Finnish electoral reform?

While I was in Estonia this past summer, I heard about an electoral reform in Finland, possibly involving the adoption of a national compensation tier. Perhaps this was in response to some of the unequal treatment of parties in the seat allocation in the “photo Finnish” election of 2007, as I wrote about at the time.

I do not have details of the proposed reform, or certainty that it has even been enacted. Perhaps a reader knows.

Thanks to Suaprazzodi in the Brazil thread for the reminder.

13 thoughts on “Finnish electoral reform?

  1. I was prompted by this to have a look. The reform is only at the committee stage in the Riksdag/Eduskunta, and will in any case not take effect until 2015. The mathematical calculations under this government bill are shown in the .pdf file at the bottom at this page (in Swedish):

    Some quick points:
    – The 15 constituencies remain as now, with separate treatment of the single-member Åland islands.
    – The voters must still vote for one candidate, which then also counts as a list vote. The lists continue to be open.
    – However, a three percent nationwide hurdle (excluding Åland islands votes) is introduced, with no exceptions. The parties may no longer have joint lists.
    – The 199 non-Åland seats are calculated nationally according to the D’Hondt method.
    – The seats of each individual party are then distributed down to the 14 constituencies using a calculation equivalent to the Hare/Niemeyer method previously employed in Germany.
    – However, this is where it gets weird: The constituencies will still have a fixed number of seats according to the latest population figures.
    – Thus, only full Hare quotas are given seats at first. The decimal remainders are then ranked nationwide, and are given seats as long as their parties are entitled to further seats, and as long as their constituencies are entitled to further seats. This would be comparable to Norway or Romania.

    Obviously, there is an inherent clash between the Hare/Niemeyer-like component and the preset number of constituency seats, but they are not irreconcilable. There is also the familiar problem of the last distributed seats having to go to whichever constituencies remain.

    The Pukelsheim/Balinski bi-proportional method was actually considered as an option, but was dismissed as being too complex and as being difficult to describe in legislative language. This is strange, because the provisions in the relevant Swiss cantonal acts are technical, but quite snappy.

  2. The electoral systems are fairly similar in the Nordic countries. But one difference is that Norway, Sweden, Denmark and Iceland have introduced leveling seats, while Finland have not (yet).

  3. Espen, would you happen to have a link to one of these Swiss cantonal acts? (Hopefully one of the French cantons, my German is essentially nonexistent!) I’m curious how they managed to describe a biproportional system, did they actually describe iteratively converging to a biproportional result?

  4. Vasi, unfortunately I found only German text. As far as I know, the system has been adopted in Zürich (in 2003), Aargau and Schaffhausen (in 2008), all German-speaking cantons. Here is a link to the Zürich act (.pdf):$File/161_1.9.03_69.pdf

    The relevant §§ are 101, 103, and particularly 104 which covers the “Unterzuteilung” down to the constituencies (all on page 26). §104, second part, roughly translated:

    “The Direktion [election authority] establishes a constituency divisor for each constituency and a list group divisor for each list group [party], so that the rounding process yields
    a. the prescribed number of seats for each constituency, and
    b. the number of seats previously calculated for each list group.”

    A naïve reading of the text would appear to give the electoral authority much leeway, which is true in the details, but in practice the process of corrective iterations (which I see no explicit reference to) would result in one optimal distribution of seats. For the theoretical possibility (?) of there being multiple solutions, the lot is decisive. If lists, votes and seats are so mismatched that a solution is impossible, by-elections seem to be the way out.

    The Schaffhausen act is almost identical, but refers explicitly to the method as the “doppeltproportionale Sitzzuteilungsverfahren”, and gives the executive some rulemaking authority.

    By the way, when I wrote last night that Hare/Niemeyer could be reconciled with a fixed number of constituency seats, I should have clarified that in some extreme cases this would have to be done by providing for exceptions to those rules, which the Finnish bill does.

  5. Thanks Espen!

    Multiple solutions are possible only in the case of ties, in which case there’s no choice but to decide by lot. I don’t think that’s unreasonable.

    I’m confused by the use of by-elections if no solution exists. Lack of a solution should mean that none of the seats are allocated, so would they have by-elections in every single constituency? Or perhaps they mean they’d find a solution restricted to some subset of the constituencies, and the remainder would have by-elections?

    A thought about an alternative: Solutions can be impossible only when some parties have zero votes in particular districts. So why not forget about by-elections, and just give each party a minimum of one vote per district, perhaps subtracted from their vote totals in other districts?

    In any case, I’m also curious whether they have any restrictions in place to prevent seemingly perverse results. Sometimes a party can get more seats in a district than a party with more votes in that particular district, and some might consider that a problem.

  6. Vasi,

    Would there not in terms of raw votes have to be ties on several levels simultaneously, or at least an extremely unlucky confluence of several factors in the subsequent calculation? I am aware that the iterations tend to loop between a few non-solutions, but slowly a solution will emerge as the first, which would then also be the most proper solution. I am however also aware of a version of the biproportional system that intentionally creates ties, developed by the Norwegian mathematician Aanund Hylland (, but I as a non-mathematician have never really understood his explanation of it. Are the mathematical properties of the biproportional system really fully explored?

    On the Zürich law: In a scenario where a party has received more seats than there are total seats in constituencies in which it has stood, a mismatch which is highly unlikely, the law would appear to give no other solution than the default procedure for filling vacancies when there are no more candidates in reserve to fill them, i.e. by-elections. These would then be held in the other constituencies, whose seats by definition could not have been filled entirely at the regular election.

    I would be opposed to the suggestion in your third paragraph – the system is robust enough that it can handle such scenarios (except in the above case) – more so than any other system with fixed constituency seats, no other seats, and total proportionality. Also, no votes presumably means no local candidates to fill those seats.

    Lastly, it seems to me that having restrictions on a smaller party receiving more seats than a bigger party in the same constituency would render the system completely self-defeating. If this is seen as a problem, the biproportional system should not be adopted in the first place. In most such cases the gap between the parties would be small.

    Now, it is possible to change the rounding mechanism. Rounding up decimals .5 and higher to one more seat mimics the Ste.-Laguë method. If the first seat would have to be won with a decimal of 0.7 and higher, this would be the equivalent of using the Nordic 1.4 first divisor. Rounding all decimals downward would mimic D’Hondt. Increasingly, these measures would tend to lump a party’s seats together in their strongest constituencies, while reducing the possibility of constituency seats being won with few votes. However, these would be artificial distortions that could adversely affect parties that are small everywhere.

  7. Espen,

    With respect to ties, they are unlikely, but they can happen even without a “horrible confluence”. Obviously ties in super-apportionment will be at least as likely as ties in non-subdistricted PR. There are also degenerate cases, such as when two independents exactly split the vote in an odd-mandate constituency. In any case, decide-by-lot is quite reasonable.

    Good point about lack of local candidates in the impossible-apportionment case. Still, if a party P wins more seats than the sole constituency C in which it ran can provide, does it really make sense to hold by-elections for all seats in every other constituency? Maybe we could partition the election into (constituency C and party P) and (all other constituencies and parties), and apportion in each partition. This would at least get as close to biproportionality as we can, while going to by-elections would remove any inter-constituency balancing.

    As to preventing perverse results, apparently the program BAZI can do biproportional-apportionment-with-restrictions. In the data file faroer2004minRestr.bazi within the BAZI distribution, the party Sambandsflokkurin receives a plurality in Norðstreymoyar district, but none of the seats there. The authors propose adding the restriction that the plurality winner in each district should receive at least one seat there, with all the other seats adjusting to accommodate this while remaining almost-biproportional.

  8. Vasi,

    I meant only for by-elections to fill those seats left unfilled at the original election, which in your example would be of a number equal to the seats of P minus the seats of C. These unfilled seats would be sprinkled across the other constituencies as remainders after the first iteration which gave the other parties all their seats and left no constituencies over-represented. Note that this is only my interpretation of what would happen, since the law is silent and would seem to leave only this default option. Such an outcome would indeed be inconsistent with biproportional logic, and certainly better models such as yours can be devised (what would BAZI do?). Of course, that would entail adding more complexity to the law, for an extreme scenario which could only happen as a result of gross malapportionment or vastly divergent turnouts, combined with parties for some reason only standing in some constituencies.

    I agree that the lot is reasonable as a last resort. I was really only referring above to the sub-apportionment, and there you of course have a good point regarding tied independents.

    Thank you for pointing out that the BAZI program has been updated. I will take a look at it. Adding restrictions would seem to me to mainly shift distortions elsewhere, increasing them in the process. However, if there is a clear view that certain kinds of apparent flaws must be avoided, then that should be done as long as the downside is acceptable. Your Faeroese case is a very good one. I am however still unconvinced that all cases of parties receiving fewer seats than slightly smaller parties in the same constituencies could be avoided, at least without creating flawed solutions that would be much more noticeable and possibly more frequent.

    Thank you also, Bancki, for pointing out that paper, which is of a later date than my investigations into this stuff.

  9. Espen,

    Sorry for the confusion about by-elections. However, I’m not certain your interpretation is in fact feasible. When biproportional allotment fails, the relevant algorithms do not yield partial results, so far as I’ve been able to ascertain. I took a look at BAZI’s samples of data with no solution, and indeed it simply fails and reports The biproportional method is not applicable since the sum of seats in “Distrikt 3” is smaller (15) than what is needed there by “[Party] =4=” (38).

    You’re correct that adding restrictions does cause distortions elsewhere, it’s a trade off. Also correct is that there’s no way of always avoiding parties receiving fewer seats than smaller parties. The constraint I mentioned last time, what the 2007 paper calls Strongest Party Constrained, is much less ambitious. It simply ensures that the strongest party in each district receives at least one seat there. There’s no guarantee that it will receive the plurality of seats in that district, nor that other parties won’t end up mis-ordered.

    My thanks too to Bancki, that paper has a much clearer explanation of the tie-and-transfer algorithm than I’d been able to find before.

  10. Well, this would be a programming flaw, probably resulting from a lack of a standard solution to this problem in Pukelsheim’s basic model. I recommend sometimes doing the calculations manually, say in Excel. Only a simple weighing matrix is needed, along with rounded checksums in both directions. There is nothing better for observing what is going on, and although it can take a little while to go through the several full iterations, otherwise one can be less constrained.

    A special method for finding the most apt constituency seats to leave vacant would then be to deliberately only readjust the constituency divisors when there is an excess of seats. It occurs to me as I write that it may be a problem that there are no legal standards on how far to adjust the divisors during the iterations, and in which direction to begin the adjustments. I am unclear on if the mathematical evidence absolutely excludes the possibility of different standards here yielding different results as far as determining which vacancies to create. However, if this is a problem, there is one final way out that would be consistent with the text of the Swiss laws: Decide by lot which seats to leave vacant, then run a normal biproportional calculation, but with fewer constituency seats. The seats of your party P would then also have to be lowered accordingly, probably by entering a proportionately lower vote for it into BAZI.

  11. If you have a primary that will mainly rank the party’s candidates, you could establish the following idea for the general election.

    According to the order of candidates, each candidate will receive a share of the party vote. A candidate that was listed 10th, in a 10-seat district, will get 0.1 points of the party vote in that particular district for example. A candidate listed 1st will get 1 point of the party vote.

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