2. rational numbers

from Ottawa Citizen online published November 18, 2016 http://ottawacitizen.com/news/local-news/kid-builders-try-out-mooneys-bay-playground

illusions and power

The 3E Senate has been advocated with great passion. Altruism and naked self-interest and xenophobia all drive its promotion. Protecting the weak from the strong by standing up to the tyranny of a democratic majority is a noble cause. Tension between brash new-rising economic players and wary established wealth is an old story. And French and English have been snarling at each another or at war with each other, off and on, for almost a thousand years.

The emotions we feel when we hear about or partake in these archetypal dramas are part of the human experience. They should be reveled in. But when it comes to redesigning our homeland, more than emotion should be engaged. We should have half a clue what we are doing! In this the 3E Senate campaign failed, for how a 3E Senate will effect decision-making in Canada is not common knowledge, even among its supporters. Because it is not widely understood, there are a few widely accepted but incorrect beliefs on which advocates for the 3E Senate, wittingly or unwittingly, capitalized.

  1. The 3E Senate has numerological symmetry; four small provinces to the west and four small provinces to the east and (maybe) 3 territories to the north, balance two large central provinces, as though all are on some great big teeter-totter.
  2. The 3E Senate will significantly increase the influence of Albertans and British Columbians in Ottawa.
  3. The 3E Senate will significantly weaken over-privileged Ontario’s, and especially over-privileged Québec’s, influence in Ottawa.
  4. The issue of 3E Senators for territories is a small detail that can be dealt with after we’ve all committed in principle to the 3E Senate.
  5. The offer of territorial exclusion in the proposed 3E Senate (assigning no senatorial representation for the residents of the territories) may be the needed bargaining chip to finally bring Ontario and Québec to accept the 3E Senate.

All of these beliefs are in some sense wrong. They can be shown to be wrong just by doing the necessary counting. By the necessary counting I do not mean a comparison of the number of ridings and the number of residents in each province and territory. I have done that in Table 1 for your review, but please bear in mind the necessary counting is more than this.


The number of residents in each province or territory is shown in column [2] of Table 1. These numbers are from Statistics Canada’s web site and are extrapolations for the year 2007 from earlier census figures. Column [3] shows the values in column [2] divided by the value in row [14] of column [2], which gives the fraction of the total Canadian population that lives in each province or territory. Column [4] shows the number of ridings in each province or territory. Each riding is represented by a seat in the House of Commons. As of 2004 there are 308 seats in the Commons, and, of course, 308 corresponding ridings distributed throughout Canada. Column [5] shows the percentage of the total number of ridings that are in each province or territory. Column [6] gives the ratio of the values in column[5] divided by the values in column [3], and I’ve called these values the representation ratios.

A representation ratio can be thought of as a comparison of odds. Select one Canadian resident at random. The probability that this resident will be from a particular province or territory is given in column [3]. Select one Canadian riding at random. The probability that that riding is in a particular province or territory is given in column [5]. Column [6] gives the ratio of the odds that a riding, chosen at random, is in a particular province or territory to the odds that a particular Canadian, chosen at random, resides in that same province or territory. The higher the ratio, the better represented are the residents. If the distribution of ridings closely matched the distribution of the population (a relationship that we could call mathematically fair) then the ratios in column [6] would all be close to unity. However, the smaller provinces and the territories all have ratios higher than one. Particularly, Prince Edward Islanders are three times better represented than what a mathematically fair distribution of ridings would provide them, and residents of the three territories are similarly well represented using this measure. The three largest English-speaking provinces all have ratios less than one. Québec’s ratio is very near unity.

It would seem there is an unspoken but generally accepted rule in Canada that more populous provinces should be less well represented and less populous provinces should be better represented. One exception to this is that residents of Saskatchewan and Manitoba are marginally better represented than people in the three largest Atlantic provinces. This anomaly is not often dwelt upon in western Canada. The more notorious exception is that Ontario and Québec are not following the rule, and are taking advantage of Alberta and British Columbia. Proponents of the 3E Senate proposal accept that this advantage is modest, but in western Canada still it rankles. The advantage is symbolic, and symptomatic, of the present system’s unfairness. It is also, like the other beliefs I listed above, illusory.

I want to draw a clear distinction between representation and political power. It is easiest to get a grasp of the idea of political power by considering a simple example of a three actor parliament. Imagine a small assembly of only nine seats, for a country with only three provinces. One province has two ridings only, and so two seats only, in the assembly. The next largest province has three ridings, and three corresponding seats in the assembly. The largest province has four ridings, and four seats in the assembly. Which province has the most power? Which has the least? Think a moment before reading further.

All three provinces have equal power. For any legislation to pass with a majority in this assembly, at least two of the provinces must vote for passage. It does not matter which two.

Now imagine further that the distribution of the nine ridings amongst the provinces was mathematically fair, as mathematically fair was defined above. In other words, if the total population of the country is, say, nine hundred people, then about two hundred live in the smallest province, three hundred in the middle province, and four hundred in the largest province. Anyone trying to make the case that residents from larger provinces must be less-well represented would be called a nut. Everyone would know that the smallest province had as much influence as the largest, and there would probably be some kind of constitutional initiative to make the system more ‘fair’ by improving the representation of the larger provinces. Mathematically fair need not mean fair in practice.

Suppose that, in fact, the people of this imaginary country initiated the constitutional change to give the larger provinces more representation. They award one more seat to the largest province and take one seat from the smallest province. The total number of seats in the assembly remains unchanged at nine, but now the largest province has five seats, the second largest has, as before, three seats, and the smallest province holds just one seat. Now which province has the most power and which has the least? Again, take a moment before reading on.

The biggest province has all the power and the two other provinces have no power. The largest province holds five seats, the majority required to pass legislation in a nine-seat assembly.

Table 2 summarizes the two distributions of seats and real influence in the imaginary country’s imaginary assembly.


Consider the following observations about Table 2’s numbers.

  1. In the first scenario, in which all three provinces have equal influence, the seat count implies three different levels of power. Seat count does not reflect influence.
  2. In the second scenario, the largest province does not, as its’ seat count suggests, wield 5/9ths of the power; it wields all the power. Similarly, the other two provinces do not have the modest level of influence their seat counts imply; they have none. Seat count does not reflect influence.
  3. In the second scenario, the two smaller provinces have different seat counts, but the same level of power; none. Seat count does not reflect influence.
  4. The middle province has, in both scenarios, the same seat count and the same percentage of the total number of seats in the assembly. However, it has significant influence in the first scenario, and none in the second scenario. Seat count does not reflect influence.

In other words, the number of seats is a strikingly poor measure of a province’s political influence. Intuition tells us that the number of seats a province or territory controls must play some role in determining that province’s or territory’s influence in the assembly. However, clearly, there must also be some other factor at work.

I described real power qualitatively in columns [4] and [7] of Table 2 because in this essay I haven’t yet introduced a way to quantify that influence. That is the next step; the necessary counting I referred to above.

the necessary counting

Let’s construct a political model. A proposal (called a motion) is brought before an assembly. Some members of the assembly will vote for the motion, some will vote against it. For our model we will assume that the representatives for each province or territory all cast their votes on the same side of the issue (no defections), and all members vote for or against a motion (no abstentions). Except for these limits, each member of the assembly is free to vote one way or the other, and the content of the motion itself could be anything. So, we will assume that there is an equal probability that the representatives from a province or territory will vote for or against the motion. Finally, we will assume that a majority within the assembly is required for the motion to pass.

Given that storyline, here is a definition: A measure of a province’s or territory’s political influence is the probability that a province’s or territory’s representatives will have determined whether the motion passes or fails. If they voted for it, the motion passed. If they voted against it, the motion failed. The votes of the rest of the members of the assembly are split such that, no matter which way the members from that province or territory vote (assuming they vote as a block and assuming no other group changes its vote) they will be on the winning side. They decide the outcome of the vote.

Now, before we go further, here is a reasonable question. Why not just use the odds of being on the winning side (given those voting assumptions above) as a measure of influence? Why introduce this more complicated idea of decisiveness? The answer is that a province or territory with no influence at all is on the winning side in exactly half of the uniformly distributed vote outcomes. Imagine yourself in the gallery overlooking the House of Commons. Every time the speaker calls for a vote you flip a coin and call out “yea” or “nay” accordingly. You will be on the winning side about half the time, though the speaker will not count your vote in the tally (and may even ask you to leave if you’re too loud). If the odds of winning are used as a measure of power, then the case of no influence would be represented by a measurement of 50%, and for that reason it is not a very satisfying measure. However, there is a simple relationship between the number of wins and the number of decisive opportunities. As far as the problem has been defined so far, the odds of a certain province or territory winning, given a uniform distribution of vote splits, is exactly equal to 50% plus half the odds of its being decisive.

To determine the number of instances of decisiveness for each province we must examine every possible combination of vote split within the assembly. The total number of these outcomes is 2 raised to the number of provinces and territories involved. For example, in the imaginary case of the three province country, there are three provinces and so 2 raised to the power 3, which is 8, unique vote splits; there is one outcome in which all three provinces vote against the motion, there are three outcomes in which only one province votes for the motion and the other two vote against it, there are three outcomes in which only one province votes against the motion and the other two vote for it, and there is one outcome in which all provinces vote for the motion.

Next we examine each vote split. We can determine the result of the vote; whether the motion passed or failed, and we can calculate by what margin the motion passed or failed. (At this time we could also determine who won and who lost, but as I mentioned earlier, that is not the best measure of political influence.) What we seek are the instances in which individual provinces on the winning side decided the outcome. More precisely, in a given vote split, a province decides a vote’s outcome when

  1. its representatives vote on the winning side, and when
  2. the number of seats it controls is greater than the margin by which the motion passed or failed.

Tally for each province the number of times those two conditions are met. That tally divided by the total number of vote splits (8 in this example) gives the probability that the province will be decisive. You can see the step-by-step calculations done to calculate decisive probabilities for the two scenarios of the example three-province country at this link. The result of the count in our imaginary three-province country, for the case of a vote distribution of 4:3:2, the first scenario, and for the case of a vote distribution of 5:3:1, the reformed assembly of the second scenario, is shown in Table 3.


Consider the following observations about the figures in Table 3.

  1. In the first scenario, in which all three provinces have equal influence, for all three provinces the probability of being decisive is the same. Each province’s odds of being decisive correctly reflects each province’s influence.
  2. In the second scenario, the largest province wields all the power, and the other two provinces have none. The probability of decisiveness reflects the relationships correctly.
  3. In the second scenario, the two smaller provinces both have no chance of affecting vote outcomes. The probability of decisiveness reflects the relationship correctly.
  4. Despite its constant seat count in the two scenarios, the middle province has some probability of deciding votes in the first scenario and no chance in the second scenario. The probability of decisiveness reflects the middle province’s different levels of political influence.

In other words, in every test in which the seat count, shown in Table 2, failed to measure a province’s political influence, probability of decisiveness, shown here in Table 3, gave an accurate measure of a province’s political influence. To learn the odds that a voting block will be decisive you must know about the other voting blocks and you must do the necessary counting. Here is a hard and fast rule: Given only a voting block’s number of seats as a percentage of the assembly’s seats, if that percentage is less than 50%, then you cannot know how strong or weak that voting block’s position is within the assembly. You simply cannot. To pass judgments about power and fairness, without doing the necessary counting, basing that judgment on, for example, the data shown in Table 1, is just silly.

the thin red line

We can now do the necessary counting for the territories and provinces of Canada. In the imaginary case of the three province country, there are three provinces and so 2 raised to the power 3, which is 8, unique vote splits. That’s easy to keep track of, but in Canada there are ten provinces and 3 territories; a total of 13 voting blocks acting, and so 2 raised to the power 13, which is 8192, unique vote splits. I wrote, in THINKPascal, a computer program that does the necessary counting, and you can view the code at this link. You are welcome, nay, encouraged, to copy the code, improve it and format it to run on your own machine, and tinker with the input data as much as you like to satisfy your own curiosity about how the necessary counting is done. The tallies of the instances of decisiveness for each province and territory, for the 8192 unique vote splits, are presented in Table 4 below.

Table 4

Table 4 is similar to Table 1. Columns [2] and [3], identical in both tables, give the number of residents and their percentage of the Canadian total, for each province and territory. Column [4] gives the number of instances, from a count of all possible vote splits, in which the voting block representing the province or territory is decisive in determining the result of a vote. At the bottom is the total number of vote splits, 2 raised to the power 13 = 8192. Column [5] gives the odds as a percentage, assuming a uniform distribution of vote splits, that a province or territory will be decisive. (The odds are the instances from column [4] divided by the total number of splits.) Row [14] of column [5] gives the sum of all the percentages; and that sum is 181%, which clearly is greater than 100%. It is greater than 100% because in many of the vote splits, more than one actor is decisive. (You may have noticed this feature in Table 3 with our imaginary 3-province assembly. In the 4:3:2 scenario, the sum of the percentages was 150%, because in each split in which some winning province is decisive, it requires two provinces to make a winning coalition. On the other hand, in the 5:3:1 scenario, the sum of the percentages was 100%, because only one province, the largest, is required for a motion to pass in the assembly.)

In Table 4, Column [6] gives the decisiveness ratio – the values in column [5] divided by the values in column [3]. These values are a ratio of the probability that a province or territory will be decisive in any vote, to the odds that a person resides in that province or territory. Column [6] in Table 4 is analogous to column [6] in Table 1, except that real influence, rather than the unrevealing odds of having a seat, is being presented on a per capita basis.

There are two general patterns that appear from the data in Table 4. First, the values in column [3] and column [5], are both in descending order. It is a general rule that more populous provinces and territories have higher odds of being decisive. This pattern is violated only when two or more provinces or territories with a different number of residents have the same number of ridings. This is to be expected, for it is the number of seats that directly determine the odds of decisiveness.

The second pattern in data is that the values in column [6] are, more or less, in ascending order. It is another general rule that less populous provinces and territories have a higher influence ratio and more populous provinces have a lower influence ratio. This pattern is locally violated in 4 instances:

  1. Prince Edward Island has a slightly higher rating than the less populous Northwest Territories;
  2. Saskatchewan has a slightly higher rating than has the less populous Nove Scotia, and Manitoba’s rating is roughly equal to Nova Scotia’s;
  3. British Columbia has a slightly higher rating than has Alberta;
  4. Ontario has a significantly higher ratio than has Québec.

While we intuit these two general rules from studying the Decisiveness ratios in column [6], the relationship between the power and population and the meaning of the two rules becomes more apparent when we plot the values from column [3] against the values from column [5], as I’ve done in Graph 1.


On Graph 1 I’ve plotted the values from column [5] on the y (vertical) axis against the values from column [3] along the x (horizontal) axis. The data points for the English-speaking provinces are shown red, Québec’s data point is plotted in blue, and the data points for the three territories are green.

The first time I saw this graph I was startled to see how well the red data points lined up. On Graph 1 I’ve drawn the least-sum-of-squares best-fit line through the English-speaking provinces’ data points, and included the line’s equation. You can see that the line is a reasonably good fit. (The value of R² is a measure of how well or poorly the data points fit the line. A value of exactly one would mean that all the data points used to generate the line would be exactly on the line.)

The slope and intercept of the line are quantifications for the two general rules about provinces and representation developed earlier. The rules were

  1. the more populous the province the more political power it wields, and
  2. the less populous the province, the more political power per capita it wields.

The slope for this line (the value of 1.7842) is positive. That it is positive means that as x (population) gets larger, y (political power) gets larger, which is the mathematical expression for our first rule, above.

The intercept is the value of y at which the trend line crosses the axis. For this line the intercept is 1.52%. (You can see in the enlargement in Graph 1 that the trend line meets the vertical axis at about 1.5%.) The intercept is positive; it meets the vertical axis above the horizontal axis. This means that any province on the line, no matter how few its residents, will still have at least 1.52% chance of being decisive in votes in the assembly. This is our second general rule.

If you drew a straight line from the graph’s origin to one of the data points, the slope of that line would be the Decisiveness ratio in column [6] of Table 4 for the particular province or territory. That the red line passes above the origin is the reason why the smaller provinces have the highest Decisiveness ratios. The territories have a high ratio of power per resident, but the residents of the territories have less than half the political influence they would have if they were on the trend line, even less than half the trend line’s intercept. What I want to suggest, then, is that the red line is a new, and more practical and real, definition of “fair” distribution. Because their decisiveness data points fall on or very near a straight line, the political power of the English-speaking provinces is “fairly” distributed. Let’s call it English Canada’s standard.

It’s apparent that Quebec’s data point, and the data points for the territories, fall below the red line. Although the number of ridings in Quebec and in the territories seems generous in Table 1, the actual political power their parliamentary seats provide is less than “fair” by English Canada’s standard. Neither Québec nor the three territories are disadvantaged because of the ethnicity of their residents; their relative lack of power in parliament is due solely to mathematics and the distribution of the seats throughout all of Canada.

I make this point because the odds that the four under-powered jurisdictions happen to also be the four with a different ethnic mix and significantly different culture and language from “the rest of Canada” is 1 to 715. Those are not astronomical odds, but clearly represent a long shot. I haven’t calculated the odds, but I expect that the probability of the data points for the English-speaking provinces aligning as well as they do is also quite a long shot.

While Québec’s relative lack of political power is due solely to mathematics, this situation may have been understood, and approved of, by power brokers in English-speaking Canada. Québec has been under-powered since confederation. I have not done the research, but it might make an interesting historic study to see if, during Confederation, Québec’s weaker position was discussed in probabilistic terms. Permutations and probability were well understood by Europeans in the 1860s; our Fathers of Confederation knew how to do the necessary counting. Did they do it? Was leaving Québec politically weak a topic of discussion? Similarly, when, if ever, was it decided that the English-speaking provinces’ data points should be aligned? Of course, the native folk who fell under Canadian jurisdiction were not even recognized as citizens till 1956 and were not all allowed to vote till 1960. No historical assessment of English Canadian intent is needed for their case.

For the purpose of this essay, however, English Canada’s standard, the linear relationship in Graph 1, is a refutation of the idea that the people of Québec and Ontario are unfairly advantaged in the existing distribution of power. Ontario has exactly the power it deserves to have by the linear relationship that all the English-speaking provinces share. Québec has significantly less political power than its population warrants. Ontario and Quebec are not unfairly advantaged. To insist that they are is just silly.

the great big teeter totter

Now, (at last) let us look at how the 3E Senate changes things. First, we can use our political model to show the way the 3E Senate changes decisiveness probabilities. The presence of the 3E Senate means that some of the previously winning coalitions, that have majority support in the House of Commons, are no longer winning coalitions. Those actors who, in some votes, were winners and were decisive when the 3E Senate did not exist, are now losers, and those actors who lost those votes previously now comprise the winning coalition and some of those actors are decisive. We just need to change the requirements for a win to reflect the 3E Senate’s effect. (The fact that the model can be modified to perfectly reflect the mathematical effect of the various 3E Senates shows that, unlike representation, Decisiveness is a valid measure of political power.) There are two 3E Senates to consider. The inclusive 3E Senate allows territorial representation, and the exclusive 3E Senate has no territorial senators. We will look at these two cases.

Table 5

Table 6

The columns in Table 5 and Table 6 are analogous to the columns in Table 3, but in column [4] are presented the new tallies for instances of decisiveness as calculated with, respectively, an inclusive or exclusive 3E Senate.

At the bottom of Tables 5 and 6 I included something called the 3E Senate effectiveness factor. The 3E Senate is effective to the degree that it blocks the House of Commons from passing motions. Without a 3E Senate, the number of ways that the Commons can pass motions, assuming provincial and territorial voting blocks without defections or abstentions, is 4067, the value given at the bottom of Table 4. (You may notice that 4067 is not exactly half of 8192. That is because there are an even number of seats in the House of Commons, and so there is the possibility of a tie, and a tie means that a motion fails to pass.) The inclusive and exclusive 3E Senates stop some of those 4067 opportunities to pass motions and allow, respectively, only 2919 and 2499 ways for passage. I have reported the rating of the effectiveness of a 3E Senate as the number of no-longer available opportunities for passage, divided by the original 4067 ways to pass a motion. With no 3E Senate there is no reduction in number of ways the Commons can pass motions, and the resulting effectiveness measure would be 0%. At the other end of the scale, a 3E Senate designed to completely stop Parliament from passing any motions would be 100% effective by this measure.

Tables 5 and 6 show the two general rules still apply. More populous provinces have greater influence and, in general, less populous provinces have higher representation ratios with, as before, a few minor violations along the way. But the violations are different. The territories follow that second rule in Table 5 when they have 3E Senators, but not when they are excluded from the 3E Senate, as shown in column [6] of Table 6. In fact, when you compare Table 4 with Table 6, you see that the territories are worse off with an exclusive 3E Senate than they are at present without one.

In Table 5 there is only one violation of the second rule. Ontario still has a higher influence ratio than has Quebec, although the gap has closed.

In Table 6, among the provinces, there are no violations of the second rule. Quebec now has a higher ratio than Ontario. In fact, Ontario has crossed a bit of a psychological barrier. Ontario’s Decisiveness ratio is less than one. With an exclusive 3E Senate, there are better odds of Ontario being home to any Canadian than of Ontario having influence in parliament.

As expected, and intended, while the two rules hold, with the 3E Senate the influence and influence ratios increased for the less populous provinces and decreased for the more populous provinces. Perhaps less expected or intended, the three provinces that change the least are Québec, Alberta, and B.C. Québec’s decreases are modest, possibly because it had so little to lose. British Columbia’s decreases are also modest, and Alberta’s gains are modest as well. This is contrary to the common notion that Alberta and B.C. will benefit dramatically; with the introduction of the 3E Senate Alberta’s gains are small and B.C.’s influence actually declines slightly. The common notion that territorial inclusion in the Senate is not an important issue is true for Alberta, B.C., and Québec. The Decisiveness and Decisiveness ratios for these three provinces do not change much between Tables 5 and 6. But it does matter to Ontario and it also matters to all the smaller provinces and to the territories. Excluding the territories makes all the smaller provinces that much more necessary in forming winning alliances, and denies Ontario 3 potential allies. Ontario is significantly better off with Territorial senators around. Therefore, the commonly held notion that Ontario and Québec can be brought on side by excluding the territories from the Senate is silly, for it is wrong. Not only is excluding the territories unprincipled, it also does not help Québec and harms Ontario.


Graph 2 plots the odds of mattering against the provincial and territorial populations for the three cases covered up to now: Canada without a 3E Senate, with an inclusive 3E Senate and with an exclusive 3E Senate. I’ve included best-fit lines through the data points for the English-speaking provinces. In all three cases, the data shows good agreement with the line. You can see the progressive decrease in slope (the quantification of our first rule) and the progressive increase of the intercept (the quantification of our second rule.) You can see the pivot between British Columbia’s and Alberta’s data points. You can see Québec still below the line, and you can see the territories at the far left end, riding the teeter totter up until they are pushed off. There is no mystical symmetry to the 3E Senate. BC is on the wrong side of the pivot for the analogy to be valid, and Québec is not even riding.

Now, here’s another kicker. It is possible, without modifying the senate, to get the power data points for all the provinces and territories roughly onto a straight line, what we could call the Canadian standard. Less populous provinces get more power than they have now, Ontario and BC get less, just as was the intent and the effect of the 3E Senate. However, with this new strategy Québec’s power increases so it is on the Canadian standard. The strategy is to give Québec and the territories more seats in the Canadian parliament, and tweak the other provinces’ riding totals a bit. I have not done an exhaustive search, but in Table 7 and Graph 3 you can see one distribution of ridings that gives a pretty good Canadian standard. Every English–speaking province on the mainland looses ridings in this distribution, yet only Ontario and, very slightly, BC loose decisive power. BC’s power in this scenario would be greater than it would be with a 3E Senate instituted.

Table 7


The effectiveness rating is, of course 0%; no alliances winning in the Commons are disqualified. It depends on your perspective, whether preventing certain alliances is a good thing or a bad thing, but consider this: by foregoing the 3E Senate and instead revising seat totals, 4062 ways to pass a motion in the Commons are maintained. While the relative power of the various provinces and territories changes to rest near the Canadian Standard, the number of ways that all actors can build winning alliances remains close to maximum.

During the Meech Lake and Charlottetown negotiations, many might have viewed a proposal like this favourably. Only Ontarians loose, and, at the time, they were willing to consider concessions “for the good of Canada”. There’s no knowing if something like a Canadian standard could have been accepted by the big players or by the voters, but we do know it was never tried; the 3E Senate swept all other options off the table. It blinded Albertans, and others, to different ways to power in Ottawa, and that was really silly.

(By the way, at the time, in 1993, I had not developed these ideas as far as they are presented here. I only had it worked out to the decisiveness ratios. I hadn’t seen the thin red line or the great big teeter-totter or worked out a Canadian standard. On the other hand, I was then, as I am now, just a private citizen scrambling through my daily existence. I was not a Canadian intellectual leader or even a humble bureaucrat toiling on negotiating positions for a premier or prime minister. Did anyone out there do the necessary counting?)

innies and outies

A major justification for the Triple-E Senate was that there are so many people living in the relatively small areas of southern Ontario and southern Québec. This great pool of voters attracts the federal parties, and they set their platforms to get as great a share of these central Canadian votes as possible, paying less attention to the aspirations of all the rest of us, the more scattered folk of, what came to be called during those debates, Outer Canada. Outer Canadians inhabited Central Canada’s, or more properly, Inner Canada’s, hinterland. The Triple-E Senate was meant to shake up that relationship. When Triple-E enthusiasts got going, they often included Central Canadian people in northern Ontario and northern Québec as honourary Outer Canadians. The argument was that these people would benefit from the existence of Triple-E Senators from other provinces who would guard the interests of all Outer Canadians.

Atlas of Canada population distribution map source = http://geogratis.gc.ca/api/en/nrcan-rncan/ess-sst/e83ac2cf-8893-11e0-a3ad-6cf049291510#distribution About 75% of Canadians live in the red-coloured areas, about 24% of Canadians live in the orange-coloured areas, and about 1% of Canadians live in the white-coloured areas.
Atlas of Canada population distribution map
source = http://geogratis.gc.ca/api/en/nrcan-rncan/ess-sst/e83ac2cf-8893-11e0-a3ad-6cf049291510#distribution
About 75% of Canadians live in the red-coloured areas, about 24% of Canadians live in the orange-coloured areas, and about 1% of Canadians live in the white-coloured areas.
North America at Night source = http://www.nightskynation.com/objects/earth-at-night/north-america
North America at Night
source = http://www.nightskynation.com/objects/earth-at-night/north-america












This was a profoundly weak argument. It was like kicking a hornets’ nest in mainstream Québec, where the widely popular Distinct Society was antithetical to the idea that any Anglos could have meaningful commonality with any québecois. But it also opened a can of worms in the ‘Rest of Canada’. Those honourary Outer Canadians in rural and small-town Ontario and Québec have a lot in common with people living in places like Trail BC, or Cape Breton Island, or Battle Harbour, or in the Lubicon Reserve in Alberta, and relatively less in common with the shakers and movers in the big cities of the east and west, and in Outer Canada’s provincial capitals, where the agendas for  3E Senators would be set.

The 3E Senate campaign was dancing around a real issue that it could not address. Yes, Outer Canadians do live in Inner Canada’s hinterland. But in every province, with the possible exception of PEI, people living outside the cities live in that province’s hinterland. This is so Canadian we seem almost blind to it.

Canada was conceived as a move in the Great Game. The intention was to deny Americans direct access to the resources of the northern half of the continent. The plan was to bring people from Britain, and, as needed, people from other parts of Europe, to populate the land in an east-west band, a necklace of communities from sea to sea. And, as often happens when Empires contest, the aspirations of the people who originally lived here were swept aside.

The paradigm that guided the making of an Inner and Outer Canada in the 19th and early 20th centuries was the same paradigm that guided our provincial borders. For all but the three smallest maritime provinces, the provincial population is distributed in a collection of towns and cities in the south, with vast tracts of lightly inhabited northern land set aside for whatever those southern city-dwellers would like. It’s all their province!

Further, the people in Outer Canada have strong advocates in their struggles with Inner Canada; they have the provincial governments. People in the provincial hinterlands have no intervening level of government to defend their interests. It is the provinces of Canada that show a clear need for local liberty from the tyranny of a democratic majority, and the 3E Senate proposal both highlighted this need and ignored it. But for a significant minority the desire is really there, and is occasionally voiced, in Sydney, in Dawson Creek, in Havre-St.Pierre, in Thunder Bay and Goose  Bay and Haida Gwaii.

Now, let us take note that provincial borders are very well protected in Canadian law. Any change to a provincial border must be approved by Parliament and the one or more provincial governments involved in any proposed change. That pretty well locks any smaller community permanently into its province’s hinterland, an Outie forever. The rules just aren’t there to allow a dissatisfied community the option to leave. It’s easier for a province to leave confederation. Part of the appeal of the Triple-E movement was the noble quest for liberty. But, this was meant to apply strictly in a provinces-vs-provinces context.  Triple-E senate advocates had to pick their battles, and standing up to the provinces on behalf of their respective Outer communities was a bridge too far. To have a chance at success, Triple-E needed Outer Canada’s provincial governments as allies. Expediently, 3E advocates simply did not address intra-provincial differences in Outer Canada, and instead built, with great success, excitement for the Triple-E Senate project in those very provincial hinterlands. I have no quarrel with this aspect of their campaign. Their pragmatism was admirable, and the enthusiasm they tapped brought, for many, a genuine sense of purpose and joy. But, the inconsistency was there to be seen if one chose to look.

The Triple-E senate program got me thinking about provincial borders and why they were immutable and whether they should be. I pondered the curious mathematical challenge faced by voters in Québec. I remembered, even as a kid, the times I had heard about communities advocating to become separate provinces, getting in the news for a while, and then falling off the radar again. So this goes back a long time. Anyways, for fun, I drew a map of imaginary Canadian provinces that minimize hinterlands.


This is not actually the map I drew way back in 1990. (Nunavut did not even exist as a jurisdiction back then.) I have tinkered with it periodically over the years, because I like the look of it, and because I think if we could change our provincial boundaries, we probably would be better off. I have some notes here about the map particulars. The map is not meant to be any kind of recommendation. I don’t know enough about many of the places to have any more than superficial opinions. It is presented here simply as an exercise in ‘what if’ artwork. Art should inspire or challenge us, by pushing the frontiers.

It is time to draw this chapter to a close. What has been achieved? Advocates for the 3E Senate can rightly say that, whatever I have shown, nothing changes the fact that urban Ontario and Québec have far more people and more seats than the rest of Canada combined. So far, I have only exposed as fallacies some common notions that buttress the 3E Senate proposal. I have not challenged its core. For the 3E Senate proposal, swept clear of the chicanery that surrounds its promotion, is, at heart, a genuine call for local liberty from the tyranny of the democratic majority in central Canada.


  1. Well, I am an immigrant living in Alberta, and I think a triple E senate is a good idea. Does that make me xenophobic

    1. Thanks for the comment, but I have to wonder… you only read to the 18th word? There are 5211 more words to go in this essay. Maybe you are logophobic.

  2. This is a very enlightening analysis. Great work!

    While the analysis seems just, I will disagree with your conclusion that seats should be readjusted in the House. I think the Senate should be used to readjust the balance of power.

    – The main limitation with the analysis is assuming the representatives of each province will vote in block. This is generally not the case now. (Of course, without that assumption you can’t analyse things, not in this way; the analysis makes some great points but does not tell the whole story).
    – Adjusting seats in the House goes against the Rep by Pop principle which is pretty basic in Canadian democracy (although it is not respected now).
    – The Senate is where seats are apportionned to represent each regions. It seems to me it would be a more natural fit to correct regional imbalances than the House of Commons.

    The approach proposed here for seat distribution is also much more complex than the simple Rep by Pop (though not necessarily that much more complex than Rep by Pop plus the current rules that bend it). This would make it a hard sell to replace the current system.

    1. Hello Benoit

      Thank you very much for your comments. What a charge it was to know someone had really read and understood this essay!

      I agree that the reps from each province will not generally vote in a block. If we are constrained to a 3E Senate, then, almost by definition, the issue becomes the relative influences of each province or territory, and this block assumption is convenient. It is also not wildly wrong. A further refinement on this study could be to see how many defections a province or territory could tolerate before loosing its decisiveness.

      I am not advocating that the seats be reassigned as described at the end of the essay, only pointing out the irony that if we want to tilt that teeter totter, (a ‘good thing’, according to 3E Senate advocates), we could do the same process another way, and in doing so, correct Québec’s dwarfed influence as well. The 3E Senate is sold as making things ‘fair’, but one major intent of the 3E Senate is to further reduce Québec’s influence.

      I’m interested to read any ideas you have about revising the Senate, but the objective of ‘correcting regional imbalances’ and ‘adjusting the balance of power’ needs to be strongly defined. Are you aiming for a particular teeter totter tilt? Is that really the problem? I hope to write further on this matter in the future. I have two more chapters on scrap notes waiting to be organized and leap out onto these pages. Soon, soon…

      Thank you again for your time and your thought, your kind words and constructive criticism.

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