Proposal for British Columbia 2018

Keith M. Edmonds & Warren D. Smith; Center for Range Voting, Feb.2018.
For your convenience this entire proposal is available online, with about 90 live hyperlinks to supporting documents, at

Our proposal: Keep British Columbia's current regional constituency system, but change the ballot from plurality voting to score voting, or its simplest form approval voting, to determine the winners.
    We further advise that all member votes inside the Assembly with more than two options, also be conducted with approval or score. This would be particularly useful for electing a Premier and leader of the Opposition from among the members. And if this or future BC referendums offer more than 2 options, it too should be conducted with approval or score – which would have the advantage of helping educate voters about the process being proposed.

  1. Definitions
  2. Typical voter's thinking-process with Approval
  3. Advantages of Score/Approval
  4. Historical experience with Approval & Score
  5. Expert consensus
  6. The Proportional Representation versus Single-Winner debate
  7. How large an improvement are we talking about?
  8. Further reading
  9. About the authors


Plurality voting (also called "first past the post"): your vote is "name one candidate." The most-named one wins. Example vote: "Trudeau."

Approval voting: your vote is "approve or disapprove each candidate." The most-approved one wins. Example vote: "Approve Trudeau & Harper, disapprove Mulroney & Chretien."

Score voting (also called "range voting"): your vote is "award each candidate a score from 0=bad to 9=good." The candidate with greatest average wins. Example vote: "Trudeau=9, Harper=9, Mulroney=3, Chretien=0."

Plurality voting is the (poor) system BC currently uses. Score voting could in principle be used with any pre-agreed set of numerical score-levels, but we prefer the single digits {0,1,2,3,4,5,6,7,8,9} for simplicity and because this was found popular in studies. Approval voting essentially is score voting when there are only two allowed scores (1=approve, 0=disapprove).

There also exist (but we shall not advocate) more-complicated systems based on rank-ordering ballots. We mention, without defining, these two:

Typical voter's thinking process with Approval voting

First, approve your favourite and disapprove your most-disliked candidate. Now, as far as the remaining candidates are concerned, the question is where to draw your personal "dividing line" between the "approved" and "disapproved" ones.

Suppose you were voting in the USA 2000 presidential election. The top three contenders were G.Bush (Republican), A.Gore (Democrat), and R.Nader (Green). It was thought that Nader, with about 1% of the funding, was unlikely to win despite his excellent qualifications.

So in this election, you probably would approve, on average, about 1½ among these 3 candidates.

Advantages of Score (and Approval) versus Plurality & other systems

  1. Ludicrously, with plurality ballots, voters are forced to provide the least possible information – A better democracy should allow voters to provide more information. With approval, they provide 1 bit of information per candidate. With score ballots, even more information: quantitatively how much they like/dislike each candidate.
  2. Plurality encourages even the absurdly small amount of information each voter gives, to be false. E.g. in USA 2000, polling showed over 90% of the voters who honestly thought the Green Party's Ralph Nader was the best candidate, voted (dishonestly) for somebody else. That's because they thought Nader had little chance to win, and did not want to "waste" their vote. A good democracy should not force such enormous numbers of voters to lie, and should not force parties such as the Greens to overcome such enormous (more than 10 to 1!) artificial obstacles. With approval and score, a voter's score for candidate C in no way affects the battle between A vs. B. Hence, you can give your honest opinion of C without fear of "wasting your vote" or hurting A. You never have an incentive to "betray" your favourite candidate by giving a higher score to a candidate you like less. (But unfortunately with STV, IRV, and plurality, favourite-betrayal often is strategically forced.) There is no longer any built-in penalty for approving a third-party candidate.
  3. The decreased importance of "convincing voters you have good chances to win" (which is expensive), as opposed to "convincing them you are good" (comparatively cheap) should decrease the importance of money. Which is good because money corrupts.
  4. Consider the situation where A has "clones" A2 and A3. In the old plurality system, the clones "split the vote" and both lose. That's especially crazy in a situation where either clone by himself would have won, but his very popularity causes the cloning, which makes him lose. With score voting, A is neither harmed nor helped by the presence of clones. "Vote splitting" no longer exists.
  5. Plurality, IRV, and STV each have, at least in some countries (USA, Australian House, Malta) yielded massive 2-party domination which quite probably (since self-reinforcing) is permanent. That's a sad fate for any democracy because the diversity of human thought is greatly diminished by being pigeonholed into exactly two boxes with no other possible views permitted to hold power. We doubt the USA's environment benefited by never permitting any Green Party member to hold a federal seat. There are good reasons (both historical, theoretical, and based on data from polls employing these methods) to suspect that Approval and especially Score can avoid that trap.
    "There is nothing which I dread so much as a division of the republic into two great parties, each arranged under its leader, and concerting measures in opposition to each other. This, in my humble apprehension, is to be dreaded as the greatest political evil under our Constitution."
    – John Adams, Letter to Jonathan Jackson (2 October 1780; reprinted in Works of John Adams, vol. 9, p.511.)
  6. More parties with more chances also should increase voter interest and hence turnout.
  7. Score and especially approval are very simple. Indeed, when you think about it, approval arguably is simpler than plurality voting, because there is no longer any special extra step needed to detect and discard illegal "overvotes." And indeed, polling studies have found lower "spoiled ballot" rates for voters using approval than plurality ballots. (Ranked ballots have the worst rates; plurality the second-worst; score better; and approval the best.) That's important because some corrupt election managers have intentionally encouraged voters to makes ballot-spoiling mistakes in some locales but not others, thus trying to bias the election. Although score might justifiably be thought more complicated than approval, timing experiments have shown voters actually vote faster with score than approval (preferential ballots are the slowest of all), and self-assessed comprehension in polls is actually higher for score than for approval, which in turn is higher than for plurality. Score voting has also been tried successfully by kindergartners, and is used each year by honeybees, despite the relatively low mental capabilities of both.
  8. With plurality voting, an accidental "hanging chad" or illegible mark can cause your vote to be discarded. With range voting, it causes only part of your vote to get discarded (converted to "no opinion") with the rest – your opinions of all the other candidates – still operational.
  9. Both score and approval voting can be counted in precincts – that is, each precinct can compute and publish a concise table of subtotals, and then the central office can determine the election results from those subtotal-tables only. (That's not true for IRV and STV; for them there is no such thing as a "precinct subtotal.") Precinct-countability is a good property to have for election transparency and reliability in the face of, e.g, possible cyberattacks and fraud conspiracies.
  10. A beats-all (also called "Condorcet") candidate is one who would beat every other in one-on-one races. Counterintuitively, in many voting systems, including PR-STV and IRV, "beats all" candidates do not necessarily prevail. (Indeed, thanks to vote-splitting, a "lose to all" candidate can easily win with plurality voting, which plausibly actually happened in Nicaragua's 2006 presidential election!) But S.Brams observed empirically that it is extremely rare for beats-all winners not to win with approval voting. (With score it likely is even rarer.) Why? Well, there is a theorem that, under certain assumptions about strategic voter behaviour, a beats-all candidate (whenever one exists) always wins. Specifically, that happens with this "assumption about voter behaviour": voters always position their personal "dividing line" between approved & disapproved candidates, such that, if A and B are the two candidates that voter reckons most-likely to win, then A and B lie on opposite sides of her line; and the beats-all and possible usurper are the two reckoned most-likely to win.
  11. A voter is "pleasantly surprised" when the election winner is better than she expected. It is a theorem that approval voting (also under certain assumptions about strategic voter behaviour) maximizes the number of pleasantly surprised voters.
  12. Score voting also reduces risk of exact and inexact election-ties.
  13. In computer simulation studies, score voting was found to have the lowest Bayesian regret (BR) among all common single-winner election methods. BR quantitatively measures how much your country's democracy suffers from using a suboptimal election method. We often hear that "democracy" improved over monarchy and feudalism. But by how much? BR enables us to measure such things numerically; and our BR measurements suggest that switching from plurality to score will cause comparable or greater further improvement!
  14. Computer simulations find that some election methods – notably plurality and IRV – artificially favour extremists. In contrast, approval has a pro-centrist bias (at least with some voter behaviours), while score-voting has little or no discernible such bias in either direction.
  15. Referenda and poll studies suggest voters want score voting and would enact it by landslide (≈60%). However they do not want various other systems including IRV and all the systems proposed in previous Canada-reform referenda. The main reason voters rejected all those previous proposals was that they were (i) too complicated and (ii) too great a departure from Canadian current practices. That's why our proposal is very simple and a small change for BC.
  16. Many schemes involve voting for parties rather than candidates. Or, in order to function, insist that each candidate must belong to a named party, and/or assume that parties have certain internal structures. We regard that all as bad. We want electoral laws to work fine even for candidates highly atypical for their party, even if parties self-destruct or merge, people change parties, or candidates not affiliated with any party seek office. We think one of Canada's problems has been the lack of independent thought associated with independent MPs and don't like proposals exacerbating that problem. With approval and score voting, all candidates are treated the same regardless of party (or lack of party).

Historical experience with Approval & Score

Exit poll pseudo-election studies were conducted (with government funding and cooperation), using non-plurality voting systems such as approval, score, and IRV, for the French presidential elections of 2002, 2007, and 2012:

ElectionNumber of candidates Official (2-round plurality)Approval voting Mean # approvedScore votingComments
200216 Chirac 1st, Le Pen 2ndChirac 1st (37%), Jospin 2nd (33%)3.15 ?Chirac & Jospin were clearly the top two with approval, but vote-splitting pathologies put the far-right Le Pen into the runoff instead of Jospin, whereupon he lost 82-18. Le Pen also would have lost enormously to Jospin.
200712 Sarkozy 1st, Royal 2ndBayrou 1st (50%), Sarkozy 2nd (45%)2.33 Bayrou 1st (mean score 3.1 on 1-5 scale), Royal 2nd (2.8)Bayrou clearly would have beaten any rival pairwise. And almost all rank-order-ballot systems would have elected Bayrou. But Sarkozy won both officially, and would have won with IRV. Retrospective polls toward the end of Sarkozy's term showed France believed electing Sarkozy was a mistake and would have (if they could go back in time) preferred Bayrou over Sarkozy by 56-35 landslide.
201210 Hollande 1st, Sarkozy 2nd Hollande 1st (48%), Sarkozy 2nd (40%)2.57 Hollande 1st, Melenchon 2nd (Bayrou also close) Hollande would have beaten any rival pairwise.

The rates of ballot "spoilage" (ballot-invalidating voter errors) in these elections and pseudo-elections were

Election Official round 1 Official round 2 Approval Other
2002 3.38% 5.39% 0.39%
2007 1.44% 4.20% 0.81% 5-level score: 1.1% spoiled. IRV: 7.0% spoiled.
2012 1.92% spoiled+blank 5.82% spoiled+blank 3.1% blank, 0.85% spoiled (total 3.95%) 3-level score: 0.76% blank, 1.07% spoiled (total 1.83%)

Large numbers of approval- and score-style pre-election polls have been conducted in many countries, especially USA. After having examined ≈100 elections in this way we are unaware of any instances where score voting yielded the "wrong" winner, although we do know cases where plurality, IRV, and approval thus-failed. It is common in such poll studies for "third party" candidates to get far (often a factor>10) more votes, relative to the top two parties, with approval than with plurality, and with score voting it is common for them (especially the smaller third parties) to get even more, 10× versus approval is common. In particular in the USA 2000 presidential election, ANES score-voting data showed Nader actually would have defeated Gore, and also beaten Bush, in 2-man races! (Other score-style polls disagreed, but all agreed Nader's vote-totals would have been of the same order as Bush & Gore's.) In any case, officially, Nader got only 2.7%. This demonstrates the enormous distortion plurality voting causes, which hurts democracy. By the end of Bush's terms his approval rating hovered around 65% disapprove, 30% approve. Approval voting uses this common quality metric to elect. In USA 2016, the two most-approved (also highest-mean-score) candidates were B.Sanders & J.Kasich – but neither even made it out of the primaries, causing the presidential election to be between two candidates with record-low approval ratings.

Score voting (∞ levels) was the method used in Ancient Sparta, and 3-level Score in Renaissance Venice. These arguably were the two longest-lasting partly-democratic states in world history, and their success far exceeded what would a priori have been expected. Neither developed either 2- or 1-party domination.

Approval voting in single-winner districts was the method used to elect the parliament of Greece 1864-1926. It appeared to be developing 2-party domination toward the middle of this period, but not at the start or end. In particular near the end of the Approval era Greece elected Eleftherios Venizelos (1864-1936), generally regarded as the greatest Greek statesman/leader during the last 300 years, as prime minister, despite the fact that Venizelos then was leading a previously unempowered and unrepresented political party. Such a changeover would have been unthinkable in the USA or Canada under plurality voting with 2-party domination. Greece appears to have improved greatly during its approval-voting era. But in 1927 it switched to a bicameral PR system and then soon self-destructed.

The United Nations' Secretary General is chosen by approval voting (essentially; there were other rules too, but they seem not to have mattered). No party-like structures seem to have developed.

China's National People's Congress is a multilevel hierarchical structure (levels: towns, counties, provinces, national) which since 1979 has been elected via approval voting (each level is elected by the preceding one, with the bottom-level elections directly by the people). It is unclear how legitimate those elections have been. But what is clear is that 1979 is precisely the year when China suddenly started dramatically outperforming India, and indeed during 1980-2016 exhibited growth, measured by GDP/capita (PPP), exceeding every other country with population≥2 million.

The Catholic Popes were elected via approval voting 1294-1621, but with revotes and extra nominations until somebody attained 2/3 supermajority approval level. Neither 2-party domination nor 1-party centrist tyranny happened. There were a bunch of evolving factions mostly each trying for a permanent takeover to convert the papacy into a hereditary monarchy, and perfectly willing to use extremely corrupt methods to accomplish that. But the voting system successfully stopped that. The Papacy is the longest-lasting elected position on the face of the Earth, and among the religions having a central government, Catholicism has been by far the most successful (just measured in terms of number of people – we are not attempting to judge the relative moral worths or historical helpfulness/not of different religions) and longest-lasting. Our study of this suggests that if they had used either plurality or IRV, the church would have self-destructed.

Expert consensus

Approval is probably the least controversial voting system. In (an approval-style!) poll at the Du Baffy voting procedures workshop in Normandy France July 2010, it was the only one among 18 voting systems enjoying majority-approval among the workshop participants. Meanwhile, plurality voting got zero approval.

Many professional societies of experts "put their money where their mouth is" by enacting approval voting for their own internal elections:

SocietyFoundedNumber of members
AMS, American Mathematical Society 1888 30,000
INFORMS, Institute of Management Science and Operations Research 199512,500 including many Nobel prize winners
MAA, Mathematical Association of America 191532,000
ASA, American Statistical Association 183915,000
Econometric Society 19307,000?; ≈700 elected "fellows"
USA National Academy of Science 1863≈2,300 members & 470 foreign associates; ≈500 Nobelists
Public Choice Society 1963(no formal membership; officers elected by conference attendees)
Social Choice & Welfare society 1984?300

Score voting is used heavily on the internet for rating movies, recipes, products, etc; it also has been used in the Olympics to determine medallists, and by Time Magazine to determine "Person of the Year."

The debate: Proportional Representation versus Single Member Regional systems

Many entire books have been written about (and on both sides of) this debate, which has raged, without resolution, for 150 years. We'll briefly outline what that debate is, and how Approval & Score voting fit into the picture. Our main point is that many PR proponents have suffered from a too-simplistic view, lacking a deeper understanding of to what extent and why PR is a good thing, what its limitations are, and how to get it. Once they do understand that, then they will see that our proposal, even though not PR, probably gives them a great deal of what they want – and indeed helps them more than anything else they can obtain.

What they are.

  1. Single Member Regional: The desire that MPs in parliament be the best representative for the citizens of each constituency.
  2. "Ideal PR": the parliament should consist of the same sort of people – statistically the same composition in terms of opinions/desires (and probably consequently representative for all genders, economic statuses, ages, educations, skills, religions, ethnicities, etc.) – as the electorate.
  3. Real-world PR (as often commonly defined): the parliament should mirror the party composition of the electorate.

Goals 1&2 are both good, but conflict.

Real-world PR. Although many countries have employed supposedly-PR voting systems during the last 150 years, none have even come close to (what we've called) "ideal PR," in the sense that a comparison of the gender balance, economic situations, etc. of parliament versus the electorate quickly reveals large differences. The best any PR system so far has accomplished is to duplicate the party composition of the electorate. [Many PR advocates have developed tunnel vision to the extent they think PR is about parties, even defining it as such. They often do not realize that ideal PR is not about parties at all; and often do not know the Binary Theorem which is its underlying rationale.] Party identity alone is a very crude likeness (e.g, many voters are "70% Tory and 30% Liberal," a reality obliterated from the picture) – inadequate for the Binary Theorem. Further, basing everything on Party merely encourages partisan division rather than cooperation. In Italy that's yielded seemingly perpetual gridlock and oscillation.

Further, in many cases "one" party actually consists of two or more subfactions. PR systems based on named parties do not even try to proportionally represent such subfactions. While candidate-based PR systems could accomplish that, they depend on multiwinner districts, most commonly 3-winner, which only yields very crude approximate proportionality (fractions rounded to 0, 33%, 67%, or 100%). More winners could be employed, but then the ballots become cumbrously large, e.g. with 10 winners there might be 70 candidates.

The debate: which is a better kind of democracy – single-winner-based, or PR-based? Attempts have been made to settle this debate by comparing the two kinds of countries using economic and health statistics... with many such comparisons later being (justifiably) attacked... but to make a long story short we feel that, so far, no clear and convincing statistics-based case has been made for the superiority of either side of the debate. Further, even supposing that in the future (with more statistics) some demonstration of PR's superiority could be produced, then considering that the single-winner countries mainly used (the poor) plurality or occasionally IRV systems instead of (the superior) score voting system, there then still would be plenty of room to suspect that improved single-winner systems could be superior to PR.

Our feeling:

  1. PR systems are usually complicated and/or party-based, while our improved single-winner proposal here is simple and candidate-based.
  2. Every Canada voting-reform referendum 2000-2018 has failed, with the main reason being complexity – to the extent that 2/3 or 3/4 of referendum voters told pollsters they knew essentially nothing about the proposal!
  3. We need to stop failing for the same reason in the same way every time. Instead, learn from this. Ask BC whether it would like the simple and clear improvement of switching to approval or score. Both are so simple that they can and should be completely defined within the wording of the referendum question. No place, ever, has asked that referendum question before. But there is poll data suggesting that if anybody ever did bother to ask, then approval (and especially) score voting would be enacted, the latter even by a large margin.
  4. Neither score nor approval voting (nor IRV, nor BC's present plurality system) are PR. You can see that by considering an election featuring 51% Red voters. It is entirely mathematically possible, with any of these systems, for the Reds to win 100% of the seats – severe disproportionality.
  5. So if Approval or Score are enacted, we expect sometimes disproportional, and sometimes more proportional, results. But overall, the results should become more proportional than now, because small parties no longer are greatly artificially handicapped.
  6. Our proposal thus improves BC with respect to both desires (1) & (2) simultaneously – giving PR proponents a lot of what they want while keeping the advantages of single-member regionality.
Most importantly, the change we propose will lay the groundwork for a possible later switch to a truly-PR system (if then deemed desirable). That's because several good PR systems, superior to most ever used in past history and also superior to all prior failed Canada-reform-proposals, already exist that are based on approval or score-style ballots.
Just one example of that superiority: with STV, giving a candidate a better score can hurt him. Such "non-monotonicity" happens 5 to 16% of the time in 3-candidate 1-winner elections. With such better PR systems as RRV or "harmonic voting," that problem cannot arise.
If PR-advocates foolishly try to get PR immediately, they will fail again (in the same way for the same reason they always fail), hurting their cause by making them look incompetent. But if they, more productively, seek score voting now, then they will get a substantial and clear improvement in quality of democracy, plus also making things more PR than now, plus also enabling a future victory with a future PR system better than those they currently know about.

How large an improvement are we talking about?

Any country or province that enacts score voting will over time accrue large (e.g. economic) advantages versus rivals. As we already said, based on computerized BR measurements, Score's advantage versus Plurality is comparable to the improvement humanity experienced by inventing democracy. How large is that? Compare Canada versus (say) Pakistan and Russia. All were about the same, economically and geographically speaking, 300 years ago. But over those 300 years (and right now), Canada was much more democratic. The result: present-day Canadian GDP/capita is US$42517, while for Pakistan it is US$1468 and Russia US$8748.

Further reading

CRV's website (with over 1000 subpages and a search box) contains a great deal of information about score voting and many other voting systems (much available nowhere else) albeit is continually under construction. CRV was founded in 2005. As of 2018 it has about 300 registered members worldwide.

CRV's subpage discussing possible options for Canada to improve its Federal voting system:

There also is the French-language score-voting website set up by about 10 French political science professors unaffiliated with CRV.

Three books on approval (the third also discusses Score and Bayesian Regret methodology):

S.Brams & P.Fishburn: Approval Voting, Birkhauser, Boston 1983; second ed. Springer 2007.
J-F.Laslier & M.R.Sanver: Handbook on Approval Voting, Springer 2010.
Wm.Poundstone: Gaming the Vote, Hill & Wang 2008.

Brams is a New York University politics professor. In 1990-1991 he was president of the Peace Science Society, and in 2004-2006 of the Public Choice Society (voting methods scientific organization, publishes journal "Public choice"). Laslier in 2009-2012 was Directeur du Laboratoire d'Econometrie de l'Ecole Polytechnique, Paris. Poundstone has written many popular science books.

Some books on the "PR versus majoritarian" Great Debate:

Douglas J. Amy: Real Choices/New Voices: The Case for Proportional Representation Elections in the United States, Columbia Univ. Press, New York, 1993.
Peter Hain: Proportional MISrepresentation, The case against PR in Britain, Wildwood House 1986.
Richard S. Katz: A theory of parties and electoral systems, Johns Hopkins Univ. Press 1980.

About the authors, and how this came to be

Keith M. Edmonds is a BC resident. He has a PhD in physics and is employed as a data scientist. Warren D. Smith is CRV co-founder (PhD applied maths). After Dr. Edmonds wrote a proposal for BC in Feb. 2018 he was told individuals were not supposed to submit them, organizations were; so then he contacted CRV and this document resulted.