It is good to see the undersized nature of the US House of Representatives get attention in the New York Times‘s Economix blog. The author is Bruce Bartlett, who “held senior policy roles in the Reagan and George H.W. Bush administrations and served on the staffs of Representatives Jack Kemp and Ron Paul”.
Bartlett notes that,
according to the Inter-Parliamentary Union, the House of Representatives is on the very high side of population per representative at 729,000. The population per member in the lower house of other major countries is considerably smaller: Britain and Italy, 97,000; Canada and France, 114,000; Germany, 135,000; Australia, 147,000; and Japan, 265,000.
The strongest empirical relationship of which I am aware between population size and assembly size is the cube root law. Backed by a theoretical model, it was originally proposed by Rein Taagepera in the 1970s. A nation’s assembly tends to be about the cube root of its population, as shown in this graph.*
Note the flat line for the USA, indicating lack of increase in House size, since the population was less than a third what it is today. This recent static period is in contrast to earlier times, depicted by the zig-zag black line, in which the USA regularly adjusted House size, keeping it reasonably close to the cube-root expectation.
At only about two thirds of the cube-root value of the population (as of 2010 census), the current US House is indeed one of the world’s most undersized. However, there are some even more deviant cases. Taking actual size over expected size (from cube root) , the USA has the seventh most undersized first or sole chamber among thirty-one democracies in my comparison set. The seven are:
As expected, the mean ratio for the thirty-one countries is very close to one (0.992, with a standard deviation of .37). The five most oversized, all greater than 1.4, are France, Germany, UK (at 1.67), Sweden, and Hungary. (The latter was at a whopping 1.80, but has since sharply reduced its assembly size.) Spain, Denmark, Switzerland, Portugal, and Mexico all get the cube root prize for having assembly sizes from .975 to 1.03 of the expectation.
One thing I did not know is that an amendment to the original US constitution was proposed by Madison. According to Bartlett, it read:
After the first enumeration required by the first article of the Constitution, there shall be one representative for every 30,000, until the number shall amount to 100, after which the proportion shall be so regulated by Congress, that there shall be not less than 100 representatives, nor less than one representative for every 40,000 persons, until the number of representatives shall amount to 200; after which the proportion shall be so regulated by Congress, that there shall not be less than 200 representatives, nor more than one representative for every 50,000 persons.
Obviously, Madison’s formula would have run into some excessive size issues over time. And Bartlett does not suggest how much the House should be increased, only noting that its ratio of one Representative for very 729,000 people is excessive. On the other hand, Madison’s ratio of one per 50,000 would produce an absurdly large House! It is just the need to balance the citizen-representative ratio with the need for representatives to be able to communicate effectively with one another that Taagepera devised the model of the cube root, which as we have seen, fits actual legislatures very well.
The cube root rule says the USA “should have” a House of around 660 members today, which would remain a workable size. (If the USA and UK swapped houses, each would be at just about the “right” size!) Even an increase to just 530 would put it within about 80% of the cube root.
As Bartlett notes, at some point the US House will be in violation of the principle of one person, one vote (due to the mandatory representative for each state, no matter how small). However, a case filed in 2009 went nowhere.
* Each country is plotted according to its population, P (in millions), and the size, S, of its assembly. In addition, the size of the US House is plotted against US population at each decennial census from 1830 to 2010.
The solid diagonal line corresponds to the “cube root rule”: S=P^(1/3).
The dashed lines correspond to the cube root of twice or half the actual population, i.e. S=(2P)^(1/3) and S=(.5P)^(1/3).
A variant of the graph will be included in Steven L. Taylor, Matthew S. Shugart, Arend Lijphart, and Bernard Grofman, A Different Democracy (Yale University Press).
An even earlier version of the graph was posted here at F&V in 2005.
Bartlett previously addressed the small size of many US state legislatures, especially California.
“Madison’s formula would have run into some excessive size issues over time.” Actually, it wouldn’t – if you read carefully, you can see that the last clause says that once the House reaches 200 members through population growth, the minimum is 200 representatives, with the ‘one representative for every 50,000 persons’ only settng a MAXIMUM.
This amendment, which was proposed along with the Bill of Rights amendments, is actually still before State legislatures, but it would make no difference if passed, as the current 435 falls between the 200 and (more than) 6,000 limits the amendment sets.
I’d vote for the cube root rule with a proviso that one rounds off to the nearest number ending in either 5 or 9. (This would make redistricting less frequent as the size of the chamber wouldn’t change as quickly. Eg, if the population is between, say, 8,365,427 and 8,869,742 – a 5.7% variation – the assembly will still have 205 seats, not 199 or 209).
Unfortunately the idea that “more legislators = bigger government, more regulation, more taxation and spending” is powerfully entrenched among people who have only thought superficially about the issue. Increasing the number of legislators is a highly visible, symbolic issue so opposition is easily mobilised. Increasing the number of permanent civil servants – who cannot be voted out – or increasing their perks, costs the public fisc far more (without the same benefits for democratic oversight) but that will never get the talkback phones running hot the way “No More Politicians!” does.
The complication for the US is that increasing the House will make the Electoral College align more closely with population (not necessarily with the popular votes cast). I would imagine the GOP would fight tooth and nail against this. There is no necessary reason why the number of Electors still needs to match each State’s total of Senators and Representatives. An amendment might be proposed fixing the ratio between per-Statum and per-capita Electors in perpetuity, rather than leaving it open to radical change if Congress resizes the House. For example, “two Electors per State, plus an additional zero, one or more Electors based on population” with the number of population-based seats being constitutionally fixed at, say, eight times the number of States, plus 39. (This would freeze the current ratio while also ensuring an odd number. DC’s should be based solely on population to avoid the anomaly that Congress could retro-cede everything bar the White House to Virgina and Maryland and thus leave Chris Christie and family constitutionally authorized to appoint three Electors on their own… the ultimate rotten borough).
(I also think that a State with population 100,000 to 499,999 should have only one Senator, and a State under 100,000 should not have any Senators of its own, but instead should be combined with the least populous adjoining State for federal Senate elections… the same should apply for House elections to a State under 20,000 population: only those over 20,000 should have a minimum one seat… I’m sure Americans are waiting breathlessly for my recommendations on these matters… These minimum thresholds shouldn’t catch any existing State but would guard against the outside risk that, say, global waring might leave Hawaii with ten inhabitants and three federal seats by 2176…)
I think expanding the House would be a seriously easy argument. The Republicans would certainly fight it tooth and nail and lay themselves open to a series of devastating counter-arguments, the best of which would be ‘We are only doing what the Founders intended’ and “Gosh this imbalances the electoral college maybe we should look at that as well’. One could also point out that in a cube root congress several small states would gain representatives.
While I do expect arguments from the right like what Alan mentions, it is at least helpful that someone who worked for two right-wing Rons has made the case. I also had a link some time back from a conservative blogger making the case. So at least it might be harder to dismiss as another one of those zany left-wing conspiracies against the republic as our forefathers knew it and ordained it to be for all time.
Do people support increasing the size of legislative bodies? Don’t most people want fewer politicians? I do agree that there should at least be a Goldilocks size of assembly bodies, not too big and not too small. If only California and New Hampshire switched places in their lower house sizes, then it would all right? What is the largest size that a legislative body can be? Is 800 members for the lower house, the largest sized for an assembly for a huge country of perhaps 1 billion? What is the smallest size that a legislative body can be?
Increasing the California state assembly to 12,000 is what John H Cox wants to do, seem a bit excessive. Perhaps his proposal could be designed with the idea of having regional assemblies with the state.
What would the cube root size of California state assembly should be?
Rob’s questions of the politics of assembly size are very interesting to me, and something I am planning to investigate further in the near future. (Caveat: I am planning to investigate a lot of things in the “near future”.)
Just a few things to note. First, it is important to recognize that Taagepera’s model is “politics free”. That is, it is based on a physics-like principle of balancing competing communication demands on a legislator, with the represented and with other representatives. It does not take into account any other features of a political system (not even whether it is democratic or not, as long as it has an elected legislature with some meaningful functions). This makes it all the more remarkable that it usually works empirically! However, it also makes for a lot of room for strictly political explanations for why some countries are below (or above) the cube-root expectation.
I believe state/provincial assemblies in federal systems tend to be systematically undersized (New Hampshire notwithstanding). There may be reasons for that, and it is worth noting that Taagepera’s model explicitly refers to size of national assemblies and makes no direct claims about sub-national assemblies (or supra-national, for that matter). In fact, it could be that federalism also is a systematic reason for undersizing national assemblies. That is, if different levels of a federal government communicate with citizens on different issues, then there may be a smaller “effective” population that the assembly needs to balance representing with its own internal communication capacity.
I should also add, in response to Alan’s comment, that I have no idea whether assembly size is related to ability to check the executive. Again, this is an important question, but not something that is within the parameters of the mathematical model that yields the cube root. And there seems to be no obvious empirical relationship to strong or weak executives (however we might conceptualize that murky concept).
It is also quite likely that the strength of political parties as coordinating mechanisms within the assembly may affect optimal size. Stronger parties presumably ease intra-assembly communication. Again, this is completely outside the model, but a prime area for further research.
The question of whether there is some absolute size that is too large is also one I have thought about, but I have no answer. Not counting the European Parliament, no democratic country’s assembly has reached 700, as far as I know. We have a few cases of mid-600s. Obviously, as these countries with large assemblies continue to grow, they could hit a point where the cube-root would be “too large”. But this is also outside the model as it currently stands. Would I recommend that India increase the Lok Sabha to over 1000 even now? Probably not. And here again, considerations of federalism enter in, conveniently given that the largest countries tend to be federal and some of those that are not (e.g. UK) may be in the process of becoming relatively so.
Could the cube root be modified with federalism, and the assumption that there are subordinant legislative bodies? Also should the cube root be applied together or separately if their is a upper house and almost all federations have upper houses? Australia’s parliament is 150 house members + 76 senators = 226 members, so is the cube root applied to the lower house number, senate number, or the combined parliament number?
Most people wanting fewer politicians is one of those happy assumptions that distorts this debate. See above in this thread where we note that total government size has no relationship to assembly size, but assembly size has a very direct relationship to the assembly’s ability to check the executive. Reducing assembly size is a bit like fairy floss, looks like its worth eating but don’t rely on it for any nutrition.
A Madisonian does not advocate ever-increasing executive and bureaucratic power. It follows that small assemblies are deeply unMadisonian and arguably deeply unAmerican.
Alan: it seems somewhat silly to me to adhere so strictly to the cube root rule, as it is ultimately also arbitrary and based on the general trend among assemblies.
” assembly size has a very direct relationship to the assembly’s ability to check the executive.”
And what exactly is that relationship? I don’t think simply ‘the more legislators, more ability to check’ covers it, as there may be a maximum beyond which a larger assembly actually hampers that ability. Actually, that begs the question, what is the effect of having an assembly in excess of the cube root rule? When is an assembly too large, either in total or in relationship to population?
Rob: It’s difficult to answer such broad questions as ‘what do voters want with regard to x?’ As finding an answer needs a lot more context. If we are to take the trends in other legislatures’ sizes and their relationship to their country’s populations, then yes, it would make sense for NH’s 424-seat legislature to switch with California’s 120-seat one. But I doubt whether voters in either state would agree to such a switch, as upsizing California’s legislature more than threefold may be a difficult sell, whereas in NH, as I understand it, they are reasonably satisfied with a large House which makes the state’s politics more open. As to a comparison between different states’ legislature sizes and their ‘ideal’ ones according to the cube-root rule, I direct you to frustratedprogressive.blogspot.nl/2011/10/rightsizing-state-legislatures.html
First bit to Tom Round, second bit to Alan, of course.
Ummm, a rule cannot be both arbitrary and based on the general trend among assemblies.*
However, and more seriously, a good start on the more members/better oversight argument is the recent report by the group of experts appointed to review the size of the ACT legislative assembly:
*When I say something like that one of my friends, a passionate admirer of Yes, Minister generally says: ‘Thank you, Bernard’.
Right, the cube root rule is not arbitrary. It is backed by a logical mathematical model (see Taagepera and Shugart, 1989, or Taagepera’s original article, 1972*), and confirmed by the general empirical pattern among world assemblies from different time periods. In Taagepera and Shugart, see pp. 173-183.
* Rein Taagepera, “The Size of National Assemblies,” Social Science Research 1:385-401.
Rein Taagepera and Matthew Soberg Shugart, Seats and Votes: The Effects and Determinants of Electoral Systems (Yale University Press).
The hardback of Seats and Votes: The Effects and Determinants of Electoral Systems is available from Amazon new for a mere US$8209.13.
It is true that Bartlett worked for two right-wing Rons (among others). He is, unfortunately, considered an apostate in those circles these days. Still, it is good to see the topic being raised in the mainstream press.
Amazing how many apostates there are from those circles.
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There is some evidence from several countries across the world where having an legislature with an effective size of one legislator does limit the amount of political dysfunction. It also limits the amount of pork barrel spending, though that may or may not be related.
Speaking more seriously, the legislator needs to be large enough to allow for effective representation. I can’t say what that number is and that number may change depending on the legislative system.
Mark, I do not understand, “legislature with an effective size of one legislator”.
As for whether we can say what is the correct number, I still can’t improve on Taagepera’s cube root. And even though presumably few practical politicians who have decided on assembly sizes for various countries have been aware of the cube root rule, time and again they choose sizes in reasonable approximation to it.
Sorry, I was making a joke about dictatorships. The dictator is the only “legislator” because the law is whatever he says it is. In more than a few countries, dictators send money to their region/ethnic group; often in the same manner as pork barrel spending in more democratic countries.: too keep the most important people (the local constituents/the dictator’s people) happy.
I am generally in favor of the cubed root rule myself, but I do remain open to the possibility of other systems working as well. In a system with single member districts, I would argue for at least a cubed root number of representatives. On the other hand, in a strictly proportional system a smaller number may work to allow for better collegiality and thus interparty cooperation and also to serve as a de facto threshold. In other words, I would feel more comfortable if a party misses out on one seat in a 20 seat legislature than for the same party to be arbitrarily stripped of 20 seats in a 500 seat legislature because it failed to reach 5%.
Sorry, arbitrary is clearly not the word I’m looking for. What I meant was that I’m not sure why an existing pattern should absolutely dictate legislature size without any room for any other considerations. I don’t see why the rule should be very strict, a 10% band seems reasonable to me. But I’m also wondering as to why it would be so good to follow that particular rule anyway – why should an existing pattern necessarily be the desirable one? But I suspect answers to such questions are in the papers MSS pointed out, which I will certainly read.
Of course, JD. That is why the graph actually shows the cube root of twice and half the population. By your (very reasonable) 10% band, the US House is still well outside (the deviation is about a third of the predicted value). Nonetheless, to be clear, the logical model has a point prediction. That does not mean that we expect no other factors to matter, or that any deviation from the cube root means there is something wrong with the country. Yet it is highly noteworthy that for these 31 countries, the mean is almost exactly the cube root (and similar conformity, on average, has been found on other, larger, data samples, including from different time period). For countries that are well off from the mean, there might be a political explanation (perhaps one of those I suggested in an earlier comment) that is outside the model, or it might mean that the model itself should be adjusted to take account of some other factor. However, I would be reluctant to complicate a very sparse model that performs so well as this one does. After all, relative to other “laws” of social science (e.g. Duverger’s), this one shows remarkably little scatter around the trend line.
There is a negative feedback between expanding the size of a legislature, so you shrink the legislator to constituents ratio, and how effective the legislature is (particularly in establishing some sort of control over the executive) and how effective an individual backbench legislator is.
This can actually be seen in the upper US chamber, the Senate, where the same rules of parliamentary debate that worked OK with 30 Senators in the 1790s cause it to be something of a joke with 100 Senators in the 2010s. Of course the House functions better with 435 members, but at the expense of giving the minority and backbenchers little includence.
A better argument for increasing the size of the House is that 435 members is still on the low side for large countries, where the standard seems to be around 600. They could make it an even 500, for example.
Though this is beyond the scope of this blog, the explosive US population growth that led to 729,000 people per district will probably reverse in the next twenty years. It actually has been predicted to reverse for some lifetime, but immigration (and large families of immigrants) have kept the US birthrate well ahead of developed nations.
Once the number of members per district gets to be too large for effective representation, I think a better solution is to strengthen sub-national (provincial and local bodies). However, the historical trend has been the reverse of this. Arguably, enough gerrymandering has taken place in US history with state boundaries -something not acknowledged as much as it should be in discussions of federalism- to make devolution effectively impossible.
Surely the declining effectiveness of a body that maintains the same rules as it grows in numbers is an argument for new rules rather than staying the same size? The UK house of commons, at 650 MPs, displays none of the confected paralysis found in the US senate. If a deliberative assembly 6 and a half times the size of the US senate can function in an effective manner, then the cause of paralysis has to be something other than the ‘large’ size of the US senate.
This slightly misunderstand my point.
My point was that the United States Senate with the same super-majority rules functioned well, or at least better than it present, in the eighteenth and nineteenth century when it was a smaller body. In fact for a long time all the Senators had to agree to cut off debate. Later it was lowered to two thirds, than 60%. The body became more dysfunctional despite the fact that what rules changes occurred were made in the direction of making it more efficient. Enlarging a legislative body makes it less effective unless the rules are changed to account for the increase in size.
This is not germane to the point, but many of the problems with the U.S. Senate could be solved by simply cutting the number of Senators elected per state down to one. And with Senate elections staggered, its hard to argue that this would increase the number of constituents per Senator.
Ed, your points here are mostly on the very same ground as the theory behind the cube root itself. It is all about the need to balance communication between representative and constituents with communication among representatives. Of course, a great deal of the internal procedures of any legislative body is all about information flow, hence internal communication.
Second chambers do not fall within the cube root to the extent that their function is not representing the population, but even the Senate has modified its procedures many times to account for the challenges of increased size and complexity (as Ed’s subsequent comment notes). Notwithstanding the changes, the US Senate is still quite an outlier due to its super-majority requirements.
Equally, reducing legislative body without changing its rules to account for the reduction in size makes it else effective. I can see an argument in relation to making the rules of procedure appropriate tot he size of an assembly, I cannot see ana regiment in relation tot eh size of an assembly.
As noted in the ACT report and the similar Tasmanian analysis, very small legislative bodies have trouble performing their functions. Maintaining a robust committee system becomes a challenge, for example, when you halve the number of legislators available to attend committees.
The total level of expertise available to the assembly is going to decline when you reduce numbers. In the US senate, and to a lesser extent the Australian senate, senators tend to take on specialised interests so that it becomes known that Senator X is an expert on cultural policy, or administrative reform or whatever. This si an important, if informal, check not her executive’s informational dominance. Halving the number of subject areas that senators can make their own is not going strengthen legislative scrutiny and oversight.
I know I’m dreaming, but I’d expand the size of the US Senate – to 250 senators. Each state would have five, elected by STV. They would have eight-year terms, with half the states going to the polls at each four-year presidential election.
House terms would be increased to four years, and the House expanded to 500 members. I’d also institute a double dissolution/joint sitting provision to resolve deadlocks (including the overriding of presidential vetoes), with those elected at such double dissolution election to serve the remainder of the four- or eight-year term only, in order to bring election timetable back into order.
People in Australia – well, the losers – often complain about how hard it is to change the Australian Constitution. (That’s because most of the changes put up are bad ones.) I think the changes I propose have no chance in the US, even though they would make the Senate more representative of each state, break deadlocks and reduce the hyper-electioneering of the nation.
Actually, there is currently an even more undersized one: Taiwan, which according to the cube-root rule should have 286 MPs but whose Legislative Yuan has a mere 113, 0.395 of expected. This is only since 2008 – before that Taiwan had 225 MPs or 0.787 of expected.
Good call, JD. Taiwan is not in the list of cases for the book, which is why it is not in the graph above, but that’s no reason not to include it in the discussion.
(sort of odd that you are an official contributor to the blog, yet the software put your comment in the moderation queue.)
No doubt others have spotted this (minor but elegant advantage) before me, but I just realised that if a country uses the cube root rule to fix the size of its lower house, then the quota per representative will be (approximately) the square of the number of assembly members. Eg, if a nation has 237 seats in its Council of Delegates because its population is 13,312,053 or thereabouts, then the population quota per seat will be around 56,169, ie 237 squared.
I also realised that it’s even easier to apply the Huntington-Hill method of equal proportions as a quota-and-round-off method than as a highest-averages method. You divide a State’s population by the quota to get a whole number plus fraction, and you round up the fraction if, and only if, whole-number-plus-fraction squared exceeds whole-number-times-the -number-above-it. So a State with, say, 6.4278 quotas of population gets only 6 seats because 6.4278 times 6.4278 (= 41.3166) is less than 6 times 7 (42). But a State with, say, 13.5851 quotas of population gets 14 seats because 13.5851 squared (= 184.5549) exceeds 13 times 14 (182). The “threshold” for rounding up a remainder under Huntington-Hill is in the vicinity of 4/9 of a full quota.
(You would have to set a firm rule in advance as to how many decimal places to round off to, otherwise rounding error could change the result).
Again, I’m sure someone would have spotted this before but I haven’t seen either point in the literature before.
Tom, no, I do not think that is in the literature. I can say that Rein Taagepera and I discussed exactly that point, and considered including something about it in our chapter using district-level data. But for various reasons, we decided not to do so. It could be worth following up on.
Has there been any study of a possible correlation between size of base-tier districts and deviation from the cube root law? In British Columbia we will have a referendum this year on changing from FPTP to PR. Such a change (almost) certainly would require some increase in district sizes, given strong public push-back in the past against proposals to increase the number of MLAs.
In BC the district size issue concerns area, rather than population. Approximately 85% of the province, much of it difficult terrain, is occupied by 15% of the voters; Stikine district is only slightly smaller than Great Britain. We have “resolved” the tension between district size and assembly size by mal-apportionment: the 2014 amendment of the Electoral Boundaries Commission Act required the boundary commissioners to allocate 20% of the seats to that 15% of the population.
Changing the electoral system from “one person, one vote” to “one person, one effective vote” must increase that tension. Does a new electoral system that changes the average size of base-tier districts also tend to see a change in the assembly size?
“Such a change (almost) certainly would require some increase in district sizes, given strong public push-back in the past against proposals to increase the number of MLAs.”
Given that a big part of the “no” vote last time was a push-back against increase in district sizes… You’re seriously going to need to find some kind of compromise between the two, if PR is to happen.
I suppose there’s no real study–if we mean empirical analysis–of such matters because there are so few cases. But obviously in New Zealand they increased the size of the assembly at the same time as they adopted a list tier to create the MMP system. The result was obviously still an increase in the area covered by each district, as they went from around 100 districts to 60-some. But had the assembly size remained fixed, the tradeoff between district area and proportionality would have been more stark. You would have had only 50-some districts or else a much smaller list tier.
As JD says, this is really a tradeoff BC is going to have to face.
The alternative is, of course, to designate some part of the province as “not reformable” and keep the existing single-seat districts (and malapportionment) for the rugged rural areas, while combining districts in the more urbanized areas to allow multi-seat districts. This would be a variant of the “urban rural” design that was discussed at the federal level in 2015-16. It does not avoid the tradeoff (it would be less proportional than having multi-seat districts everywhere, or an MMP system), but maybe it is more politically palatable.
In addition to New Zealand, we have the case of Prince Edward Island where assembly size decreased when 16 dual-member districts were converted to 27 smaller single-member districts. On the other hand, Italy’s current system has 630 in the Chamber of Deputies, of whom 232 are uninominal — exactly the same assembly size as in 1993 when there were 475 base-tier districts.
I agree that the best course in BC probably would be to leave some districts as SMD and live with the malapportionment while instituting PR in the rest of the province. As the French have it: on avance par les petits pas — one advances by small steps.
In BC, turning the eight northern seats into five local seats and three regional top-up seats is not a big trade-off in area. What was rejected in 2009 was turning them into three multi-member STV districts (two 3s and a 2), too large to be local but too small to elect a Green, so, few were cheering for it. If BC had MMP regions with an average of 12 MLAs (like Wales), the 24 in the Interior and North could be 8 and 16, or 10 (putting Cariboo in the North) and 14, or 9 (putting Cariboo North in the North) and 15. So there is no need to add MLAs.
Granted, an increase of 50% or 60% in district areas for MMP is less than the 100% or 200% increase proposed for STV in the North. However, another basis for comparison is the 2015 adjustment of BC electoral boundaries: neither Liberal nor NDP legislators dared suggest even a small step towards the ~30% increase in district areas of North and Interior that would have given fair apportionment (absent any increase in the total number of MLAs). Could the NDP say in 2018 that a 50-60% increase was now OK?
Yes, because the three regional MLAs would still be from the North. You have a local MLA who will champion your community, and three competing regional MLAs. One of the four will likely include one whose views best reflect your values, someone you helped elect in your local district or at least in the North. The best of both worlds.
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