than the norm. To address one of the commentators, these do not exist in Alberta (which is still, even after the redistribution under the Harper government, under-represented) or Quebec, but consist of the territorial ridings, Labrador, and a couple of ridings in Manitoba and Saskatchewan. But at the provincial level, attempts to introduce proportional representation have foundered on this issue. It doesn’t make much difference if mixed member proportional, party list proportional, or single transferable vote is used, though working it out STV actually seems to work slightly better due to fewer members per electoral district.

Since areas of lower density population are already over-represented in the House of Commons, allowing them to maintain single member districts augments their over-representation and is not desirable, unless some sort of complicated compensatory feature is added to the proportional system.

The constitution has two effects. One is to preclude a nationwide tier, which is probably the only possible solution to the remote areas problem. The second is the existence of the relatively low populations in the Maritime provinces, which again are already over-represented in the House of Commons, meaning not many ridings for a second tier.

Not many people realize how mal-apportioned House of Commons ridings are between provinces, and also how mal-distributed the national population is between the provinces. Reform of the provincial system is more urgently needed than that of the electoral system, to get a better balance of population between provinces. If apportionment was fairly equal, the five Atlantic provinces should be sending about 20 MPs to the House of Commons, not 32. The two prarie provinces are also over-represented, though not as badly, they should have about 22 MPs instead of 28. The three territories should either combine to send one MP to the House of Commons or their MPs be made non-voting delegates following the American practice. Ontario is pretty significantly under-represented and so is Alberta (Quebec’s delegation is pretty much exactly as large as it should be, and I forget about what the case is with BC), and this is after the addition under the Harper government of more ridings for Ontario, Alberta, and British Columbia.

This is another case that if a proportional element is going to be introduced into the system, it would be better to introduce it into upper chamber, which is already the subject of numerous reform proposals, is currently not elected at all, and is already organized on a regional basis. However, Senate reform opens enough of a can of worms that there may be no choice than to leave well enough alone. But the election of Senators using proportional representation on a regional basis is an improvement over the standard current reform proposals, excepting the NDP proposal to abolish the upper chamber entirely.

• Tom Round says:

> “Since areas of lower density population are already over-represented in the House of Commons, allowing them to maintain single member districts augments their over-representation and is not desirable, unless some sort of complicated compensatory feature is added to the proportional system.”
My own preferred STV-PR model would have 2-seaters in any electoral district that would otherwise exceed one million square kilometres (sorry, MSS, no idea what that is in miles, but I suppose after yesterday’s referendum I’ll need to relearn imperial measurements again) and 5- or 7-seaters elsewhere. A maximum of one 4, 6, or 8-seater if necessary to fit districts within an electoral region (State/ Province/ Territory) but I would also argue for the apportionment formula to be explicitly weighted to avoid allocating a region an STV-inconvenient number of seats.* Eg, if your divisors are 4.1, 5.9, 6.1, 7.9, 8.1, 9.5, 11, 12.9, 13.1, 14.5, 15.9,** etc, then you are probabilistically going to have States/ Provinces/ Territories being allocated 5, 7, 10, 12, 14 or 15 seats than 6, 8, 9, 11, 13 or 16 seats.

* Five and seven are convenient numbers. Each multiple of a convenient number is also a convenient number. The sum of two or more convenient numbers is also a convenient number. Any other number is an inconvenient number.

** Basically Sainte-Laguë divisors except that if “downgrading” from a convenient to an inconvenient number (eg, 12 to 13) you add 0.9 to the existing number of seats to get the divisor: if “upgrading” from an inconvenient to a convenient number (eg, 11 to 12) you add 0.1 to get the divisor: if moving between two convenient numbers (eg, 14 and 15) or two inconvenient numbers (eg 8 and 9) you add 0.5, ie use the normal Sainte-Laguë divisor in that case
I did once flirt with the idea that only convenient numbers should be allocated (ie, the divisor would always be the next convenient number up) but this could mean that a tiny extra gain in population could shift two or more seats at once, which is inconsistent with the idea of proportional representation, and a bug that I dislike about both MNTV and MMP. This way, a State/ Province/ Territory with 5.9 to 6.1 Sainte-Laguë quotas will still have 6 seats, not 5 or 7, but the coin has to land on its edge to get inconvenient numbers.

• Alan says:

1 million sq km (386102158.542 sq mi) seems a fairly high bar. At midnight next Friday the redistribution will transfer me from Farrer (126 590 sq km) to Parkes (393 413 sq km). It will now be a 1500 kilometre round trip to visit the divisional electoral office instead of a 1400 kilometre trip.

I’m not clear on what the magnitude of a 1 million plus district would be.

For myself the only difference between a magnitude 2 district and a magnitude 1 district is going to be size and distance. The two largest parties will almost inevitably share the representation as they do in the magnitude 2 senate districts for the ACT and NTA. You’d also breach the important principle that an STV district should have an odd magnitude.

• Tom Round says:

The area threshold is open to adjustment. The basic point is that all, and only, districts over N huge geographical size are two-seaters. In Australian terms I’d envisage all such electorates being in the NT, far north Queensland and northern WA, so with all respect to the good burghers of Broken Hill, own time-zone and all, they would have to take their chances in a seven- or (probably) five-seater. And having two seats, with a likely 1-1 tie between left and right, is a feature, not a bug, of this proposal, as it is for the Territory Senators. It could be sold to remote rural voters as “you get two MPs to help each other cover this huge electorate, just as UK counties and shires had for centuries before 1832”.

• Alan says:

The largest electorates in descending order by area are Durack (WA) 1629858, Lingiari (NT) 1352371, Grey (SA), O’Connor (WA) 904881, Maranoa (QLD) 868576, and Kennedy (QLD) 731297 and Parkes (NSW) 393413. The next largest after Parkes is Leichhardt (QLD) 148988, less than half the area of Parkes.

Only Lingiari and Durack exceed the Round threshold in area. If you look for pairs of electorates that together exceed the Round threshold the only pairs available are Durack-O’Connor, Maranoa-Kennedy and possibly Lingiari-Solomon.

The AEC classifies divisions as inner metropolitan, outer metropolitan, provincial and rural. The rural classification is defined as divisions without a majority of enrolment in major provincial cities. The disadvantage of the Longiari-Solomon pair is that it would be possible for both representatives to come from inner metropolitan Solomon rather than rural Lingiari and the good burghers of Darwin would find communicating with and influencing their representatives much easier than the far-flung electors of the rest of the NT.

There is no obvious reason to exclude Grey, O’Connor, or Maranoa on the grounds that they do not lie in an expected geographical zone. There is no obvious reason to exclude Parkes, which is more than twice the area of the next smallest electorate and would, were it a country, be larger in area than Zimbabwe, Japan or Germany. For that matter Parkes is larger than Norway whose electoral system makes provision for area as a representational criterion.

Sadly I have been unable to find a single list of Canadian ridings that includes area information. All I can say now is that the largest federal ridings in Ontario and Quebec appear smaller than Parkes and Nunavut is gigantic. Watch this space.

• Tom Round says:

“The reason there are two Senators for each [US] State is so that one can be the designated driver.” – Jay Leno

• Dominic Paris says:

Could you define what you consider convenient vs. inconvenient numbers?

• I remain of the opinion that reforming the Senate to be elected by PR, with a small reduction of its powers would be an altogether superior solution. Could also be a great way to compromise on a more logical representation formula, overrepresenting the smaller provinces in the upper house while eliminating most of the inter-provincial malapportionment in the Commons.

• Alan says:

jd

I would propose dividing the seats by the Penrose method – proportional to a square root of the population. With 110 provincial seats, the distribution is: Ontario 25, Quebec 20, BC 15, Alberta 14, Manitoba 8, Sask. 7, NS 7, NB 6, Nfld 5 and PEI 3.

That would not require abolishing provinces. It would also have the signal advantage of reducing the impact of the senatorial clause on the house of commons, although of course it would have limited impact unless it were combined with ending the grandfather clause.

I also cannot see how eliminating territory MPs or making them nonvoting would really improve matters. Yes, none of the Canadian territories are anywhere near the electoral quotient but reducing them to an electoral quotient of zero hardly improves matters. Equally, giving them a single joint MP would create an electorate of 3921739 sq km and submerge Nunavut in a non-indigenous district. That area, combined with the northern climate, would make the task of representation almost impossible and reduce the MP to a state of permanent jet lag. 3 MPs in a house of 338 is really neither here nor there.

9. Ed says:

Ideally the country should go to just six provinces anyway, split Ontario into two, combine the five Atlantic provinces into one province, and combine Alberta, Manitoba, and Saskatchewan. People will howl but it would make all sorts of constitutional issues easier if there were just five provinces, and the population difference between the most and the least populated was 4x instead of 240x like it is now. With just six provinces, giving a single province a veto over all sorts of changes would not be as big a deal, which works very well with handling Quebec.

Of course the chances of something like this happening are pretty much nil.

• Tom Round says:

I’ve always thought Canada was on to something by detaching “regions” as units of representation in the national legislature from “provinces” as units of subnational government. (And yes, that will be the first and only time I say anything in this place in praise of Canada’s system of government).

In just about every other federation or union I can think of (apart from Russia’s/ the USSR’s complex system, with its various “autonomous krasnoyarsks” etc, which I still haven’t gotten fully across in 30 years), “region” = “province.” This has the unfortunate effect of deterring anyone from creating new provinces, or rearranging the existing provincial boundaries, because it will play havoc with the balance of numbers in the national legislature.

So in the USA, where the frontier has been closed since 1910 and where the Constitution mandates an equal number of Senators for every State, no-one wants to carve California up into three or four States that are not each larger than most EU member nations, because this will give the existing California six or eight Senators instead of two.

The same goes for Australia, where the frontier was closed before Federation and where the Constitution (very foolishly) both allows federal Parliament to specify the minimum representation in both Houses for any new States *AND* then gives every single State a veto over even constitutional amendments that would reduce its minimum representation.

It would be better to specify a number of regions, by reference to latitude and longitude; to base federal representation on these regions; and then enable provinces to be rearranged relatively easily within these regions.

In Canada’s case, the one-province veto was clearly intended as an indirect way of giving the Francophone 22% an equal veto power with the Anglophone majority, with Quebec’s provincial government as the proxy for all of Canada’s Francophones. This has worked serviceably in the past (and is certainly easier than, eg holding elections for French-speaking Canadians to elect some equivalent of Ireland’s Gaeltacht council… and let’s not mention Belgium), but it faces three problems:

(a) If you’re writing a Constitution that will endure for centuries (and the USA’s has now lasted nearly a quarter of a millennium), it’s not safe to assume that the existing geographical distribution will continue forever. If, for example, non-Francophones were one day to become a majority in Quebec, Canadian Francophones might number one-fifth of all Canadians yet not have a provincial premier to exercise the veto on their behalf.

(b) Because it formally treats all provinces as having an equal veto, it means that Prince Edward Island gets the same legal power as does Quebec (with a vastly bigger population and, as noted above, typically serving as an institutional voice for Francophone Canadians dispersed throughout the ROC).

(c) The interests of Francophones in a province where they are a majority might not always coincide with the interests of Francophones in a province where they are a minority. An obvious example would be proposals to relax the obligations on provincial governments to fund linguistic minority education. This may suit the premier of Quebec but not the ten or eleven French-speakers who live in Alberta. In practice, this dilemma is avoided by the standard Gallic practice of demanding respect for the linguistic rights of minorities in Anglophone areas while treating non-French-speakers in Quebec with the solicitous tenderness with which speakers of Corsican, Occitan and Breton are well familiar. Heads the (Parisian, or at least Montreal) Francophones win, tails they lose, as regards linguistic majoritarianism.

• You haven’t mentioned the problem of illogical representation of provinces (e.g., BC and Alberta having lower representation than NS and NB, despite having greater population sizes.

• Ed says:

Tom makes good points. Reducing the number of Canadian provinces to six at least addresses b), though not a) and c) and makes the existing arrangements much more workable.

Five would work even better, but the only way to get to five is to avoid breaking up Ontario, and with over a third of the Canadian population that province really needs to be broken into two parts (three parts would work even better). You could also break up Quebec, making Montreal island its own province, and have two Francophone provinces out of seven, but that would be likely vetoed by Quebec and more messy.

Incidentally, the US Senate even with all its strange parliamentary procedures would work much better simply by reducing the number of Senators. This could be done either by going to one Senator per state or by reducing the number of states. If you look at the history of the Senate it actually functioned fairly well as a legislative body in the nineteenth century when there were fewer Senators.

I do think as a rule that if you base representation on states or provinces, then what should be represented should be the governments of those states and provinces, as with the Bundestag and the nineteenth century US Senate, and not the people. Otherwise you just get a legislature with malapportioned electoral districts.

• If your strategy for making federalism work is drawing and re-drawing federal subject boundaries whenever it suits, you’re going to have a bad time.

• Tom Round says:

Why? India and Germany have redrawn State boundaries relatively frequently since 1949, and it seems to resolve more dissatisfaction than it creates. Especially remarkable given that most German Lander and Indian states were once independent kingdoms or principalities with histories a millennium (or even longer) older than the colonies that make up Canada, the US and Australia.

• Alan says:

I agree that state borders should not be set in stone. However, India, Mexico and Brazil all show a tendency for the number of states to increase over time. India is a little confusing because the present union territories were originally classified as Part C and D states. Abolishing and merging states is much rarer than creating new states.

I’d also contest the historicity of German and Indian dynastic states. Their borders were determined by dynastic ambition rather than a common culture or language (Tu, Austria felix, nube) and in any case some of them were surprisingly late in developing.

The kingdom of Prussia was only founded 62 years before the Province of Quebec (although that Quebec included Ontario) and 75 years before the colony of New South Wales. New France was founded in 1608. Newfoundland, founded in 1583 is considerably older than Prussia.

If you count the foundation of Russia from Ivan IV’s assumption of the title of tsar in 1533 then Russia is not that much older than Newfoundland. Some historians date the Russian empire to 1721 making it more recent than Prussia or Newfoundland. The borders of dynastic states fluctuated wildly over time. The Russian empire did not reach the Black Sea until 1764.

The States Reorganisation Act 1956 was aimed squarely at abolishing India’s vestigial dynastic borders in favour of linguistic areas.

• I should have been more specific. Redrawing federal subject boundaries with the aim of equalising their populations is a bad strategy. None of the examples you gave redrew borders with that aim in mind. As Alan points out India’s reorganisations have had the creation of new ethnic/linguistic-based states as their aim, and most recent creations have caused a more unequal distribution of population among the states.

How have the boundaries of German states been altered (not added) since the 1952 creation of Baden-Wurttemburg?

10. Dave Hutcheon says:

Alan, a list of areas and populations of Canadian ridings is at
(Elections Canada is given as the reference but the link gives only populations, not areas.)

To clarify my earlier suggestion that 3 ridings in Alberta might be among those remaining as SMC rather than be enlarged under MMP: the reason was not the populations of these ridings — they all were close to standard, just over 100,000. The reason was geography: their areas (105k, 109k and 147k sq-km) were the 10th, 11th and 12th largest of all provincial ridings.

• Alan says:

Thanks. I will play wth the numbers for a while. I took the Australian areas directly from the AEC site. I have to say I’m not at all enthusiastic about abandoning one vote one value for any reason.

Obviously, I think Tom’s threshold is far too high. I’m trying to find a more rational number. I am beginning to think either 125 k or 250 k looks good.

• Tom Round says:

I could live with 250,000 as the threshold. The analogous “huge district” threshold in Queensland is “only” 100,000 km2: http://www.austlii.edu.au/au/legis/qld/consol_act/ea1992103/s45.html My main concern would be that Australia, the US, India or a country of similar area not have more than,say, 2 or 3 “small-magnitude districts” whether one or two-seaters. Canada and Russia could have three or four of them.

• Alan says:

On a precious occasion when I mentioned tiered STV, 5 members in metros, 3 in provincial nd rural and 1 in remote districts, Henry remind us of the Tullymander and suggested a system of urban STV5s and rural STV3s (not what I’d actually proposed) could lead to electoral distortions.

Tom’s proposal for STV2s in remote districts has the reverse problem to Henry’s critique. Rather than one party sweeping the remote districts Tom would lock them permanently in one-each stasis in a sort of anti-Tullymander.

If we take the bar as 250 000, which I think is rational, we can examine the tendency for all those districts to go to one party more closely. Neither party has swept the remote districts since at least 1993 before that ended was often a labor seat and Lingiari has changed hands repeatedly. The Coalitions stranglehold in Durack, O’Connor, Kennedy and Maranoa is more a reflection of the wider politics of Queensland and Western Australia than anything happening in those particular seats.

On current figures the Coalition will win Durack, O’Connor, Maranoa and Parkes. Labor will win Lingiari, Grey remains too close to call. The Katteristas hold Kennedy. So that’s not quite a sweep. A better solution than being alarmed by the prospect of 7 STV1 districts in a house of 150 would be to accept that small assemblies are harder to distribute properly and increase the house to a more rational size.

11. Dave Hutcheon says:

I return to the question of electoral ratios in FPTP vs MMP vs STV, raised in the very first Comment and echoed later. The calculation of electoral ratio for MMP appears to exclude all members except those of the base tier. The flavour of MMP (dual candidacy required/permitted/required; closed/flexible/open list or best-loser) isn’t specified, but it affects very much the roles played by district and regional members.

Consider the following repurposing of 10 SMCs, each of electoral ratio 10:
1. STV, two 5-member districts
2. SNTV, 5 dual-member districts, elector marks X for 1 candidate, two candidates with the most votes are elected
3. MMP a la simplified Baden-Wurttemberg, 5 SMCs and 5 regional members, X for 1 candidate, regional members chosen from each party’s best losers
4. DMP, like #3 except choosing best-possible losers subject to the condition that there is exactly 1 regional member from each district
5. MMP, 6 SMCs and 4 regional members, 2 votes, closed list with 3 list members having lost in an SMC contest (I.e. New Zealand after the 2014 election)

What is the electoral ratio in each case? If different, what aspect of “MP usefulness” is affected? The incentives for an MP hoping for re-election look very similar in cases 2, 3 and 4.

• Alan says:

The electoral ratio is number of electors divided by the number of MPs.

I will not address SNTV because its defects are well known and it is not, for very good reasons, on the table.

If regional members are to be counted towards the electoral ratio than the 5-member MMP district will be twice the area of the 5 member STV districts. We are repeatedly told on this blog that STV is inappropriate in Canada because the districts (all other things being equal) are larger in area than the corresponding MMP 1 member district. Depending on the precise ratio of district and list MPs that is not always true and as you argue so persuasively, area on its own is not really a decisive issue.

If, as I would argue it should, STV is tiered so that smaller magnitudes are used in remote areas, then the argument fades away entirely.

Lastly, the test of an electoral system is the choices that it offers to the electors, not the chance that candidates have of getting elected.

As it happens I am just getting to the relevant chapters of The People’s Choice – Volume One: 1901 to 1927
Electoral politics in 20th century New South Wales. NSW is I think the largest area ever to be governed, if fairly briefly , by an STV assembly and it will be interesting to read how STV actually performed in a large state with tiered STV.

Second last note: there’s been some talk in the Canadian press about the time to set up a new system. I assume that Canada today has a significantly greater administrative capacity than NSW in 1918. The Parliamentary Elections (Amendment) Act 1918 was assented to on 18 Decem­ber 1918. The act altered the legislative assembly from single member FPTP districts to 5 and 3 member STV districts. A proviso to Section 13 read:

Provided that the first distribution under this Act shall be completed not later than the thirtieth day of June, one thousand nine hun­dred and nineteen.

On December 20, 1921 the Government of Sir George Fuller achieved a record – the shortest lived government in NSW history. It lasted 7 hours. On this day of three Governments, James Dooley’s Labor Cabinet resigned in the morning, after having lost a vote in the Legislative Assembly a week earlier. The Governor of NSW, Sir Walter Davidson, asked the Leader of the Opposition, Fuller, to form a Government, and this was duly sworn in. However, as Fuller did not have a majority in the Legislative Assembly he immediately met a deadlock once he went back to Parliament. Fuller then asked the Governor to call an election but as Dooley could demonstrate that he now had a majority in the House, the Governor declined, Fuller resigned and Dooley’s Ministry was sworn in again and lasted 4 more months.

12. Ed says:

This isn’t a federalism thread, but there is something of an iron law that creation or spinning off of new states is something that happens fairly often, while consolidations of small states into a larger state is effectively impossible. One commentator mentioned the merger of Baden and Wuerttemberg. This and the merger of Nord Rhein and Westphalen are the only examples I can think of off hand, both happening in a postwar era where all sorts of institutions were being recast.

Voters don’t like large states because their votes become devalued in a larger electorate, and politicians like new small states because it means additional jobs to hold or hand out. There is also more opportunity for gerrymandering to enable short term political outcomes. This tendency has been operable throughout US history as well.

Petty states cause bureaucracies to proliferate, cause coordination problems, and create democratic deficits if the polity has any institutions were representation is on a state-by-state basis instead of according to population. These issues can be worked around by carefully drawing boundaries and institutions to minimize the need to co-ordinate between state governments, and avoiding representation on a state-by-state basis. Btw, this is the case with India and with India if anything the problem is that some states, such as Uttar Pradesh, are too populated and should be broken up. Otherwise, there has to be periodic re-sets, as happened with France in 1792, Germany in 1945, and South Africa in the 1990s.

States having equal populations mis-characterizes my argument. The rule should be that the largest state have no more than 5x the population of the smallest state, to avoid proliferation of petty states and over-large states. Populations could shift around quite a bit and not violate this range. Where that is impossible for historical and/ or cultural reasons, schemes of autonomous territories or regions, Puerto Rico style commonwealths, or devolution are usually more appropriate.

To bring this back on topic, federalism in Canada is actually much more unbalanced than in the US, but isn’t as much of a problem and doesn’t get the attention, mainly because of the difference in the structure and functions of the Senates in both countries, and in Canada only one city of any size straddles state boundaries, and there are mitigating circumstances in that case. So its not a big problem, but does contribute to imbalances in House of Commons referendums, complicates electoral reform, and comes up sometimes when the provincial premiers have to be consulted on some issue.

• Alan says:

None of those cases were periodic resets. All of them were one-offs associated with regime change. The French departments were actually carefully structured to ensure that they would cut across traditional provinces and be hard to defend against military intervention by the central government. The German states of 1945 were largely motivated by the breakup of Prussia. The South African provinces were an attempt to recognise linguistic/cultural areas that had been ignored by the minority regime.

I don’t think that state borders should be set as hard as they are in Australia, Canada and the US, but I don’t think trying to redistribute them on a population basis at regular intervals is viable.

• Rob says:

Most countries that are federal, state boundaries and the states themselves are set in stone, they are never altered or abolished. Seems odd to have a provision that say states can merge if they want to, but what state would want to especially in a federation that gives each states equal representation. If two states merge, they are going to get half representation in the upper house. Maybe states would be more likely to merge if they got to keep their representation or get more in the upper house. One could have a federation that requires redrawing states of equal population sizes, but that would have to be built into a constitution from the get go, not something that can be added as an amendment.

It is more likely that states within a Federation want to break apart except that some Federations require that if a region of a state wants to leave, then everyone in the state has a veto over that part that wants to leave especially if a referendum is used. It is surprising why can’t a country use a special majority like 2/3rds or 3/5rds to create and merge states, but simple majority to make minor adjustments. It may be wise to require a simple majority and an election inbetween and the next parliament ratifies the change. Also require in the Constitution that the Federation has a bare minium number states, so that the central government can’t use a special majority to make the country de-facto unitary.

13. There has been discussion about the phrase “adding an element of proportionality to Canada’s electoral system.”

It should be noted that the Report of the Law Commission of Canada (2004) stated:
“Recommendation 1

• Alan says:

No matter how illustrious the source of the phrase, it is not an accurate description of MMP, a fully proportional system. No-one who witnessed the kind of material put out by No2AV could possibly imagine that ‘But that’s what the law commission said in 2004’ is going to fly as an explanation or indeed as anything more than an invitation to No2AV style nonsense.

14. A question. (I will post it in this thread for convenience.) Is it true that Canada has had more expert and citizen processes on electoral reform than any almost other country in the world? In 2001-4 the Law Commission of Canada conducted a three-year study on electoral reform. In 2002-3 Quebec’s Estates General on the Reform of Democratic Institutions (the Béland Commission) visited 20 towns in Quebec and held 27 public hearings. The British Columbia Citizens’ Assembly on Electoral Reform spent nearly one year deliberating on electoral systems. In 2006 a Select Committee of the Quebec National Assembly held public consultations in 16 cities across Quebec when 379 groups and individuals made presentations. The Ontario Citizens’ Assembly on Electoral Reform spent most of a year in 2006-7 on public consultations and deliberations. And I am skipping over four other processes. Now, this year, after three parties won a mandate to end First Past The Post and “Make Every Vote Count,” hundreds of MPs have held town halls, the Special Committee has traveled the country, the Minister has done her own parallel tour, and televised hearings will resume for another two weeks soon. Can we say we have consulted and studied PR to death in comparison to other countries?

• Alan says:

In Australia, the federal parliament has had a joint standing committee on electoral matters since 1983. After every general election there is an automatic review of the electoral system after each general election and particular matters can be referred by the minister or either house. While not as wide-ranging as the Canadian inquiries,this processes generated very significant reforms,in particular the adoption of ticket voting or the senate and then the its abolition earlier this year.

There have been a plethora of expert and parliamentary inquiries at the state and territory level, most notably the ACT inquiry which recommended a move from the Modified D’Hondt system to Hare-Clark. The ACT also gives us an unusual example of an electoral reform referendum that actually passed. Since 1983 Australian states and territories have experimented with list systems, modified list systems, and Hare-Clark. About the only system never tried here is MMP.

Aotearoa had a very wide-ranging royal commission before the adoption of MPP and a second before the recent referendum that rejected attempts to abolish MMP.

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