Tentative suggestion for a voting system for electing the parliament of Canada, 6

Warren D. Smith, October 2015

Here is one concrete tentative system suggestion for Canada. I am putting it here (/CanadaSA6.html) just to serve as a reference point for further discussion. I obtained this system by hybridizing score voting within ridings, with Sainte-Laguë party-list-based top-up, with a pseudo-party consisting of independent candidates to try to remove what otherwise would be unfair pro-party anti-independent biases built into the top-up system. If T=0 our proposal simplifies to become pure score voting to elect MPs in ridings.


  1. Design goals
  2. Defects (and advantages)
  3. Rules of proposed voting system (on a single page)

Design goals

The goal is to elect a W-member parliament, from W-T ridings (0≤T≤W), in such a way that:
  1. The system has two stages. In the first stage, exactly one MP is elected from each riding (hopefully the one that riding considers the best available!); call these the "local" MPs.
  2. In the second stage, a further T "top up" MPs are elected, K per "region." If the values were W=307, T=51, K=3 we'd be imagining Canada divided into W-T=256 "ridings" electing 1 MP each, and also divided (more coarsely) into T/K=17 "regions" each electing K=3 MPs. (Any K≥1 is allowable, albeit I suspect 3≤K≤5 is best. It is not necessary that all the K's be equal, e.g. we could have some regions elect 2 and some 4.)
  3. In such a way as to obtain or approach "proportionality."
  4. System is simple.
  5. The ballots are "ratings style" which allows voters to provide the most possible information, but also (if that voter desires) less.
  6. The system is immune to "candidate cloning."*
  7. Raising a candidate's score on your ballot cannot hurt him*, while lowering it cannot help him* ("monotonicity properties").
  8. The system is "precinct countable," i.e. each precinct could publish a compact table of "subtotals," in such a way that the whole election process could be performed using only these precinct subtotals tables as input.

* Essentially the same asterisks apply as in my first proposal.

Defects (and advantages)

Advantages: It is quite simple. If the "regions" are removed (i.e. make there be only one region, the whole of Canada) it would get even simpler. This system is very similar to the MMP systems currently used by Germany and New Zealand, but with the following differences, all of which seem to be improvements:

  1. Score voting, not (which Germany and New Zealand use) plurality voting, within ridings.
  2. The use of an "independents' (pseudo)party" for Canada to try to redress unfair pro-party anti-independent biases. These have afflicted Germany & New Zealand so severely that New Zealand has never elected any independent MP ever since they adopted MMP in 1996, while Germany elected three in their first MMP election in 1949 and zero ever after.
  3. The use of "regions." The proposed scheme for Canada is "tunable" by adjusting the number of regions and by adjusting the relative numbers of ordinary and top-up seats. These two "knobs" tune how much regionality to have and how much PR to have. Many people believe MPs that exist without regions, are inherently worse. Whether or not you believe that, a second argument for why regionality could be good, is the rain argument.

So if Canada adopted this proposal and tuned it decently, it should become like, but better than, Germany and New Zealand.

The most obvious defect of this proposal (at least in my view) is its reliance on party-labels to provide proportionality. If, say, parties did not exist, everybody ran independent, but some candidates were similar and others dissimilar, then this system would be unable to know anything about those similarities and hence would become totally helpless about proportionality. Also, by explicitly inserting party names into the voting system definition, we become inherently unable to treat independent candidates fairly, and also this system definitely will be severely vulnerable to candidates "gaming the system" by switching parties, creating ad hoc parties, etc. (As a partial cure for that, we create a pseudo-party consisting of all the independents. This is misleading in the sense that independent candidates can be quite dissimilar. But it will counteract some of the global unfairness against independents.) To stop the gaming, it probably would be felt necessary to enact laws forbidding such party switches, but any such anti-switching laws themselves would seem quite damaging! Remember, the ultimate cure for "too-whipped" parties is for unhappy MPs to be able to switch parties.

Another problem with this system: it can be poor voting strategy to honestly top-rate your favorite. If you did, then you might be helping some party to get more top-up seats, except that your vote would be "wasted" for that purpose since they were doomed to get none, or doomed to be unable to move from 1 to 2 seats in your region... hence you would have been better off lying about your favorite to help boost some other party's seat count. The more lying happens in votes, the worse off Canada is going to be.

Neither of those two defects afflicted my first proposal.

Rules of proposed voting system (on a single page)

I will regard voters as "female" and candidates as "male" just to make wording clearer. Various numbers (2, 9, 1000, 3) in our description have been selected pretty arbitrarily and could perfectly well be replaced by other numbers. And we could demand T=⌊W/5⌋, where again "5" is a pretty arbitrary value.

1. Each voter rates each candidate in her riding, on an 0-to-9 numerical scale. (Voters also allowed to leave some candidates unrated, if that voter wishes not to express any opinion about that candidate.) Refinement suggested by J.Quinn: "Any voter who did not explicitly rate any candidates at 0 is considered to have given 0 to any candidates they left blank. Any voter who did rate at least one candidate explicitly at 0 is considered to have expressed 'no opinion' about any candidates they left blank. (I think this rule is the safest way to interpret 'intent of the voter'.)"

2. In each riding, the candidate with the highest average score wins that riding's MP seat. Slight optional refinement: each candidate could receive 1000 artificial scores of 2 before voting begins. Then the candidate with the highest average among both his genuine and artificial scores, wins.

[At this point we have elected W-T of the W seats in Parliament, each via the excellent "score voting" single-winner system. The "top up" now commences, whose mission now is to fill the remaining T seats.]

3. We now compute how many seats each party "deserves" in the full, "topped-up" parliament. This is done by the Sainte-Laguë method: each party's total vote V is the number of voters who rated their candidate top (if a voter had rated K candidates coequal top, then each party gets 1/K share of her vote). We successively assign seats as follows: whichever party has the greatest V/(2S+1) wins the next seat (provided it hasn't run out of candidates). Here V is the votes owned by that party, and S is the number of seats that party's members currently occupy (initial S-values arise from the seats elected in step 2, and increment each time we award a new seat to that party). We keep going in this way until each of the T top-up seats has been assigned a party label. [Each candidate had pre-specified his party label. Parties can expel people by 2/3 supermajority vote.]

[At this point we have elected W-T of the W seats in Parliament, and assigned party labels to the remaining T seats. We now must assign actual people to those T seats.]

4. Each party's candidates are sorted into decreasing order by their average scores they received from the voters in their ridings. We simply elect, from each party deserving S top-up seats, the top S as-yet-unelected members of their list. [Note: independent candidates are regarded for the purposes of steps 3 & 4 as members of the "independents' (pseudo)party."]

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