Yes, It’s Proportional An introduction to DMP for electoral reform advocates

Canadians interested in electoral reform are becoming aware of a newly invented voting system called Dual Member Proportional, or DMP. What makes DMP stand out is that it’s a form of proportional representation, yet it retains the following widely valued qualities of our current system:

  • The ballot is simple.
  • The ridings are small.
  • All elected representatives are accountable to their local constituents.

Having so much in common with First Past the Post, some electoral reform advocates wonder if Dual Member Proportional is really proportional at all. Are you among them?

This article will fill you in on the core principles, the key people, and the research behind this exciting new option for electoral reform. Read on to see 3 reasons you can be sure that DMP is proportional.

Reason #1: DMP has received support from Elizabeth May.

Elizabeth May is leader of the Green Party of Canada, and MP in a southwestern BC riding. After one of her recent visits to Prince Edward Island, the following appeared in an article in the Journal Pioneer (May 2, 2016):

May encouraged Islanders to vote for the two proportional representational options, dual member and mixed-member electoral systems.

Here’s the context.

This coming November, a province-wide plebiscite will give PEI voters a chance to demand a new electoral system for their provincial legislature. And it looks like they’ll have several options to choose from. An all-party committee recommended that Islanders be asked to indicate their preferences among five voting systems. The image below, taken from the committee’s report, shows what the plebiscite question might look like:


Two of the five options are forms of proportional representation. At the top we have Dual Member Proportional, and 2nd from the bottom is Mixed Member Proportional (specifically Open List MMP; PEI rejected Closed List MMP in the 2005 referendum).

Elizabeth May wants Islanders to respond to the upcoming plebiscite in one of two ways: either by ranking MMP 1st and DMP 2nd (as follows)…


…or by ranking DMP 1st and MMP 2nd (see below).


As long as Islanders rank both DMP and MMP, the votes from the less popular proportional option will ultimately be transferred to the other.

(Update: MMP won the plebiscite after votes transferred from DMP; see the results.)

For those aware of Elizabeth May’s position on electoral reform (see this statement), her expression of support for DMP is strong evidence that it’s proportional. Yet DMP has no party lists, and it gives nothing up in terms of local representation. Instead of 1 representative in each current-size riding, there would be 2 representatives (hence “Dual Member”) in a riding twice as large. Advocates of electoral reform are often surprised that DMP can achieve proportionality with such a small departure from First Past the Post. But here’s another reason you can trust me that DMP is proportional.

Reason #2: DMP’s mechanism for achieving proportionality is clearly explained in a video by PEI activist Anna Keenan.

Anna Keenan is a PEI resident with a background in mathematics and economics. She is also the province’s foremost advocate of DMP, and has produced a 2-minute video explaining how the system works. As we’ll see in the video, there are 3 steps which take place after the votes are counted.

Step 1: Allocate seats to each party based on its share of the popular vote.

Step 2: Award the first seat in each riding to the most locally popular candidate, just like First Past the Post. Seats awarded in this fashion are subtracted from the seats allocated in Step 1.

Step 3: Award each party’s remaining seats to their best performing candidates. A “best performing” candidate is one who received a relatively high percentage of the votes in his/her riding.

Time for the video. If you click PLAY below, you’ll see just a 1-minute clip that illustrates the 3 steps. The example is based on the most recent provincial election in PEI. It should become clear to you how the system produces a proportional result overall, even though only 2 candidates are elected in each riding.

(Click here to watch the entire 2-minute video on Youtube.)

The coloured dots in the video show us that DMP maintains Island-wide proportionality as the 2 seats in every riding are filled. DMP also respects the local votes within each riding.  Let me illustrate.

In a close two-way race at the riding level, both leading candidates are likely to be elected. For example, if the vote shares are as follows…


…the riding will almost certainly end up with both a Liberal representative and a Conservative representative.

If one party wins in a landslide, they are likely to get both seats in the riding. So in this example…


…the Conservatives can be expected to obtain both seats. Under DMP, parties are well-advised to prepare for this possibility by nominating 2 local candidates. Both names appear beside the same circle on the ballot, and an ‘X’ in the circle supports both of them. That’s the only difference between a DMP ballot and the ballots we’re used to with First Past the Post.

In this one last example…


…the votes are fairly evenly distributed. So who gets elected? Well, the NDP received the most votes, so they get the 1st seat. But the 2nd representative is going to depend in part on the votes cast in other ridings. If I had to guess, I’d predict that the Liberal Party’s remaining seats would be awarded to candidates in other ridings, since I expect these other candidates would have received more than 26%. Same with the Conservatives. So the Green Party has good chances to elect a candidate here.

Some might argue that the top 2 candidates in a riding should always be elected. I sympathize with that point of view. And yet, the only compelling reason to even bother changing our electoral system is to make politicians take all voters seriously, and to do that Canada must adopt some form of proportional representation. DMP achieves proportionality by occasionally awarding a seat to the 3rd- or 4th-best candidate in a riding, particularly in ridings where the vote is spread out. Let me point out that by imposing a suitable district threshold, say 5%, candidates with little support will never be elected. Of those candidates who surpass the threshold, DMP inherently favours the best of them.

So now you have two good reasons to believe that DMP is a proportional voting system. But let me throw in one last reason for good measure.

Reason #3: DMP has been thoroughly tested by its inventor, Sean Graham, and others.

Sean Graham is a University of Alberta graduate who hails from Fort McMurray1. He invented DMP in 2013, and now maintains the definitive website on the voting system: On this website, you can find an 80+ page report that elaborates on numerous aspects of the system. You’ll also find several computer simulations of DMP based on actual votes cast in past federal and provincial elections. The pie charts on Sean Graham’s website make it absolutely clear that DMP is proportional.

I should point out that professors, politicians, and elections officials have looked at Sean Graham’s work, and to the best of my knowledge no expert has found any technical flaws. In addition, I happen to know that Anna Keenan has performed a number of simulations on past provincial elections in PEI, which further increases my confidence in the system. But since it doesn’t hurt to have a third set of experiments on something as important as democracy, I did some work on the system myself.

Here’s what I did.

  • First, I went to the Elections Canada Website and downloaded a record of all the votes cast in the 2015 federal election.
  • Next, I came up with a new set of federal-level ridings by looking at the existing boundaries (see my favourite election map) and merging adjacent ridings in pairs.
  • Finally, I wrote my own version of a computer program that simulates an election under DMP, and I ran the program using the 2015 Elections Canada data with the merged ridings.

Here are the results that I obtained:


Canada-wide simulation of DMP based on 2015 federal-level votes

On the left, we see the popular vote across all of Canada in 2015. In the middle, we see how the seats would be distributed under DMP. On the right, we see how the seats actually were distributed under First Past the Post. As is usually the case, the First Past the Post results are embarrassingly dissimilar to the popular vote. But with DMP, every party ends up within 2 percentage points of its fair share of the seats.

The only party noticeably underrepresented by DMP, in my simulation, is the Greens. Let me explain why this happens. Almost all proportional voting systems protect in some way against the proliferation of parties. Typically, small parties face the prospect of complete elimination due to the use of an election threshold (see Wikipedia article). Simply put, any party receiving below a certain percentage of the popular vote is eliminated. In my opinion, DMP works best with a different kind of threshold: a district threshold. This means any candidate receiving below a certain percentage of the local votes is eliminated. A district threshold gives each riding the ability to reject an unpopular candidate. It also requires a party to demonstrate local support in order to get any seats at all.

My simulations use a district threshold of 5%. This threshold eliminates many of the Green Party’s candidates, and that’s why the party doesn’t get its full 3% of the seats. It is perfectly normal, and in many ways desirable, for a proportional system to slightly favour large parties over small parties. What’s important is that small parties have a fair opportunity to grow should they succeed in gaining both local and widespread support.

So now you have 3 reasons to be confident that DMP is a form of proportional representation:

  1. It has received support from Elizabeth May.
  2. We can see how proportionality is achieved.
  3. Simulations by multiple individuals verify that the system functions as intended.

Okay, I get it. DMP is proportional. But why the simple ballot?

Good question.

Before I answer, let me show you just how simple the ballot is. Here’s an example of what it might look like2:


The only difference between a DMP ballot and a First Past the Post ballot is that with DMP, some of the circles will have two candidates’ names beside them instead of one. That’s the only change. You would vote by marking one ‘X’, just like you do now.

But advocates of change don’t necessarily want to keep the ballot that simple. Many desire the ability to rank candidates (STV) or to cast separate votes for local and list candidates (Open List MMP). These comparatively elaborate ballots offer voters more ways to express themselves. In addition, many experts believe that certain systems with elaborate ballots may promote women’s representation in politics, though DMP also has interesting prospects in that regard3. But why does DMP basically keep the existing ballot? Because with DMP, that single ‘X’ would no longer be symbolic, as it is for many voters under First Past the Post. With DMP, every voter has an impact on the popular vote, and hence a potential impact on who gets elected.

It is hard to ignore the reality that there is currently only one major right-wing party at the federal level, but multiple parties regarded as left-wing or center-left. This means that voters on the right of the political spectrum will see less benefit in a ballot that allows them to distribute their support across multiple parties. And this in turn will deepen the harmful yet understandable perception that proportional systems are intended to promote a left-wing agenda. Done right, proportional representation doesn’t advantage either side of the political spectrum. It would give just as much power to conservative voters in urban centers as it would to progressive voters in rural areas. Yet elaborate ballots complicate this message by providing what could be interpreted as a benefit to the political Left, at least in the near future.

Let me summarize.

Convincing Canadians of the need for a more sophisticated ballot is a challenging endeavor, made all the more difficult by the fact that even proportional representation advocates cannot agree on the best ballot type. By contrast, we all agree that every voter should have an influence over how he/she is governed, and DMP grants all voters this fundamental right as effectively as any other proportional system.

Interested in DMP?

DMP was designed in Canada to enhance our democracy while retaining the current system’s most widely approved characteristics:

  • The ballot is simple.
  • The ridings are small.
  • All elected representatives are accountable to their local constituents.

But yes, it’s proportional.

Are you interested in DMP? Do you have any questions? Please take the time to comment below or email me.


  1. Sean Graham was among the 88,000 residents of Fort McMurray who were forced to leave their homes as a wildfire claimed much of the city. I was shocked and saddened to learn of this tragic event, which occurred as this article was being written. To all the people of Fort McMurray and affected areas: my deepest sympathy, and best wishes as you recover and rebuild.
  2. The ballot entries could also be formatted with the party name on top and the candidates numbered below, as recommended by Sean Graham (see His version clearly identifies a party’s 1st and 2nd candidates. Note that the 2nd candidate can only be elected if his/her party wins both of the riding’s seats.
  3. The issue of women’s representation in politics deserves it’s own article, but I’ll try to outline the key points here. First Past the Post is widely regarded as disadvantageous for women because, with a single candidate per riding, parties disproportionately nominate a man. We know that countries with proportional voting systems elect higher percentages of women on average, though some particular voting systems seem to fair better than others in this regard. A common theme in these discussions is the idea that a sufficiently long party list will almost always feature both male and female candidates, and that voters will naturally elect both men and women from such a list if given a chance. However there are many complicating factors at play, such as the shortness of the “party lists” in STV, the single-nominee constituencies in MMP, and the somewhat limited evidence from countries that use STV or the specific variants of MMP being recommended for Canada. DMP is new, so there are no other countries to look at. Yet it strikes me as plausible that with exactly two candidates on every campaign sign, major parties will try to nominate one man and one woman in as many ridings as possible. This may expand opportunities for women to gain name recognition at the local level, which in the long run should improve gender balance among elected representatives.


  1. I have two questions about a feature of DMP as described in
    where you are credited with the concept of a reserve factor.

    First, to which districts are the reserve seats are assigned? (I guess that they are the ones that (necessarily) did not have any 2nd MP assigned to them by the core allocation.)
    Second, compared to a no-reserve allocation, which are the standings of the parties and the ranking of candidates within them that see the most change?
    I expect that it is the smaller parties that suffer the most bumping of top candidates by those of the stronger parties, but it’s not obvious to me that they are helped much by the reserve. Is the reserve meant to deal with some unusual situation (e.g. regional landslide)?

    1. Hi David,

      The reserve factor is possibly the most complicated aspect of DMP. But it works like magic, which is why it is being recommended. It won’t be easy to explain here with no images, but I’ll do my best…

      If you want the Liberals to elect their best candidates, DMP should do that with or without the reserve factor.

      If you want the Conservatives to elect their best candidates, DMP should do that with or without the reserve factor.

      If you want the Green Party (or any small party) to elect their best candidates, DMP should do that, but you really need the reserve factor.

      I think you correctly understood how the reserve factor is applied. Basically, you set aside a few of the top parties’ seats and place them in the reserve. Let’s suppose a total of 2 seats go into the reserve. Once all the other seats get awarded, there will be 2 ridings with one unfilled position. The top parties get these last 2 positions using their reserve seats.

      So what effect does a 2-seat reserve have on the Green Party?

      It means that in order for a Green candidate to be elected, she must perform better than at least 2 other Green Party candidates. As a result, the Green Party will elect better candidates in general. But when Sean Graham re-ran his simulations using the reserve factor, I was surprised at how effective it was at electing top candidates from every party. To understand why it works so well, you need to know a little probably theory. Consider these two math problems.

      Problem 1: There are 10 candidates ranked 1st-best, 2nd-best, 3rd-best, etc. You choose one at random. What is the probability of selecting the worst, 2nd-worst, or 3rd-worst candidate?

      Answer: 1 in 10, 1 in 10, 1 in 10

      Problem 2: There are 10 candidates ranked 1st-best, 2nd-best, 3rd-best, etc. You choose three at random and select the best of them. What is the probability of selecting the worst, 2nd-worst, or 3rd-worst candidate?

      Answer: 0, 0, 1 in 120

      That “1 in 120” result might seem counterintuitive. But to select the 3rd-worst candidate in Problem 2, you would need to randomly select the three worst candidates, which is very unlikely. The point is that the probabilities are being dramatically shifted in favour of the best candidates.

      Back to DMP. When a small party wins seats, it does become a bit hit-or-miss in terms of which candidates they elect…unless you adopt the reserve factor. The reserve factor transforms the odds by electing the best of several candidates when the small party’s seats are awarded. It makes the situation look a lot less like Problem 1, and a lot more like Problem 2, as far as small parties are concerned.

      So to answer your question, the reserve factor is not intended for outlying scenarios. Rather, it addresses a typical scenario where you have parties with varying degrees of support. It is based on the principle that if any party qualifies for seats, they should have a high likelihood of electing their best candidates.

  2. Thanks Rhys,

    Originally I had totally misunderstood the purpose of “reserve” seats — thought that they were the ones to which the better candidates of small parties would be assigned. As I now understand it, they are allocations that are deferred until after the core assignments have been made and frozen in place.

    I then tried to answer my second question by using the Saskatchewan 2015 federal election results to see how the reserve system might work when 14 top-up seats were to be assigned. I calculated that Conservatives and NDP each should get 4 of these seats and the Liberals 6 seats.
    With 0% reserve seats, the Conservatives and NDP each placed their top 4 candidates and the Liberals placed candidates #1, 2, 9, 10, 11, 13.
    At 20% reserve, holding back 2 Conservative seats, 1 NDP and 1 Liberal seat, the result was: Liberals placed candidates 1, 2, 6, 8, 9, 11 while the NDP placed candidates 1, 2, 3, 6 and the Conservatives #1, 2, 3, 5.

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