California statewide election vote totals

All of the offices elected statewide in California now have only two candidates in the November election, due to the “top two” runoff system. However, because the first round is no longer a primary in which various parties can pick nominees for the November ballot, the contests can feature two candidates of the same party or one or more independents instead of candidates of one or the other major party. (This is also true of district contests like US House and state legislative seats.)

Thus I thought I would exploit these features–constant number of candidates, but variable affiliations–to probe how a party’s failure to place a candidate in the top two affects voting. I am not claiming any causality or doing any subtle analysis here. Just blunt comparisons of statewide totals, which are suggestive.

Two contests, including Lt. Governor and US Senator, featured two Democrats. One featured a Democrat and a non-party candidate. One contest features two non-party candidates, because the state constitution mandates that the Superintendent of Public Instruction (SPI) is a non-partisan post. (This is the one office that could be decided in the June first round; it is a straightforward majority-runoff system.)

The bottom data row averages the Democratic and Republican votes across the five races that were Democrat vs. Republican. The right-most data column indicates how the votes cast compare to the governor’s race: a ratio of the vote total in a given race over votes cast for governor. Not surprisingly, governor drew the highest total.

We can see that the average Democrat won just over 5.1 million votes and the average Republican 3.1 million, in contests that had one and only one candidate of each of these two parties. Moreover, all the contests that were D:R straight fights had roughly 98% of the votes of the governor’s race.

On the other hand, if there were two Democrats, the total was under 90% of the governor total (83% for the Lt.Gov and 88.5% for the US Senate). This obviously is partly because many Republican-leaning voters simply skipped the intra-party Democratic contest. (The SPI race, where I believe both candidates were actually Democrats, has a similar ratio.) Nonetheless, that is not the entire story, as the total for the two Democrats in both these races is a lot more than the average single Democrat, at the same time as the leading Democrat did considerably worse than the average single Democrat. In other words, at the same time as Democrats split their own votes across their two candidates, clearly the candidates also picked up some Republican votes. This would be really interesting to investigate on a more granular basis.

Finally, the Insurance Commissioner race is notable. The “no party” candidate in the race is actually a Republican. In fact, he served under that party affiliation in the office before. But candidates choose, before the June first round, what party “preference” to indicate on the ballot (from the approved list), or whether to indicate no party preference. In this contest, the Democrat got far below the average for his party. It could be that there are Democratic-leaning voters who remember Poizner and think he did a good job, although he left the office in 2011, so I have some doubts. Alternatively, it could be that not running under the party label is a good strategy for a Republican in this state. He did not win, but he did get 49.0% of the votes, running around half a million votes ahead of the Republican gubernatorial candidate and around 700k ahead of the average Republican on the statewide ballot. Maybe other candidates of the weaker party in the race will hide their party label in the future, given the current electoral system makes it possible to be one of the top two without a stated party preference.

NYT endorses a larger House, with STV

Something I never thought I would see: The editorial board of one of the most important newspapers in the United States has published two separate editorials, one endorsing an increase in the size of the House of Representatives (suggesting 593 seats) and another endorsing the single transferable vote (STV) form of proportional representation for the House.

It is very exciting that the New York Times has printed these editorials promoting significant institutional reforms that would vastly improve the representativeness of the US House of Representatives.

The first is an idea originally proposed around 50 years ago by my graduate mentor and frequent coauthor, Rein Taagepera, based on his scientific research that resulted in the cube root law of assembly size. The NYT applies this rather oddly to both chambers, then subtracts 100 from the cube root result. But this is not something I will quibble with. Even an increase to 550 or 500 would be well worth doing, while going to almost 700 is likely too much, the cube root notwithstanding.

The second idea goes back to the 19th century (see Thomas Hare and Henry R. Droop) but is as fresh and valid an idea today as it was then. The NYT refers to it as “ranked choice voting in multimember districts” and I have no problem whatsoever with that branding. In fact, I think it is smart.

Both ideas could be adopted separately, but reinforce each other if done jointly.

They are not radical reforms, and they are not partisan reforms (even though we all know that one party will resist them tooth and nail and the other isn’t exactly going to jump on them any time soon). They are sensible reforms that would bring US democracy into the 21st century, or at least into the 20th.

And, yes, we need to reform the Senate and presidential elections, too. But those are other conversations…

Is the effective number of parties rising over time?

I was recently having a conversation with another political scientist who showed me a graph that suggests the effective number of vote-earning parties in established democracies has been increasing over time. I was skeptical that it was, relative to baseline. Of course, if we do not have a baseline, we do not really know what is causing any such possible increase. The baseline should be the Seat Product Model, which tells us what we should expect the effective number of parties to be, given the electoral system. When we do the baseline, the increase over time remains, but is not significant.

Here is a graph with no baseline. It is just the the effective number of vote-earning parties (NV) in Western Europe (most countries–see below for notes on coverage). The scatterplot marks elections by a three-letter abbreviation for each country. The x-axis is years since 1945, the earliest election year in the dataset. The graph’s y-axis is unlogged, but the plotted regression curve and 95% confidence intervals are based on a logged NV.

(The regression is a GLS with random effects by country. It would not be much different if OLS were used.)

There does seem to be an increase over time. The regression estimates NV averaging around 3.42 in 1945 and around 4.60 in 2011. The 95% confidence intervals on those estimates are 2.96 – 3.96 and 3.98 – 5.32, respectively. So, yes, the vote is getting more fragmented over time in Western Europe!

But hold on a moment. We should look at the fragmentation relative to baseline. As shown in Votes from Seats, the seat product (mean district magnitude times assembly size; in a two-tier system, also taking into account the size of the compensatory tier) explains around 60% of the variance in key party-system outcomes, including the effective number of parties. It would be useful to know if the Seat Product Model (SPM) is on its way to being unable to account for party-system fragmentation if current trends continue. It would be useful to know if recent fragmentation is part of that other 40% (i.e., the amount of variance in NV that the SPM can’t account for). That is, are we witnessing some inexorable fragmentation of party systems that is resulting from the breakdown of existing party alignments in the electorate, and which electoral systems have begun to lose their ability to constrain? Should Western European countries go so far as to reduce their proportionality, in order to contain fragmenting trends?

So the next data visualization asks the question from a different perspective. Is the ratio of observed fragmentation to the SPM prediction increasing over time? We can take any given election’s actual NV, divided by the SPM-predicted NV to arrive at a ratio, which is equal to 1.00 for any election in which the result exactly matches the predicted value. (In other words, if R2=100%, all elections would have a ratio of 1.00.)

Here it is, for NV, again with the estimates from a GLS regression and the 95% intervals. In the regression, the ratio is entered as its decimal log, but the graph uses the underlying values for ease of interpretation.

What we see is indeed an increase (note the slope of the dashed line). However, the reference line at 1.00 (the log of which is, of course, zero) is easily within the 95% confidence interval of the regression throughout the six and a half decades of the data series. The regression estimates a ratio of actual to SPM of 0.911 in 1945 and 1.054 in 2011. The 95% confidence intervals are 0.782 – 1.062 and 0.905 – 1.228, respectively.

In other words, the increase is not statistically significant. There may in fact be an increase, which is to say that something in that other 40% is driving, over time, the SPM to be less successful at predicting the fragmentation of the vote. However, it could just be “noise”; we really can’t say, statistically, because of 1.00 remaining well within the confidence interval.

If it continues on current pace, then 1.00 (or rather its log) will be outside the confidence interval on NV as soon as the year 2065. I will put it on my calendar to check how we are doing at that time.

Independent of the statistical significance, there could be something of interest going on. Note that the regression trend does not cross the 1.00 line till about 42 years into the time series (i.e., 1987). This suggests that, prior to that time, the average election in Western Europe saw the vote be less fragmented than it “should have been”, according to its electoral system. That could suggest that major party organizations were partially overriding the electoral-system effect (producing party systems on average around 90% as fragmented as expected) in the early post-war years. In more recent times, the weakening of party alignments could be making the electoral system expectation finally be realized, with some tendency to exceed in recent times. But we really can’t say, given that the main conclusion is the SPM is all right, and should be for a little while yet, even if the current trend continues (which, of course, it might not).

I also wanted to checked the parliamentary party systems, that is, the effective number of seat-winning parties (NS).

Here it is even more clear that the SPM is doing all right! It is only about now that the regression estimate has finally reached 1.00, but the rate of increase is more minor than with NV, and clearly of minimal significance.

The regression estimates a ratio of actual NS to SPM prediction of around 0.909 in 1945 and 0.991 in 2011. Confidence intervals are 0.773 – 1.068 and 0.843 – 1.164, respectively.

It is somewhat interesting that the trend in the ratio for NV is rising above 1.00 before the ratio for NS. Perhaps there’s an explanation of interest in there. The electoral system more directly constrains NS, after all, and voters perhaps are more willing to “waste” votes as party alignments decrease. But it could just be noise.

(If I do a graph like the first one, with NS with the baseline, there is an increase, but less significant than for NV.)

The conclusion is that there is indeed some truth to the notion that West European party systems are fragmenting. However, relative to the Seat Product Model, they are fragmenting at a slow and hardly significant pace. How can that be? Well, perhaps it is obvious, or perhaps it is not. But a country’s seat product tends to increase over time. Most countries included here have expanded their assemblies over time, and some have also increased district magnitudes and/or adopted upper (compensatory) tiers. So, the effective number of parties should increase to some degree over time, even if voters were just as moored to their party organizations and identities as they ever were!

_________

Appendix: some details.


On the last point above: Specifically, a GLS regression on expected NS says we should have seen on average NS=3.58 in 1945 but 3.67 in 2011. That is not much, but it means some increase is “baked in” even before we look at how actual voters behave. Some part of the increase is in the 60% rather than the 40%.


I dropped Belgium and Italy from the regressions, although they are included in the scatterplots for recent years. The reasons for dropping are that we could not obtain data for the share of seats allocated in upper (compensatory) tiers for the years when these countries used multi-tier PR systems; without that, we can’t calculate the extended version of the SPM (for 2-tier PR). In the later years in the Italy series, when we have such data, these are actually even more complex rules (involving a majoritarian component and alliance vote-pooling), and so the SPM really can’t predict them. In Belgium, the electoral system has been “simple” since 2003, but I think we can agree that there is no semblance of a national party system in that country.


France is also not included, partly due to the importance of the elected presidency (after 1965) and partly due to the two-round system for assembly (after 1958). We do show in Votes from Seats that the SPM works pretty well for France nonetheless. So I doubt its inclusion would have altered the results much. But I wanted to stick to the PR systems and FPTP, which the SPM is designed to handle.

Open lists in MMP: An option for BC and the experience in Bavaria

One of the options for electoral reform in British Columbia is mixed-member proportional (MMP) representation. The criteria for the potential system allow for a post-referendum decision (if MMP is approved by voters) on whether the party lists should be open or closed. The guide that was sent to all BC voters shows a mock-up of a ballot that looks like New Zealand’s, with closed lists. However, the provincial premier has stated that, if MMP is adopted, lists will be open.

When it comes to lists, it is my opinion that citizens will elect all of the members of the legislature. They will select names that are representative of their communities.

I remain uncertain about the value of open lists under MMP. Is it worth the extra ballot complexity? What additional gain does one get from having preference votes determine order of election for those winning compensatory seats? The MMP Review in New Zealand after the 2011 referendum (in which voters voted to keep MMP) looked at this question extensively. It came down firmly on the side of keeping lists closed.

Nonetheless, the statement by the premier suggests he believes the system is less likely to be chosen if voters expect the lists to be closed. And, given regional districts on the compensation tier, as explicitly called for in the system proposal, the lists would not be too long and thus the ballots not too complex.

It happens that there is one MMP system in existence in which the lists are open. Such a system has been used in Bavaria for quite some time. I actually proposed such a model in a post way back in 2005, quite early in the life of this blog. At the time I had no idea that what I had “invented” was, more or less, the existing Bavarian model.

Of course, Bavaria just had an election. In the thread on that election, Wilf Day offered some valuable insights into how the open lists worked. I am “promoting” selections from Wilf’s comments here. Indented text in the remainder of this post is by Wilf.

The Bavarian lists are fully “open,” and the ballot position has no bearing on the outcome, except to the extent the voters are guided by it, especially seen in voting for the number 1 candidate.

Of the 114 list seats, 31 were elected thanks to voters moving them up the list, while 83 would have been elected with closed lists.

Did the first on the list always get elected? Almost. In the region of Lower Bavaria, the liberal FDP elected only 1 MLA, and he had been second on their regional list.

Did the open lists hurt women? I did not check most results, but the SPD zippers their lists, and I noticed in Upper Palatinate the SPD elected 2 MLAs, list numbers 1 and 3 (two women). Conversely, in Middle Franconia the SPD elected 4 MLAs: 1, 2, 3, and 5 (three men).

Little known fact: a substantial number of voters in Bavaria, being used to voting in federal elections where their second vote is just for a party, blink at the Bavarian ballot, look for the usual space to vote beside the party name, it’s not there, so they put an X beside the party name anyway. A spoiled ballot? No, they count it as a vote for the party. Not a vote for the list as ranked, it does not count for the ranking or for any candidate, but it does count in the party count. Just like Brazil, where a vote for the party is not a vote for the list ranking, except Bavaria does not publicize the option of voting for the party.

Among the more interesting new Free Voter MLAs:

Anna Stolz, lawyer, Mayor of the City of Arnstein; she had been elected Mayor in 2014 as the joint candidate of the Greens, SPD, and Free Voters; the local Greens said they were very proud of her as Mayor. The Free Voter delegates meeting made her number 5 on the state list, but the voters moved her up to second place as one of the two Free Voter MLAs from Lower Franconia.

From Upper Bavaria, the capital region, list #12 was Hans Friedl, with his own platform: “a socially ecologically liberal voice, an immigration law based on the Canadian model, no privatization of the drinking water supply, a clear rejection of the privatization of motorways”). The voters moved him up to #8, making him the last of 8 Free Voters elected in that region.

Note: the comments are excerpted, and the order of ideas is a little different from where they appear in the thread. I thank WIlf for his comments, and for his permission to make them more prominent.

PR-USA: We still need it

Thanks to a shout-out at Twitter by Michael Latner, I went back and re-read a few very old posts (from 2005 and 2006) that I did in the category, PR-USA.

Although all were written with respect to politics of the moment, here on Election Day, 2018, the urgency of significant electoral reform remains. For instance, take the Fivethirtyeight.com forecast for the House. Using their “classic” forecast, we see that “Democrats are favored to win a majority of seats if they win the popular vote by at least 5.6 points”.

That’s right. Democrats could win the popular vote by more than FIVE percentage points and we could still have a Republican House seat majority. That would be a scandal of representation. No electoral system should be considered justified on democratic (or republican–note small initial letters) grounds if it is within the realm of realistic probability that a reversal of the voting plurality could occur even with a five-point edge for one party. (Their forecast gives Republicans about a 14% of retaining their seat majority; if they do so, it will almost certainly be without a plurality of the vote.)

It hardly matters whether the root of such an outcome would be gerrymandering (partisan-biased district-boundary drawing) or simply the geographic distribution of votes (i.e. Democrats running up huge margins in their safest seats while Republicans eke out many more close wins). Both causes are inherent to use of the single-seat plurality (or sometimes majority) electoral system.

Of course, it is easier, in principle, to fix the gerrymandering cause. And there are several such measures, along with other electoral-reform measures, on ballots around the country today. As I said in a post in 2005 opposing (with some reluctance) a measure in my state that was billed as terminating gerrymandering, these do not solve the fundamental problem, even though they would help.

In addition to almost totally ensuring that the party with the most votes also has the most seats, proportional representation would limit polarization, open up alternative dimensions of issue competition, and institutionalize a voice for the sort of anti-establishment sentiment that now only bursts forward in spasms of “radical middle” or “populist” voting.

Henry Droop made many of these points a century ago. I made variants of them a dozen or so years ago. And they remain relevant today. Literally today.

California Prop. 7: NO!!!!

One of the odder measures on the California ballot in some time (which is indeed saying something) is this year’s Proposition 7. It is a vote to confirm a bill passed by the state legislature earlier in 2018; because it repeals provisions of an earlier initiative (from 1949), it requires voter approval.

Some of the measure is technical “clean up”–for instance, the act on the books currently gives the dates of Daylight Savings Time (DST) as distinct from what is being done in practice, in conformity with federal law. For instance,

The [1949] act also requires, from 1 a.m. on the last Sunday of April, until 2 a.m. on the last Sunday of October, the standard time within the state to be one hour in advance of United States Standard Pacific Time. […]

The bill [Prop. 7] would require the advancement of this time by one hour during the daylight saving time period commencing at 2 a.m. on the 2nd Sunday of March of each year and ending at 2 a.m. on the first Sunday of November of.each year…

The March-November application of DST is what we are actually doing, as mandated by federal law (aside from Arizona and other states or portions thereof that do not use DST at all).

But then comes the part to which I strenuously object. Prop. 7:

(c) Notwithstanding subdivision(b) [concerning the current DST period], the Legislature may amend this section by a two-thirds vote to change the dates and times ofthe daylight saving time period, consistent with federal law, and, if federal law authorizes the state to provide for the year-round application of daylight saving time, the Legislature may amend this section by a two-thirds vote to provide for that application.

In other words, the objective of the sponsors of this measure is to change California, way out here on the Pacific Coast, to the equivalent of Mountain Standard Time year round. We would be on the same time zone in the winter months as Colorado and western South Dakota. It does not make a lot of sense.

For example, under the shift to so-called DST, in early January San Francisco would be looking at sunrise times of 8:25 a.m. That’s awfully late to see daylight; that’s a lot people with typical morning job or school start times out on the road in what will be only very low light at at time when most normal people’s body clocks are still barely out of sleep mode. I struggle to figure out why this is a good idea. (For the record, in Rapid City, SD, near the far eastern edge of the Mountain time zone, and much farther north, sunrise is at 7:27 MST in early January. The time zones do have some logic to them, as currently set up!)

I am old enough to remember when we were going to do DST for a full year nationwide for alleged energy savings in the 1970s. It was considered such a bad experiment that it was suspended, and we went back to standard time, well before the planned end. (Those were the days, when Congress could act quickly on a national issue.)

Really, we should go back to what it says in the original 1949 California act, which was six months on DST (more accurately “summer time”), six months off. That makes too much sense! If we have to get rid of time changes, which apparently bother some people and have some negative impacts, then stick to Pacific Standard Time all year. But this proposal to, in effect, move the state to the Mountain Standard Time zone all year is just DUMB. Please, Californians reading this, vote NO on 7!

Canadian provincial elections and the SPM: Those assemblies are too small

After posting my earlier overview of expectations from possible electoral reform in British Columbia, I was wondering how well the Seat Product Model has performed over time in Canadian provincial assembly elections. Spoiler alert: not nearly as well in the provinces as a whole as in BC, and better for votes than for seats. The latter is particularly puzzling; the model works by first estimating seats (which are more “mechanically” constrained by district magnitude and assembly size than are votes). That is why the book Rein Taagepera and I published in 2017 is called Votes from Seats. The key to the puzzle may be the serious under-sizing of Canadian provincial assemblies. As I will show in a table at the end of this entry, many provincial assemblies should be almost twice their current size, if we go by the cube root law.

I have a dataset originally constructed for my “to keep or change FPTP” project (published in Blais, ed., 2008). It has most provincial elections back to around 1960, although it stops around 2011. Maybe some day I will update it. For now, it will have to do.

The first graph shows the degree of correspondence between a given election’s observed effective number of vote-earning parties (NV) and the expectation from its seat product (i.e., for FPTP, the assembly size). The black diagonal is the equality line: perfect prediction would place an election on this line. The lighter diagonal is a regression line. Clearly, the mean Canadian provincial election exhibits NV higher than expected. On the other hand, the 95% confidence interval (dashed curves) includes the equality line other than very trivially near the middle of the x-axis range. Thus, in statistical terms, we are unable to reject the hypothesis that actual NV in Canadian provincial elections is, on average, as expected by the SPM. However, the regression-estimated line is systematically on the high side.

It might be noted that we never have NV expected to be 2.0, and in the largest provinces, the assemblies are large enough that we should expect NV>2.5. (“Large enough” here meaning independent of what they “should be”, by the cube root; this is referring only to actual assembly size.) So the classic “Duvergerian” outcome is really only expected in the one province with the smallest assembly. And such an outcome is more or less observed there, in PEI. Nonetheless, a bunch of elections are very much more fragmented than expected, with NV>3! And several are unexpectedly low; many of these are earlier elections in Quebec.

All individual elections are labelled; in a few cases the label generation did not work well (some elections in 2000s). The regression coefficient is significant, although the regression’s R2 is only 0.15. The basic conclusion is a marginally acceptable fit on average, but lots of scatter and some tendency for the average election to be more fragmented than expected.

Now, for the largest seat-winner in the assembly (s1). Here things get a little ugly.

This might be considered a rather poor fit. There is a systematic tendency for the largest party to be bigger than expected: note that the equality line is essentially never within the 95% confidence interval. When we expect, based on assembly size, the largest party to have 60% of the seats, it actually tends to have more like 68%. More importantly, the scatter is massive. In fact, the regression coefficient is insignificant here; please do not ask what the  R2 is!

The size of Canadian provincial parliaments is never so large that the leading party is expected to have only 50% of the seats (note the reference lines and where the equality line crosses the 50-50 point). Yet there is not a trivial number of elections with the largest party under 50%. More common, however, are the blowout wins, where the largest party has 80% or more of the seats. This has been a chronic feature of Canadian provincial politics, especially in a few provinces (notably Alberta, New Brunswick, and Prince Edward Island).

Why is Nv so much better predicted (even if not exceptionally well) than s1? It is hard to say. It is an unusual situation to have both NV and s1 trend higher than expected. After all, normally the more “significant” parties there are the smaller the largest party should tend to be. In the set of predictive equations, s1 (and the effective number of seat-winning parties, NS) are prior to NV, because the seat-based measures are more directly constrained. This is why the book is called Votes from Seats. In our diagram (p. 149) deriving the various quantities from the seat product, we show NV and s1 coming off separate branches from “Ns0” (the actual number of parties winning seats), which is expected to be (MS)0.25, where M is the magnitude and S the assembly size. Thus for FPTP, it is S0.25. A parliament with 81 seats is expected to feature three parties; the other formulas would predict that NS=2.08, s1=0.577, and NV=2.52. If the parliament had 256 seats, we would expect four parties, NS=2.52, s1=0.50, and NV=2.92.

Unfortunately, the dataset I am using does not (yet) have how many parties won seats–actual or effective number. Thus I can’t determine whether this is the point at which the connections get fuzzy in the Canadian provincial arena. Nonetheless, there should be a relationship between NV and s1. It can be calculated from the formulas displayed in Table 9.2 (also on p. 149). It would be:

s1=(NV1.5 -1)-0.5.

In this last graph, I plot this expectation with the solid dark line, and a regression on s1 and NV from Canadian provincial elections as the lighter line (with its 95% confidence intervals in dashed curves).

The pattern is obvious: there are many elections in Canadian provinces in which the leading party gets a majority or even 60% or 70% or more of the seats despite a very fragmented electorate. We should not expect a leading party with more than 50% of the seats when NV>2.92. And yet 17 elections (around 15% of the total) defy this logically derived expectation. Six have a party with 2/3 or more of the seats despite NV>2.92 (in order of increasing NV: BC91, AB04, NB91, QC70, AB67, BC72; in the last one, NV=3.37!).

I think the most likely explanation is Cube Root Law violations! Canadian provincial assemblies are much too small for their populations. So, the cause of the above patterns may be that voters in Canadian provinces vote as if their assemblies were the “right” size, but these votes are turned into seats in seriously undersized assemblies, which inflates the size of the largest party. (Yes, votes come from seats in terms of predictive models, but obviously in any given election it is the reverse!)

There is some support for this. I can calculate what s1 and NV would be expected to be, if the assemblies were the “right” size, which is to say the cube root of the number of voters (which is obviously smaller than the number of citizens, but this is what I have to work with). I will call these s1cr and NVcr. Then I can take ratios of actual s1 and actual NV to these “expectations”. The mean ratios are: NV/NVcr=0.994; s1/s1cr=1.19. If the assemblies were larger, the votes–already with a degree of fragmentation about as expected from more properly sized assemblies–would probably have stayed about the same. However, with these hypothetically larger assemblies, the largest party in parliament would be less inflated by the mechanics of the electoral system.

Canadian provinces would have a greatly reduced tendency to have lopsided majorities if only they would expand their assemblies up to the cube root of their active voting population. Of course, this assumes they stick to FPTP. The other thing they could do is switch to (moderately) proportional representation systems, like BC is currently considering. That would be seem to be a good idea regardless of whether they also correct their undersized assemblies.

Below is a table of suggested sizes compared to actual, for several provinces. (“Current” here is for the latest election actually in the dataset; some of these have been increased–somewhat–subsequently.)

Prov. Current S Increased S
Alberta 83 121
British Columbia 79 152
Manitoba 57 94
New Brunswick 55 91
Newfoundland 48 81
Nova Scotia 52 95
Ontario 107 208
Prince Edward Island 27 55
Quebec 125 197
Saskatchewan 58 95

_________

(By the way, the R2 on that s1 graph that I asked you not to ask about? If you must know, it is 0.03.)