“Votes that count” in different electoral systems

Throughout the discussion on electoral-system reform in Canada, I have seen various social-media posts that purport to compare the percentage of votes that “count” in Canada vs. in existing PR systems. Typically, these posts will cite a figure of 50% of votes counting in Canada and 95% or more in PR countries.

The numbers seemed fishy to me. I do not doubt that votes are substantially more likely to “count” towards election of a representative under PR than under FPTP or other majoritarian systems. But the 95% figure seemed too high.

As I happen to have a dataset of district-level electoral results in many countries at my disposal, it was not too hard to subject the claim to a test. The harder part is knowing how to operationalize “count”. I chose two methods, based on my understanding of the complaint that reform advocates have against FPTP. The problem, it will be seen, as I suspect both methods are being used by these advocates, but different methods for different systems.

The first method is the one that I believe they are applying to Canada, which is: “did my vote contribute to the election of someone in my district?” Guess what–when your district elects one, for many voters the answer is “no”. (And this may be sufficient reason to want to ditch the system!) The second method is one that I suspect the authors of these posts apply when looking at PR systems: “Did the party I voted for win representation?” That is, I suspect a district-level standard is being applied to FPTP, but a national-level one to PR countries. My calculations seem to bear that out.

If we use the first method–district-level count of votes for parties (or candidates) that did not win in the district, we almost nail the 50% figure for the most recent Canadian election for which I have data. In 2011, I get 50.4% of votes across the country “counting” in the sense that they were cast for the winner in the voter’s district.

Across the 25 FPTP elections for which I have complete data, the average figure is 55.8%. The lowest figures are around 47% in several UK and Indian elections, with the highest being 62% or more in the US and Barbados. (What do these latter two countries have in common? Very few votes going to parties other than the top two.)

I then apply that same standard to PR systems. A pause is needed here. Canada is very highly unlikely to adopt nationwide PR, either with a single national district (which I think we can say is politically and constitutionally impossible) or with districts but also nationwide compensation (as in Germany or Denmark, among others). Thus I consider the relevant metric to be those PR systems that employ districts, plural, and no nationwide compensation.

Using the same standard–votes “count” when cast for a party that wins a seat in the district–the mean for (districted) PR systems is 87.2%. That figure is a lot higher than 50%, I will grant. It is also a good deal lower than 95%.

If we look at nationwide (single-district) PR, guess what? 96.5%! A few specific elections come in at 99%, such as the Netherlands, 2002, and Israel, 1951. (Most Israeli and Dutch elections are over 97%, but Netherlands, 1952, was at a paltry 94.7%.) That’s great! However, most PR advocates, unless they are real purists (and not at all realists) do not advocate the adoption of the Dutch or Israeli type of PR.

What about the second standard? Under this one, your vote “counts” if it was cast for a party that won representation somewhere (at least one seat), even if it did not win in your district. As I noted above, I suspect this is the standard being applied, at least implicitly, to the PR countries in the social-media posts I have seen.

By this standard, districted PR systems’ average percentage of votes that count rises to 93.7%. We are almost to 95%! For nationwide PR, it obviously does not change (there’s only one district). What about for FPTP? 97.1%. Canada, 2011, comes in at 99.1%.

I do not actually know if a Canadian voter feels “represented” if she voted NDP but the NDP candidate in her district lost. I suspect many do feel so represented, or else the NDP would not get more than trivial vote shares in districts where it has no chance of winning. Yet it does. Greens can also get votes near or above their nationwide percentage even in many districts that are totally hopeless for them. Perhaps they feel represented by Elizabeth May (the one Green MP) even if they reside in a different district or province. Not as well represented as if their own MP was Green, presumably, but my point is that voters probably tend to think of national party systems when voting, even in districted systems. Yes, even in systems in which districts have one seat apiece.

There may be many reasons to prefer PR over FPTP. I can think of quite a few myself. But the idea of a vote “counting” towards representation may not be one of the more meaningful criteria to use. Or, if it is used, it might be OK not to exaggerate. The difference between 50% (Canada, 2011) and 87% (mean for districted PR) is impressive enough, using the first (district-based) criterion. We don’t need to pretend that twice as many votes “count” under PR as under FPTP. 1.74 times as many is still a lot more!

24 thoughts on ““Votes that count” in different electoral systems

  1. One view of “wasted votes” is that a vote is wasted if it did not contribute towards the election of an MP for the preferred party. Put another way: “there is no way to order the counting of votes such that my vote is the one which gives my party its last elected member.”

    Under pure PR or MMP, the wasted votes are for parties that fail to reach a regional (formal or de facto) threshold or fractional left-overs after PR seats have been allocated. The wastage will depend upon the number of smallish parties and the design parameters of the system. (I must admit to being a co-author of a brief that (rashly?) estimates 5-10% wasted votes for MMP with a total of about 25 Canadian regions/provinces.)

    This definition does not count as wasted those votes that are surplus to requirement in election of a member. STV would score well if such votes are moved into the “wasted” column.


    • “a vote is wasted if it did not contribute towards the election of an MP for the preferred party” would be my second method of calculation, if I understand correctly. But by that standard, Canada in 2011 was already at 99% not wasted.

      Your definition of wasted votes under “pure” PR, which I will take to mean nationwide PR, would be correct. It is (mostly) governed by the threshold. Same, with some possible complications arising from local parties, for MMP, if compensation is nationwide.


      • My definition was intended to be closer to the first method of calculation. That is, under FPTP the elector’s vote “contributes” only within the local district. Under MMP or PR with many regions it would be wasted unless contributing to election of an MP from within the region. So, much less than 99% non wastage in the 2011 election.


  2. Canadian PR activists have also often given simulated PR results that seem based on nationwide PR (very unrealistic for Canada constitutionally as well as politically), with the Greens winning seats completely proportionate to their nationwide vote percentage, despite the fact that under many PR systems, they would not have achieved any representation, having received less than 4% of the vote.


    • Yes, that is partly what inspired this. Most of the statements about what would happen under PR have the (implicit) assumption of nationwide. It is even more egregious for the BQ, which of course, would not get its national proportionate share. (It has sometimes been overrepresented under FPTP.)

      The Greens do well enough in BC and parts of Ontario that I think there’s little doubt they’d get seats under even a pretty low-magnitude PR system. But not necessarily commensurate to their nationwide vote share.


      • Of course, it’s worth noting that if voters were free of the tactical pressures they are currently under, the vote for the Greens and other minor parties could increase. I recall reading a paper that used data from an online survey from the 2011 Ontario election that showed that the Green vote would go from 3% to 7%, and the general ‘other’ vote would go from 1% to 6% under a proportional system (although, admittedly, this was obviously a sample of people who had some understanding of proportional representation, given that it was an opt-in survey). So these two factors might balance each other out.


      • That may be assumed outside Canada, but not here. Proportionality cannot be calculated in regions larger than a province. Furthermore, if we had a 4% or 5% threshold it would very likely be applied province-by-province as Germany did at first. The Greens would pass the threshold in BC easily, but would struggle to meet a 5% threshold in Quebec.


      • Wilf, to be clear as to what I mean, it is assumed, at least implicitly, in various social-media memes I have seen from Canada. In fact, almost all of them, including one posted on a page we both follow just today. The one in question said that if the Liberals got 39% of the vote under a system in which “every vote counts”, they would have 39% of the seats. Even with pure nationwide PR, that is not strictly true. But given that in Canada, for the reasons you note, there won’t be nationwide calculation of PR, there will be some disproportionality even beyond the usual large-party bonus that even the Dutch and Israeli systems produce.

        I realize it may be hard for advocates to say something like “39% will get you about 42.5% of the seats” (a figure I just completely made up). But the discourse is written AS IF it were nationwide PR, even though it can’t be.


      • Wilf, I don’t think I said that proportionality would be calculated in regions larger than a province. What I meant was that while a calculation assuming nationwide proportionality would not be totally accurate, neither would a calculation showing the Greens missing the threshold in most provinces, given that voters would no longer be tactically required to support their personal ‘lesser of two evils’.


      • Perfect province-wide proportionality would give the Liberals 40.5% of the seats on 39.5% of the 2015 vote. This is because 0.8% of the votes were for “other than the five parties,” and also because the Liberals still win the three single seats in the three Territories. So province-by-province does not create significant distortion compared with national compensation. As for various actual models, I have one I use that gives the Liberals the same 40.5%, another that gives them 41.7%, another at 42.0%, and a deliberately moderate one that gives them 42.9% (no threshold, but an average top-up region size of only eight MPs). So your completely made up number of “about 42.5%” was, as one would expect, not out of line.


    • Simulating an absolutely proportional result may be a disadvantage. Anecdotally, the average undecided citizen may see the unfairness in the party winning zero, one or two seats for 20-25% of the votes, but is also troubled by a party with 1% winning 3 seats out of 300 and potentially ‘wagging the dog”. These voters tend to be reassured that there are thresholds – explicit and/or due to regional districting – that keep out the micro parties.
      Not only does 1% seem to be too low to worry about – and certainly too low to entrust with a potential balance of power if the majors end up in a dead heat, something that is unrelated to the electoral strength of the minor party – but (a) it seems arbitrary to have the threshold for a “serious” party reduce as the assembly expands according to population (why should 0.5 miss out on representation when the assembly has 150 seats, but become deserving when the assembly grows to 250 seats?) and (b) a small absolute number of members in a minor party caucus leaves them vulnerable to personal feuds (see: Democrats, the Australian) or to a single mini-dictatorial figure (see: Healey Rae, Jackie). Watching how the Call to Australia team in the NSW Legislative Council basically ended up as the Nile Family when not at prayer suggests to me that if a minor party is going to hold a balance of power, you want its caucus to be large enough in absolute terms to get some genetic diversity.


      • I submit that are effective way of ensuring genetic diversity is for the constitution to require minimum standards of democracy in political parties. Germany provides:

        1. Political parties shall participate in the formation of the political will of the people. They may be freely established. Their internal organisation must conform to democratic principles. They must publicly account for their assets and for the sources and use of their funds.
        2. Parties that, by reason of their aims or the behaviour of their adherents, seek to undermine or abolish the free democratic basic order or to endanger the existence of the Federal Republic of Germany shall be unconstitutional. The Federal Constitutional Court shall rule on the question of unconstitutionality.
        3. Details shall be regulated by federal laws.


    • Henry, you noted that “it’s worth noting that if voters were free of the tactical pressures they are currently under, the vote for the Greens and other minor parties could increase.”

      Yes, absolutely. That is why by one of the measures I use (the second one), there is not that much difference across electoral systems. When few people feel there is any point of voting for a party, few vote for it, and so fewer votes fall to “count”.

      Or another way of putting it: to a substantial degree, votes adjust to seats.


  3. Clarifying a point. I say, ” voters probably tend to think of national party systems when voting, even in districted systems” (even M=1). This obviously is not the case for someone who votes for a regional party, such as the BQ. The point still could hold, but on a provincial scale. You don’t have to live in a district the BQ is likely to win to feel “represented” by your vote for the BQ.


  4. I think that many voters could feel “represented” by an MP elected in another riding (for example, Green supporters feeling that Elizabeth May represents their views) but at the same time feel that their SMC vote “didn’t count” if they voted for a candidate who didn’t get elected. That is, the “representation” is done, not by their vote, but by other MPs (elected elsewhere in the region, province or nation).

    Whatever the definition of “a vote that counts”, it is correct to argue that an estimate of wasted votes must assume reasonable sizes for PR regions.


  5. The discussion in Canada is about ineffective votes, votes that do not count to help elect anyone. Some people call them “wasted votes” which is often counter-productive, when some civic enthusiast complains that getting off your ass and voting is never a waste of time even your vote turns out to have been ineffective at a given time.

    Ineffective votes are currently counted riding-by-riding. In a country like Sweden, any vote for a party getting over 4% is never ineffective. Occasionally a vote for a party in a given district might elect one MP even if the party falls below 4% (one Christian Democrat in 1985). I would add the CDU votes in that district to the total votes for parties meeting the threshold in the total of “votes that counted.” In Sweden’s 2014 election 96% of votes counted. In 2010 98.6% of votes counted in Sweden. In Canada it is usually just below 50%.


    • Yes, because Sweden has nationwide compensation. As we’ve discussed elsewhere, that is unlikely in Canada.

      On the “wasted votes:, years ago (2001, to be precise) I gave some talks at local League of Women Voters chapters about alternative electoral systems. They were interested after the 2000 debacle in the US presidential contest, so I took the opportunity to teach about STV, MMP, etc.. in addition to other ways to elect the president. At one meeting, I had an objection raised to the concept of “wasted votes” because the nice lady could just not believe any vote was wasted. It is the civic activity that counted for her, not the votes-seats translation. I actually found that refreshing, because it is easy for me, in my academic cocoon, to think that “seats and votes” are all that matter! So our experience on that is the same, apparently.

      This, by the way, is why I preferred in the post to focus on the positive side of “counting”, which I felt had the connotation of there being some calculation of votes-seats relations, rather than from the negative side of whether it was a waste of some sort to have voted as one did.


  6. Sorry to resurrect an old thread, but would not the % of wasted votes be related to the effective threshold of exclusion? So roughly 50% for DM of 1, 33% for DM 2, etc etc?


    • Plantings never die in the virtual orchard!

      Theoretically, it should be related somehow, but thresholds of this sort are not as straightforward as that. What I did and reported in the post was simply to tote up the actual votes and seats, via the two methods I sketched (one by district level votes and seats, the other by nationwide party votes and seats).

      In other words, it was a purely empirical exercise. It should be possible to connect these output indicators to specific institutional features (M, S, etc.). That could be an interesting extension.


      • Do you still have the dataset handy by any chance? I would be curious to take a look.

        I should probably reread Taagepera’s paper on effective thresholds, as I would think a similar approach would be relevant


        • Do you use Stata? It was a Stata DO file working off one of my standard district-level data files.

          I have an Excel sheet with the summary data, but I am not sure how helpful it would be on its own.


        • I don’t use Stata, but I believe I can convert Stata files using R? So by all means I would appreciate the Stata file.

          Looking at those data sets, am I correct in reading it as only recording the top 5 vote getting parties?


        • All parties are in the original, which is mostly from the CLEA project (one line per party-district-election). It may be that only the top five in a district are indicated with a code in the dataset we uploaded (which is one line per district with mostly summary indicators–an important detail I had forgotten).

          A Stata DO file is just a text file. It could be re-jiggered for R. Obviously the commands are all different, so it is not straightforward. I’ve done the reverse at times, so if I can do it…

          The data file, of course, can be saved as a CSV (you’d be better off using my original than the ones we uploaded, and I have no objection to sharing).

          Send me an email (I think we’ve been in contact before, or it is available elsewhere on this site) and I will contact you with the materials.


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