Tag Archives: MMP

Strategic overhangs and ways to prevent them in MMP systems

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In mixed-member proportional (MMP) electoral systems, an “overhang” seat can result if a party wins more seats via the nominal tier (of, typically, single-seat districts) than it would be entitled to if a regular proportional-representation (PR) system were used (i.e, one lacking a nominal tier, whether proportionality is jurisdiction wide or calculated region-by-region). Sometimes these excess seats come about simply because one of the parties happens to be strong enough to win a lot of district races–usually decided by plurality–against a fragmented set of opponents. Such a case occurred in the recent election in Baden-Württemberg. Sometimes one or more overhangs occurs because some small party wins one or more district contests but gets such a small list-vote share that it would not have won so many seats (or any at all) under a standard PR system. Such cases have happened several times in New Zealand and a few times at the federal level in Germany,

The case of a party dominating the nominal tier is not a strategic choice by the party, at least not in the sense that I would understand party strategy. It is not really the party’s fault if it happens to have broad enough support to win a lot of districts. However, the case of a smaller party winning overhangs might be strategic. That is, it might be seeking district wins as part of a plan to boost the seat total of a group of two or more parties beyond what the bloc’s actual support level is in terms of the list votes. A party can do this by entering candidates in one or more key seats where it might win, while encouraging its voters to give their list vote to some larger allied party. Many critics of MMP would say the this sort of strategy is a “rort”–a way of manipulating the system for advantage by undermining the system’s design goal of proportionality. (I am not necessarily making that argument myself, and there may be cases that are manipulation and others that are not, by whatever standard we might choose to apply. For one example much discussed at the time, see the “Tea tape scandal.”)

There is, of course, another type of strategy that I think almost anyone would agree is manipulation–the case where a major party sets up a “decoy list,” and encourages voters to vote for its district candidate and its decoy list. This strategy, if successful, actually converts the MMP system into a majoritarian system: the big party wins its typical large haul of the nominal seats and the decoy wins seats off the list as if it were an independent party. Because the main party and its decoy are technically separate parties, the decoy wins compensatory seats that are not limited by the “entitlement” of the main party, but rather as if it was a party that failed to win district seats and therefore is entitled to a large chunk of of the compensation tier. This has happened in one election in Lesotho (which occasioned a long and interesting comment thread here about how to prevent this), and one in Albania. It also has happened in South Korea recently, although that system is not strictly MMP.1 (I am going to put up a separate new post with some detail on these incidents in Albania and Lesotho.)

Whenever MMP is proposed, among the questions that come up are how you cope with overhangs (the preceding post deals with this question in some detail), and how can you prevent strategic manipulation of the overhang provision?

A post by Craig Rikihana from last December caught my attention on these points for sketching out a case of a potential “overhang gambit” in the upcoming 2026 election in New Zealand. (If you are not familiar with how MMP works or how it came about in New Zealand, he offers useful overviews of these points as well.) The “gambit” concerns the Maori Party and the special constituencies within the system’s nominal tier in which voters who register on the separate Maori voter roll cast their district votes. The party leader is hoping to win up to six of the Maori seats,2 “while deliberately keeping the nationwide party vote for Te Pāti Māori low.” Rikihana goes on, “This alters the mathematics of government. A major party needing TPM’s seats to reach a majority in a 123-seat Parliament (where 62 are needed) must negotiate from a position of weakness. The overhang makes TPM’s support more costly and valuable.”

Something like this has happened before, although perhaps Rikihana is claiming it was somehow less deliberate or less a “gambit.” For instance, in 2008, the Maori Party won five electorate seats but its 2.4% of the list vote would not have entitled it to any seats had it not won at least one nominal-tier seat. The threshold in New Zealand is 5% of the party vote or at least one electorate plurality. By winning one electorate, a party is then eligible for full compensation if it has a party vote sufficient for additional seats; 2.4% would have entitled the party to three seats (again, conditional on having won an electorate). However, by doing so well at the electorate level, it won five. Under New Zealand’s procedure for dealing with overhangs, this meant adding seats to parliament so that other parties do not have their total number of seats reduced. Parliament in 2008 thus increased from its baseline 120 seats to 122. National, the major center-right party, won a total of 58 seats and its main ideological ally, ACT, won 5. These 63 seats actually would have been sufficient for a majority regardless of the Maori Party overhangs. The latter party’s five seats, however, made it an attractive additional partner for National (reducing the leverage of ACT) and it was brought in as a party having “ministers outside cabinet” as is often practiced in New Zealand since MMP was adopted.

If we were to condemn the ambitions of the Maori Party to win multiple overhangs and the potential thereby to make itself pivotal through such a strategy–and again, I am not engaging in any such condemnation–then we might ask what could be done to prevent it. Rikihana claims this gambit is “unique” to New Zealand. He says that other MMP systems “add “balance seats” to fully compensate for overhangs, neutralising any leverage.” It is true, of course, that Germany’s recent MMP systems have allowed the Bundestag to increase greatly in size if needed to restore full proportionality. This was also the case in the recent Baden-Württemberg election, as outlined in the preceding planting. (Remember that this is no longer done at the federal level in Germany, and in fact due to other changes, that system no longer should be considered MMP.)

But is he right about Wales and Scotland?3 I am not aware of any such provisions. In Scotland, every election since the current Scottish Parliament and its electoral system were established has had 129 seats, 73 single-seat districts, and 56 compensatory list seats (determined in regional compensation districts, not Scotland-wide). Overhangs are actually quite common in Scotland, as I define the term. Again, an overhang is any seat a party wins in the nominal tier that puts it over its proportional entitlement. (It is not the seat added to an expanded parliament to counter any such overhang, if the rules call for such a procedure, although the term is sometimes used that way.) Scotland actually has often seen overhangs, inasmuch as the Scottish National Party has been so strong at the district level that it often wins considerably more seats than it would win if the regions were multi-seat PR districts with no single-seat constituencies within them. For instance, in 2011, the SNP won over 70% of the constituency seats on 45.4% of the nominal vote. The party also won 16 lists seats (because there were compensation areas where it had been underrepresented within that region), so it had 69 of the 129 seats (53.5%) despite having won only 44.0% of the party list vote. No “balance” seats were added to prevent such a substantial overrepresentation.

Similarly, every election in Wales under its former MMP system had exactly 60 seats elected. No seats have ever been added to deal with overhangs. As recently as 2021, the leading party (Labour) won 27 of the 40 constituencies despite only 36.17% of the list votes, an obvious overrepresentation that was compensated only to the extent possible under the fixed number of seats available from the list tier. (Similar to Scotland, in Wales the compensation is carried out in regions; Labour also won 3 list seats in 2021.) It should be noted that Wales will no longer use MMP in the upcoming election.

This factual error about “balance” seats in Scotland and Wales notwithstanding, I do not know if there have been cases of “overhang gambits” in elections in these jurisdictions. We had a discussion about some potential “gaming” prior to the 2021 election in Scotland. I was doubtful that the case counted as manipulation, but it did raise some eyebrows. The party that led to the concern, Alba, ended up winning no seats. So if it was a gambit, it was a failed one.

If readers know of other cases in either Wales or Scotland (or London, which also has MMP) in which there was an “overhang gambit,” successful or otherwise, I’d be grateful for the primer. Also, do these jurisdictions have any specific provisions in law or administrative practice that would prevent strategic overhangs, decoy lists, or other obvious or alleged manipulations? It is not clear precisely how one would prevent this sort of alleged manipulation of MMP that comes from small parties seeking seats beyond their proportional entitlement. Such strategies are perhaps inherent in the system. As I have alluded to with respect to the Scottish case, it is not even clear that this sort of strategic overhang is an actual problem needing a fix. In that sense, it is different from the issue of decoy lists, which do seem like a straightforward manipulation, but also one that may have fixes that can be implemented within the context of MMP rules.

In his blog post, Rikihana claims that in Lesotho “overhangs are common and uncompensated” but are “incidental,” rather than a “crafted strategy.” This is, of course, incorrect with regard to one specific election. The case in Lesotho in 2007 was a classic decoy-list strategy. Its occurrence led to the two-vote MMP system being changed before the next election to a single-vote version: now there is no separate list vote, but instead the votes for candidates are accumulated across districts to arrive at list totals for purposes of determining compensation seats. This is a different response from the one taken in Albania, where MMP was abolished entirely in favor of a simple districted list-PR system, since 2009.

Because this post has already become rather long, I will make a separate one with some details about the decoy list strategies in Albania and Lesotho.

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  1. There is also the case of a former system in Italy, used in 1994–2001, but that also was not MMP, and the setting up of allied parties there was occasioned by a specific feature of that system. ↩︎
  2. The total number of such seats depends on how many voters opt to register on the Maori roll. In 2023 there were seven Maori seats. ↩︎
  3. Terminology note: In Wales and Scotland, what I would call a variety of MMP is referred to as an “additional member system.” I dislike this term and do not use it. The list seats are not “additional”; they are compensatory. ↩︎

Tie for coalition parties in Baden-Württemberg 2026, and the varieties of MMP

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The German state of Baden-Württemberg held its state legislative election this past Sunday, 8 March 2026. The incumbent government is headed by Winfried Kretschman of the Green Party in coalition with the Christian Democratic Union (CDU). The latter is the party of the federal Chancellor Friedrich Merz. The government following this election is sure to be a continuation of this two-party coalition, now with new Greens leader Cem Özdemir at its head.

In addition to reviewing the election outcome under the mixed-member proportional (MMP) rules in place–which were reformed prior to this election–this planting will also consider how some alternative rules, including other variants that remain MMP but are not as fully proportional, would have worked.

In the voting result, the two parties were almost tied, with the Greens on 30.2% and the CDU on 29.7%. In third place is the far-right Alternative for Germany (AfD) on 18.8%, followed by the Social Democrats (SPD) on a mere 5.6%. The legal threshold for winning any list seats is 5% of the party vote, and no other parties cleared it. This year’s result is actually a substantial gain for the CDU compared to the state’s election of 2021, when it had 24.1%, and a small decline for the Greens, who had 32.6% in the preceding election. These vote figures are not fully comparable across years, for reasons having to do with the electoral reform, discussed later.

A table at Wikipedia has the full 2026 results, broken down by list and nominal (constituency) vote, given the mixed-member proportional (MMP) system in use. Interestingly, the CDU did quite a lot better in the nominal vote, with 34.3% to the Greens’ 25.5%. Unlike the reformed national system, the B-W system still has the possibility of increasing the total size of the assembly in the event that there are “overhangs” from a party having earned more constituency seats than what its proportional entitlement should be. In addition, like the former federal rules, the B-W rules still allow for the possibility of further “leveling” seats to restore full proportionality (for above-threshold parties).

In nominal seats, the CDU won 56 of the 70 total. The assembly has a minimum size of 120 seats, implying 50 list seats. According to the brief description at Wikipedia, the law requires proportionality statewide. The CDU’s 56 constituencies won would already be almost 47% of the minimum 120 seats, which would be a substantial overrepresentation given their 29.7% of the list vote (which, as noted, was a second-place finish). Thus the CDU is entitled to no list seats, given that MMP mandates these be allocated as compensatory seats (not in “parallel” as in the other main type of mixed-member system, MMM–see Japan’s recent election, for example). [Deleted from this paragraph was an earlier point about proportionality also being required across administrative district. See comment by Thomas for correction.]

Other parties, however, need compensations seats, and the mandated full proportionality can be achieved only by a substantial increase in the size of the assembly, which will have 157 seats. In the final result, the Greens win 43 list seats in addition to the mere 13 districts they won. This total of 56 puts them on par with the CDU, whom they essentially tied in party-list votes. It also leaves each of the two large parties on 35.7% of the total expanded assembly. Given that 15.75% of votes were cast for parties below the legal threshold, the Greens and CDU each have approximately 35.6% of the above-threshold vote. Thus indeed full proportionality has been restored through the allocation of the expanded pool of compensatory list seats.

As for the other parties, only one nominal-tier seat was won by a party other than the top two. This was an AfD seat, and that party’s 18.8% of the total vote translates to 22.3% of the above-threshold vote. It has been allocated 34 list seats to go along with its one constituency seat, and that total of 35 is, yes, 22.3% of the total 157. The only other seats allocated are 10 list seats to the SPD.

Now I want to turn to potential alternative ways in which seats could have been allocated and still be consistent with the principles that define MMP, as well as one that would not be.

The system would still be MMP, albeit less fully proportional, even if there were no expansion of the size of the assembly to deal with the overhang. If the number were fixed at 120, with 70 single-seat constituencies and 50 compensatory list seats, the CDU’s 56 constituency victories would have been 46.7% of incoming assembly. The three other parties that cleared the party-vote threshold would have split the 50 list seats. There are various ways this might be calculated, but a straightforward way if we want a simple estimate* is to recalculate list vote shares for only those parties that are entitled to list seats. The parties that are not so entitled obviously include those that are below the list-vote threshold. Also included among such parties are any that already have obtained at least their proportional entitlement in the nominal tier. In our case, that means we exclude the CDU votes in addition to all those below the threshold. When we do this, the recalculated vote shares of parties eligible for list seats are: Greens 0.554, AfD 0.345, and SPD 0.102. These shares are applied not to the total 120 seats, but to the number of seats remaining to be allocated, which in this case is 64: our fixed number of 120, minus the 56 already credited to the CDU from the nominal tier. When we apply these adjusted vote shares for parties eligible for list seats, we get approximately1 35 seats for the Greens, 22 for the AfD, and 7 for the SPD. Some of these parties already have nominal seats, so their list seats will be these adjusted entitlements, minus nominal seats: Greens 22 (because they won 13 districts), AfD 21 (they have one nominal seat), and finally the SPD which gets all of its seats from the list (7). The resulting percentages of the full 120 seats would be: Greens 29.2%, CDU 46.7%, AfD 18.3%, SPD 5.8%. [*See footnote #1 (second paragraph) for a more detailed way that is probably more accurate.]

Recall that the Greens obtained 30.2% of the list vote, which was a plurality. They are somewhat underrepresented in this scenario, with an advantage ratio (%seats/%votes) of only 0.966. The CDU’s 56 seats give them an advantage ratio of 1.57, and those of the other two parties are 0.975 (AfD) and 1.05 (SPD). These differential advantages ratios (1.00 would be pure proportionality) are due to the overhang, as well as the lack of any seats to be added in response to those overhangs. This is assuredly MMP, and the result is far more proportional than if there were only single-seat districts (the CDU, after all, won 80% of those!) or if it were mixed-member majoritarian (under which the CDU still would have won list seats–probably 15 of the 50) despite having won so many districts.

An intermediate approach between the model just sketched and the actual procedure would be to add seats to the list tier for each overhang, but no further “leveling” seats beyond those. This would be similar to how the New Zealand MMP system works (see in 2023 or 2008). In this scenario, because the CDU has 14 overhangs (as we shall see), the assembly would be increased from 120 to 134 seats. The resulting 64 list seats would be used to compensate the other parties. Under this procedure, each party that does not have an overhang still gets the same number of seats it would have had in the absence of the overhang. Given the parties’ shares of the above-threshold vote, the seats should be, under the no-overhang scenario: Greens 43, (CDU 42), AfD 27, SPD 8. The CDU’s share shows us where the 14 overhang seats come from, given it actually won 56 single-seat districts. Because of the nominal seats won, these imply list seats for these parties of Greens 30, (CDU 0), AfD 26, SPD 8. Note that these sum to 64 list seats–the baseline of 50, plus the 14 added in response to the overhangs. In terms of seat percentages (and advantage ratios), we now have Greens 32.1% (1.06), CDU 41.8% (1.41), AfD 20.1% (1.07), and SPD 6% (1.08). All parties are now slightly overrepresented (advantage ratio over 1.00), but the CDU remains substantially more overrepresented than the others. The MMP system still effectively rewards it for having many candidates who could win districts, yet it does not cut any other above-threshold party’s number of seats from what it would have been in the absence of overhang. The shares are still reduced relative to the no-overhang situation, because there are no further “leveling” seats added to restore full proportionality, as there are in the actual system in use in B-W.

And then there is yet another possible solution to the overhangs. The CDU could be required to give them up, and the 14 weakest of their 56 districts would be left without local representation,2 leaving full proportionality to be achievable for all above-threshold parties out of the original 120 seats. Note that this is utterly inconsistent with the principle behind MMP, which is that candidates hold seats if they have been able to win the local plurality, and parties win proportional representation up to the limits of the total seats available (expanded, as necessary and permitted under the rules). This is the reason why I no longer consider the federal system of Germany to be a mixed-member system. It violates the key principle that the nominal tier results are decisive. It is instead a form of PR with constituencies serving as a local-nominating and overall intraparty ranking mechanism. B-W, however, retains a very pure form of MMP, with maximum proportionality (for above-threshold parties) as its design goal.

As alluded to earlier, this system is itself a recent reform, passed after the 2021 election. B-W used to have no separate party list. Instead, the compensation seats were awarded to the best-performing constituency candidates who did not win local pluralities. Again, this is fully consistent with MMP, and we could say simply that the compensatory “list” is composed of constituency-nominated candidates who are non-winners by that tier. (The 2021 system also had added compensatory seats in case of overhang and additional “leveling” seats to restore proportionality, like the 2026 system. That is, how the list is constructed and whether there is a separate vote for it are separate dimensions of MMP from how the system deals with overhangs.)

Because there was only a single vote in 2021, arguably a direct comparison of vote changes between these elections is not straightforward. In 2021, a voter could vote for the “list” of a preferred party only by voting for the party’s constituency candidate. If we compare nominal votes for constituency candidates in 2026 to the 2021 fused vote, the CDU gained over ten percentage points (34.3% from 24.1), while the Greens fell by 7.1 (32.6% to 25.5%). If we compare across list votes it is +5.6 for CDU and –2.4 for Greens. Which is the better comparison? Arguably we can’t know. Voters under single fused-vote MMP must make a choice between endorsing their preferred local representative or their preferred party (if these are different for a given voter), and that means some may vote for a a small party with no chance of winning their district in order to boost its overall seat total via compensation. Others may vote for a candidate even if they do not really like the party, simply because they want that local representative. This is why I think one-vote MMP undermines the “best of both worlds” potential of MMP! However we look at the cross-election change, the CDU gained and the Greens lost, yet both will remain in coalition and the Greens presumably will retain the state’s Minister-President position on account of their narrow plurality of the separate list vote.

The voters indeed did take advantage of the ticket-splitting option. The effective number of vote-earning parties was 4.50 in 2026 in list votes, which is higher (albeit not by a lot) than the effective number on nominal votes, which came in at 4.34. The effective number on seats is a good deal lower, due to the large below-threshold vote, at 3.24.3 In 2021, the effective number of parties via votes was 5.01 and seats 3.89. The 2026 result is less fragmented (lower effective numbers) because the votes and seats are more dominated by the top two parties, even if those two combined for not quite 60% of the total votes and barely over 70% of the seats.

Regarding the legal threshold, two parties obtained over 4% of the list votes but below the mandated 5%. The Left Party won 4.41% and the Free Democratic Party (FDP) won 4.38%. No other party won over 2%. As I have noted before, it is quite possible that the 5% threshold is now too high for the party system that Germany and its states actually have, and that it should be lowered to 4% or even 3% or lower to avoid such a high total of wasted votes.4 The wasted votes were close to a sixth of the total, and would have been cut by more than half had the threshold been 4%. Having the Left and FDP in this assembly almost certainly would not have changed what governing coalition could form based on this result. But in other cases, it could have such an effect.

I always enjoy looking at the list of also-rans, the parties that fall far below a legal threshold. In this election, my favorite might be the “Party for Rejuvenation Research,” which earned 3,590 list votes (0.07%).

The Baden-Württemberg election of 2026 results in a tie in seats for the top two parties, Green and CDU, because (1) those parties had almost tied list-vote shares, and (2) the rules of MMP in use provide for additional seats to correct for overhang and further additional “leveling” seats to restore full proportionality for parties that clear the list-vote threshold. There are, however, other potential means of handling such a large overhang as the 14 CDU seats that were above its proportional entitlement, and two of those that we have reviewed remain within the parameters that define MMP. A third one we reviewed–which would be similar to that used since 2025 in federal elections in Germany–would be outside the family, as strictly defined. Baden-Württemberg is one of several German states holding elections in this Superwahljahr. Most German states use MMP, with some variation in the details of system design that we may explore further as these upcoming elections occur.

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  1. For ease of calculations, I am applying the adjusted vote shares directly to the number of available seats and rounding. The method used in the actual allocations is Sainte-Laguë divisors, generally considered one of the most “proportional” allocation formulas. Thus my shortcut method should be okay for illustrative purposes. However, running the full algorithm could produce marginally different seats totals by party than what I report here.
    Later, I did a full Sainte-Laguë allocation that produced slightly different numbers: list seats by party as Greens 24, CDU 0, AfD 20, SPD 6. The updated seat percentages (and advantage ratios) by party are then 30.8% (1.02), 46.7% (1.57), 17.5% (0.93), 5.0% (0.90). For this revised calculation I actually ran the full divisor set on the vote totals of all above-threshold parties, with the initial divisor being the number of nominal seats won, plus 1. This, of course, cuts the CDU vote total down far enough that it can’t win one of 50 list seats, and ensures that each of the others obtains its compensation share. This should be more accurate, but note that the initial method I used was a lot faster and differed by two seats out of the 50. Not too bad. If you want to see what the table of quotients looks like, click here [Dropbox link to a PDF]. The bolded quotients in the table are the ones that were sufficient to earn a seat for the indicated party. ↩︎
  2. Or those districts could be represented by the candidate who came second in the nominal contest (provided that party’s list was eligible for seats), without changing the overall number of seats this or any other party would win. However, the current federal system simply leaves the district without an officially designated constituency member. ↩︎
  3. By my calculation (sketched earlier), had there been a rule allowing for no additional compensation seats in the event of overhangs, the effective number of seat-winning parties would have been only 2.92 (2.89 by the revised full allocation referenced in footnote 1). ↩︎
  4. See the final paragraph of the linked post. ↩︎

South Korea 2024

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South Korea held its National Assembly election on 10 April. The result was a strong opposition majority. Given that this was approximately a midterm election, held at about 42% of the president’s term, a strong result for the opposition should be expected from standard electoral cycle effects in presidential systems.

The president is elected for five years, and the last election was in March, 2022. The assembly is elected for four years. Thus the last presidential election was held about two years into the assembly term; it, too, produced an opposition win, with the minority in the assembly seeing its candidate win the presidency. The President is Yoon Suk Yeol, of what is now called the People Power Party. (Its main component was known as United Future in 2020.) The 2022 election was close, with Yoon winning 48.6% and the Democrats’ candidate, Lee Jae-myung, winning 47.8%. The Korean presidency is elected in one round, by plurality. Plurality election of the presidency combined with nonconcurrent elections is a good recipe for frequent opposition majorities–even more when the assembly electoral system is majoritarian in effect even if not clearly in design. Since 2020, that system has been designed to be more proportional than had been the case for previous elections. But as we shall see, it has not worked that way in practice.

The electoral system, as best I understand it, is a combination of MMP and MMM.1 In addition to the single-seat districts, decided by plurality, there are two sets of list seats, totaling 47 seats. Of these, thirty are elected as compensatory seats (allocated from list votes after taking into account districts won by each party, as under MMP) and 17 are parallel (added on based on proportions of list votes without regard for district results, as under MMM). This was already the system adopted for the 2020 election. If this helpful Twitter thread by Raphael Rashid got it right, then the system seems indeed to be the same as in 2020. In prior elections, the system had a purely MMM design.

Where I could use some help is figuring out the detailed outcome by party and bloc. The table at the Wikipedia page for the election is less helpful than usual. Below is the main part of it as a screenshot. The part I am reproducing should include all the parties that won seats.2 There are many more parties in the full table, but none of them won representation.

Rashid’s thread indicates that the two main parties each formed a “satellite” party (also sometimes called a “decoy list”) to exploit the compensatory provision. This sort of behavior by parties has occurred before under MMP3 and is a well known pitfall of the system, if the electoral law or election administrators do not take steps to counter it. A party can win its nominal-tier (single-seat district) seats as usual but not present a party list, while setting up a formally separate party that competes only for list seats. In doing so, its list wing (the satellite) would get its full proportional share of the compensatory list seats without having to deduct the nominal seats won by the main party, given that they are formally separate parties. This was done in 2020 in Korea as well, although as best I could tell at the time, the use of a satellite was not the reason for the majority won by the Democratic Party in that election.

Rashid indicates that for the 2024 election the Democratic Party created a Democratic Union as its satellite while the People Power Party (President Yoon’s party) created a People’s Future as its satellite.

Unfortunately, the Wiki table does not break these out. In fact, it does not even indicate anything called Democratic Union. We see that various partners within “Democratic Alliance”4 won list (“proportional”) and nominal (“constituency”) seats, or both, and that their total is 176 seats, of which 14 were list seats. The combined list votes of these parties is only 26.7% of the total, whereas 176 seats is 58.7% of the total 300. So this certainly has an MMM (parallel) feel to it. In fact, winning a large majority on barely a quarter of the votes is a rather extreme manifestation of disproportionality! (Assuming these numbers are correct; I note the table shows no nominal votes, even though voters get both a nominal and a list vote.)

Those 14 list seats for the various parties of the Democratic Alliance would be about 29.8% of the total 47 list seats. This is again quite consistent with how an allocation would work under a fully MMM system, in that the list seats–as distinct from the seats overall–are themselves roughly proportional to the list-vote share. And that is exactly what the satellite-party strategy does: it effectively converts MMP to MMM for a group of “parties” pursuing this strategy. Note that if all 47 list seats were allocated in a compensatory matter, and the Democratic Alliance were treated as a single party for purposes of calculating seats, it would have won zero list seats, given that its number of nominal seats (districts) won was already (far) above its proportional entitlement, at 162 (54%).

The Wiki table combines People Power and People Future. It shows 36.7% of list votes for this combine, with it winning 18 list seats. That is 38.3%, again almost proportional to the list votes, and these seats are added on to the 90 nominal seats won. Again, just like MMM.

So the satellite-party behavior clearly achieved its intended result, by circumventing the compensatory feature of the 283 seats supposedly allocated via MMP (253 constituencies plus 30 list seats). I wish the breakdown included how many of the two types of list seats each party won (i.e., separating the 17 parallel seats from the 30 supposedly compensatory), as well as breaking down the “real” and “satellite” parties within the blocs. Maybe someone can point me towards an analysis that did so. I tried to locate something of this sort and did not turn it up.

South Korean democracy would probably be better served by a more proportional system. Or by proper enforcement somehow of the intended compensatory nature of the current system (although just ten percent of seats supposedly allocated in that manner is pretty tepid proportionality). It would also perhaps be served better by concurrent elections and a presidential election method other than plurality. Various sources report some degree of backsliding in Korean democracy in recent years, and while possible institutional reforms I mention here would surely not be sufficient to halt such trends, they just might help.

  1. Mixed-member proportional and mixed-member majoritarian, respectively. ↩︎
  2. For some reason the table shows 46 list seats and 254 constituency seats, but this seems to be incorrect. In any case, this small discrepancy barely changes the analysis and puzzles I am writing about. I also wonder why the table indicates two “independents” having won via party lists. ↩︎
  3. See past plantings on Lesotho, and in particular the interesting discussion in the comment thread on MMP manipulation in that country in 2007. It also happened in Albania, and is the main reason why that country became an ex-mixed member case. ↩︎
  4. Likely just a translation variant, but even so, the grouping in the table does not clearly indicate the satellite phenomenon. ↩︎

MMP as sub-category of two-tier PR–some basis for doubt

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In yesterday’s review of the German election outcome, I used the extended Seat Product Model (SPM) formula for two-tier PR systems. I have done this many times, and Rein Taagepera and I (in our 2017 book, Votes from Seats) do explicitly include mixed-member proportional (MMP) in the category of two-tier PR systems.

However, there is one problem with that characterization. All other two-tier PR systems that I can think of entail a single vote, which is then used both for allocating seats in the basic tier and pooled across districts for national (or sometimes regional) compensation.

MMP, of course, usually entails two votes–a nominal (candidate) vote used only in the basic tier, and a second, party-list, vote used for determining overall proportionality. (In MMP, the basic tier is a “nominal tier” because the vote there is cast for a candidate, and the district winner earns the seat solely on votes cast for him or her by name.) This two-vote feature is a complex feature of MMP that is actually emphasized in my more recent coauthored book, Party Personnel Strategies, but which I may have tended to underplay in my comparative work on modeling the effects of electoral systems on party systems. Of course, by being two-tier, it is already a non-simple system, as Taagepera and I define that term. But we also say that two-tier PR, including MMP, is as simple as an electoral system can be and still be included in the complex category (see p. 263 and 299 of Votes from Seats).

Maybe that is not an accurate statement for two-vote MMP. Our definition of simple (pp. 31-36) concentrates on two features: (1) all seats allocated within districts, and (2) adherence to the rank-size principle, such that the largest party gets the first seat in a district, and remaining seats are allocated in a way that respects their relative sizes (i.e., by any of the common PR formulas). We further say that for simple PR, “the vote for candidate and for party is one act” (p. 35). This latter condition still holds for any two-tier list-PR system, because there is a list vote that applies both for allocating seats within a district, and also for the “complex” feature of the supra-district compensation mechanism. Obviously, however, MMP as used in Germany violates the principle that “the vote for candidate and for party is one act.” So maybe it is not “simple enough” to qualify as an almost-simple complex system. (Yes, that was a complex statement, but that’s kind of the point.)

If MMP were to tend to produce a party system more fragmented than expected from the extended SPM, it might be due to the “second” vote, i.e., the list vote. To test this, one could aggregate all the nominal votes and use them as the notional list votes in a simulated compensation. (This is how MMP in Germany worked in 1949, albeit with compensation only at state level. It is also how MMP now works in Lesotho.) The aggregation of basic-tier votes should work better from the standpoint of modeling the party system impact of the key features of a given MMP system–the size of the basic tier and the share of seats in the compensation tier.

The catch in all this is that, of course, till quite recently German MMP was under-fragmented, according to the SPM, despite using a separate list vote. Thus the issue did not arise. The New Zealand MMP system also has matched expectations well, after the first three post-reform elections were over-fragmented relative to model prediction. The graph below shows the relationship over time between the expectations of the SPM and the observed values of effective number of seat-winning parties (NS) in both Germany and New Zealand. For the latter country, it includes the pre-reform FPTP system. In the case of Germany, it plots NS alternately, with the CDU and CSU considered separately. As I noted in the previous discussion, I believe the “correct” procedure, for this purpose, is to count the “Union” as one party, but both are included here for the sake of transparency. In both panels, the dashed mostly horizontal line is the output of the extended SPM for the countries’ respective MMP systems1; it will change level only when the electoral system changes. (For New Zealand, the solid horizontal line is the expectation under the FPTP system in use before 1996.)

The German party system from 1953 through 2005 was clearly fitting quite poorly, due to how under-fragmented it was for the electoral system in use. The old CDU/CSU and SPD were just too strong and overwhelmed the considerable permissiveness of the electoral rules.2 So clearly the question I am raising here–whether the two-vote feature of MMP means it should not be modeled just like any (other) two-tier PR system–is moot for those years. However, perhaps it has become an issue in recent German elections, including 2021. The underlying feature of voter behavior pushing the actual NS to have risen to well above “expectation” would be the greater tendency of voters towards giving their two votes to different parties. At least that would be the cause in 2021, given that we saw in the previous post that the basic tier produced almost exactly the degree of fragmentation that the SPM says to expect. It is the compensation tier that pushed it above expectation, and the problem here (from a modeling perspective) is that the formula implicitly assumes the votes being used in the compensation mechanism are the same votes being cast and turned into seats in the basic (nominal) tier. But with two votes, they are not, and with more voters splitting tickets, the assumption becomes more and more untenable.

The previous planting on this matter emphasized that the SPM is actually performing well, even in this most recent, and quite fragmented, election. I am not trying to undermine that obviously crucial point! However, the marked rise in NS since 2009–excepting 2013 when the FDP failed to clear the threshold–may suggest that the model’s assumption that the two votes are pretty similar could be problematic.

Maybe two-vote MMP is more complex after all than its characterization as a two-tier PR system–the simplest form of complex electoral system–implies. In fact, maybe I should stop referring to MMP as a sub-category of two-tier PR. Yet for various reasons, it is a convenient way to conceptualize the system, and as yesterday’s discussion of the recent German election showed, it does work quite well nonetheless. It could be based on a flawed premise, however, and the more voters cast their nominal and list votes differently, the more that flaw becomes apparent.

A work in progress… in other words (fair warning), more such nerdy posts on this topic are likely coming.

Notes

1. The “expected NS” line for Germany takes the tier ratio to be 0.5, even though as I argued in the previous entry, we really should use the actual share of compensation seats in the final allocation. This would have only minimal impact in the elections before 2013; in 2021, it makes a difference in “expected” NS of 0.36.

2. Partly this is due to the 5% list-vote threshold, which is not a factor in the version of the SPM I am using. In Votes from Seats, we develop an alternate model based only on a legal threshold. For a 5% threshold, regardless of other features, it predicts NS=3.08. This would be somewhat better for much of the earlier period in Germany. In fact, from 1953 through 2002, mean observed NS=2.57. In the book we show that the SPM based only on mean district magnitude and assembly size–plus for two-tier PR, tier ratio–generally performs better than the threshold model even though the former ignores the impact of any legal threshold. This is not the place to get into why that might be, or why the threshold might have “worked” strongly to limit the party system in Germany for most of the postwar period, but the permissiveness of a large assembly and large compensation tier is having more impact in recent times. It is an interesting question, however! For New Zealand, either model actually works well for the simple reason that they just happen to arrive at almost identical predictions (3.08 vs. 3.00), and that for the entire MMP era so far, mean NS has been 3.14.

The Germany 2021 result and the electoral system

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The German general election of 2021 has resulted in a situation in which neither major party can form a government without either the other, or more likely, a coalition that takes in both the liberal FDP and the Greens. With the largest party, the social-democratic SPD, under 30% of seats, it is an unusually fragmented result compared to most German elections. Naturally, this being Fruits & Votes, attention turns to how much more fragmented this outcome is than expected, given the electoral system. The answer may be a bit of a surprise: not all that much. I expected this outcome to be a significant miss for the Seat Product Model (SPM). But it is really not that far off.

For a two-tier PR system, of which Germany’s MMP can be thought of as a subtype, we need to use the extended version of the SPM developed in Votes from Seats.

NS = 2.5t(MSB)1/6,

where NS is the effective number of seat-winning parties (here, meaning the expected NS), M is the mean district magnitude of the basic tier, SB is the total number of seats in the basic tier, and t is the “tier ratio” defined as the share of the total number of assembly seats allocated in the compensatory tier. For Germany, basic-tier M=1 and SB=299. The tier ratio could be coded as 0.5, because the initial design of the system is that there are 299 list tier seats, allocated to bring the result in line with the overall party-list vote percentages of each party that clears the threshold. However, in Germany the electoral law provides that the list tier can be expanded further to the extent needed to reach overall proportionality. Thus t is not fixed; we should probably use the ratio that the final results are based on, as NS would necessarily be lower if only 299 list seats had been available. In the final result, the Bundestag will have 735 seats, meaning 436 list seats, which gives us a tier ratio of t=436/735=0.593. Plug all this into the formula, and you get:

NS = 2.50.5932991/6=1.72*2.59=4.45.

Now, what was the actual NS in the final result? We have to ask ourselves whether to count to two Christian “Union” parties, the CDU and the CSU, as one party or two. The answer really depends on the question being asked. They are separate parties, with distinct organization, and they bargain separately over portfolios and policy when they are negotiating a coalition with another party. However, for purposes of the SPM, I firmly believe that when two or more parties in a bloc do not compete against each other (or, alternatively, do so only within lists over which votes are pooled for seat-allocation1), they should be treated as one. The SPM does not “care” whether candidates of the bloc in question are branded as CSU (as they are in Bavaria) or as CDU (the rest of Germany). It simply estimates the effective number of “agents of the electorate” given the electoral rules. In terms of national politics, these are the same “agent”–they always enter government together or go into opposition together, and they jointly nominate a leader to be their Chancellor candidate.

Taking the CDU/CSU as a “party” for this purpose, we get actual NS =4.84 in the 2021 election. So, given an expectation of 4.45, the actual outcome is just over 8.75% higher than expected. That is nothing too extraordinary. For comparison purposes, we can just take the ratio of actual NS to expected NS. Here are some elections in the dataset used for Votes from Seats that are in the same range of over-fragmentation as Germany 2021:

      country   year   simple   Ns   exp_Ns   ratio 
     Barbados   1981        1    1.87   1.735597   1.077439  
       Norway   1965        1    3.51   3.255616   1.078137  
    Sri Lanka   1970        1    2.49   2.307612   1.079037  
Dominican Rep   1990        1    3.05   2.810847   1.085082  
     Trinidad   2002        1    1.98   1.824064   1.085488  
      Iceland   1963        0    3.33   3.060313   1.088124  
       Israel   1961        1    5.37   4.932424   1.088714  
     Trinidad   2001        1       2   1.824064   1.096452  
     Trinidad   2000        1       2   1.824064   1.096452  
      Iceland   1999        0    3.45   3.146183   1.096567  
      Denmark   1950        0    3.98   3.624933   1.097951

(The table indicates as ‘simple’ those with a single tier; others are two-tier.)

The ratio variable has a mean of 1.021 in the full dataset and a standard deviation of 0.359. Its 75th percentile is 1.224 (and 25th is 0.745). So the German election of 2021 is actually very well explained by this method. The degree of fragmentation we saw in this election is not too surprising. It is about what should be expected with MMP consisting of 299 nominal-tier M=1 seats and a very generous and flexible compensation tier.

As an aside, if we used the initial tier size (299, so t=0.5) in the formula, we would get an “expected” NS=4.09. This would mean a ratio of 1.183, still short of the 75th percentile of the 584 elections included in the book’s main statistical test. Here is the company it would be keeping in that neighborhood:

            country   year   simple   Ns   exp_Ns   ratio 
            Germany   2009        0    4.83   4.121066   1.172027  
St. Kitts and Nevis   2000        1    1.75   1.491301   1.173472  
         Luxembourg   2009        1    3.63   3.077289    1.17961  
             Canada   2004        1    3.03   2.560218   1.183493  
            Denmark   1998        0    4.71   3.965222   1.187828  
          Venezuela   1963        0    4.32    3.63006   1.190063  
        Korea South   1988        0    3.55   2.981969   1.190488  
     Czech Republic   2010        1    4.51   3.767128   1.197199  
            Iceland   1991        0    3.77   3.146183   1.198277

This would put the German 2021 election about as “over-fragmented” as the Canadian election of 2004. In other words, still not a big deal. If we count the two “Union” parties separately, obviously the degree of over-fragmentation goes up considerably. As I have said already, I think for this purpose counting them as one is the correct decision.2

As far as size of the largest seat-winning party is concerned, the SPD has 206 seats, for 28.03%. The SPM would predict, given expected NS=4.45, that the largest should have 32.6% (240 seats out of 735); that’s a ratio of 0.860 (which is a slightly bigger miss than the NS ratio of 1.088, the reciprocal of which would be 0.919). It is worth pausing on this for a bit. Polling before the election said the largest party might be only on a quarter of the votes. This was accurate, as the SPD won 25.7%. The advantage ratio (%seats/%votes) is 1.09, which is rather high for an electoral system that promises as near-perfect proportionality as Germany’s current system does, with its compensation for overhangs (cases in which a party has won more nominal-tier seats in a state than its list votes would have entitled it to). This bonus is a result of a rather high below-threshold vote. Not as high in 2013, of course, when two parties (FDP and AfD) narrowly missed the nationwide 5% threshold. But still considerably high, at 8.6% combined for all parties that failed to win a seat.

It is also worth asking whether the logic behind the extended SPM for two-tier systems holds for this German election. The formula says that the basic tier produces an initial allocation of seats consistent with the SPM for simple systems, and then inflates it based on the size of the compensation tier. So we can ask what the effective number of seat-winning parties is in the basic tier alone. It should be NS =(MSB)1/6= 2991/6= 2.59. In fact, the basic-tier NS in this election was 2.51 (as before, taking CDU/CSU as one party). The ratio of 0.969 is a pretty trivial miss. We should expect the largest party to have won 0.490 of these seats (about 146). Actually the Union parties, which together won the most single-seat districts, won 143 (0.478). Thus Germany’s MMP system, in the 2021 election, actually did produce a basic-tier (nominal-tier) party system pretty much just like it should, given 299 seats and M=1 plurality, and then augmented this through a large compensatory national tier. The actual inflator is a factor of 1.93=4.84/2.51, rather than the expected 1.72=2.50.593. Had it been 1.72 instead, the final effective number of seat-winning parties would have been 4.32, about “half a party” less than in reality, implying almost exactly one third of seats to the SPD instead of just 28%.

This surprised me (pleasantly, of course). When I saw that the Greens and AfD each had won 16 seats in the nominal tier, I thought that was too many! But in fact, it works out. Maybe sometimes even I think Duverger had a law, or something. But given 299 single-seat districts, this is pretty much in line with expectations.

The outcome is interesting in the many ways that it serves as a primer on details of the electoral system. Here I mean not only the substantial expansion of the Bundestag from 598 to 735 seats, due to the way the compensation mechanism works, but also the thresholds. One of the best known features of the German electoral system is the 5% nationwide threshold. But of course, the threshold is more complex than that. It is 5% of the national party-list vote or three single-seat wins, except if a party is an ethnic-minority party. All these provisions were on display. For instance, the Linke (Left) party fell below the 5.0% threshold, yet is represented at full proportionality. That is because it won three individual mandates, thus fulfilling the “or” clause of the threshold. There was a point on election night when it looked as if the Linke might hold only two single-seat districts. In that case, with less than 5% of the list votes nationwide, it would have held only those seats as its total. By winning three, it is entitled under the law to full proportional compensation, and as a result it was awarded 36 list seats. Then, for the first time in a very long time, an ethnic party has won a seat. The South Schleswig Voters’ Association (SSW), which had not contested federal elections in decades, ran in this one and was able to win a single (list) seat, because as a representative of the Danish and Frisian minorities, it is exempt from the usual threshold provisions, as long as its votes are sufficient to qualify it for a seat when the threshold is ignored. Its 0.1% of the national vote was good enough. The SSW has had some renewed success in state elections in Schleswig-Holstein recently, and now it has scored a seat in the federal parliament for the first time since 1949. In 1949, the MMP system was a bit different, in that the 5% threshold was determined state-by-state, rather than nationwide. If the threshold had been state-by-state in this election, one other party would have earned seats. The Free Voters won around 7.5% of party-list votes in Bavaria. However, they managed only 2.9% nationwide (and no district seat), so they are shut out.

Now attention turns to what the coalition will be. Two options are on the table: SPD+Greens+FDP (“traffic light”) or CDU/CSU+Greens+FDP (“Jamaica”). The possibility of a broad left coalition has been ruled out by the election results: SPD+Green+Linke is not a majority. It was never likely anyway; the SPD and Greens did not spend recent years convincing voters they were safe options near the center of German politics to team up with the far left. Nonetheless, had it been mathematically possible the SPD might have used it as leverage against the FDP. My guess is that the traffic light coalition will form. Despite some serious policy differences between the FDP and the other two, it would be a government made up of the winners of the election, as these three parties all gained votes compared to 2017. On the other hand, one led by the CDU/CSU would be led by a pretty big loser, even though it is mathematically possible and the Greens seem to have been positioning for it over the last several years.3 Following the election, the DW live blog has been reporting on comments by various prominent CDU and CSU politicians that could be interpreted as saying the bloc needs some time in opposition, after the disappointing result. I suspect this is the view that will prevail, and after a lot of intense and difficult bargaining, Germany will be led by a traffic light coalition for the first time.

____

Notes

1. Here I am thinking of cases like Chile, where alliance lists contain candidates of different parties, but for purposes of how the electoral system assigns seats between competing teams of candidates, we should count the alliances, not the component parties. The same condition applies in Brazil and Finland, only there it is essentially impossible to aggregate to a meaningful national alliance category because the combinations of parties are not always the same across districts. In Chile, and also in the FPTP case of India–as well as in the current case of Germany–there is no such problem, as the alliances are nationwide in scope and consistent across districts.

2. For the record, counting them separately yields NS=5.51 in this election, which would put the ratio just barely above the 75th percentile.

3.To be clear, they are much happier working with the SPD, but what I mean is that their positioning for the possibility of a coalition with the CDU/CSU should make finding common ground with the FDP easier than it otherwise would have been.

How the German overhang and compensation system works

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Heinz Brandenburg on Twitter walks readers through a very useful explainer on how the current Germany version of MMP deals with overhangs through a multi-layered compensation mechanism, and why it could mean the new Bundestag will top out at more than 800 seats!

It is best to read it in its native Twitter, but following is the text of most of it (courtesy of the ThreadReader app) . The starting point, not quoted here, is a poll of current party standing in the state of Bavaria.

[the remainder of this text is not mine, but Brandenburg’s; numbers correspond to tweets in the thread]

____________________________________________________________________________

Last time around, the CSU won 38.8% of the vote but all of the constituencies in Bavaria (they even swept all of Munich). That results in so-called overhang and compensatory seats.
How are these calculated?

1/ Well, there are 93 regular seats allocated to Bavaria, 46 of which are constituencies. CSU winning them all meant 46 seats, but they only had 38.8% of the list vote or about 42% of the vote once you discount votes for parties that did not get into the Bundestag.

2/ 42% of the vote would mean their proportional share of seats was 39, not 46. So they got 7 Ueberhangmandate (overhang seats), i.e. 7 more seats than their proportional share.

3/ Since 2013, these seats have to be compensated for. So other parties get additional seats, to the extent that the 46 seats the CSU won amount to 42% of the total number of seats in Bavaria.
So Bavaria actually had 108 seats in the Bundestag, not 93. 

4/ But that is not the end of it. Bavaria’s 93 seats are proportional to its population size. If the state’s seat share increases to 108, then the 15 other states also need a larger share. And it wasn’t only Bavaria. 

5/ Baden-Wuerttemberg got 96 instead of 76 because of the CDU winning all constituencies, Brandenburg 25 instead of 20 because CDU won all but one constituency, Hamburg 16 instead of 12 because SPD won all but one constituency, and so on.

6/ What happens then is that to keep the 16 states’ share of seats in the Bundestag proportional, not only overhang seats within states need to be compensated, but overhang and compensatory seats within states have to be compensated across states.

7/ So North Rhine-Westphalia (NRW), the biggest German state, did not produce any overhang seats, because SPD and CDU are more evenly balanced there. But it got 14 compensatory seats, to make up for additional seats given to other states. 

8/ It is not a perfect compensation across states. Bavaria and Baden-Wuerttemberg have 15 and 20 seats, respectively, more than their normal share in the 2017 Bundestag. NRW only 14, despite being the larger state.

9/ Berlin, Niedersachsen and NRW were the only states where no overhang seats were dished out in 2017, largely a reflection of dominance of the CDU in a fragmenting party landscape. 

10/ CDU won all seats in five states, almost all seats in over a dozen states, despite having their worst election result in history, with 33%.

Could be very different this time around, with them down to 20% and the SPD at 25%. More states could get away without overhang seats.

11/ But one single state can make a big difference, and if the result in Bavaria is anywhere close to the recent polls (CSU 28%) it could be a dramatic effect.

12/ Even at 28%, the CSU would like win almost all constituencies. These are the four most marginal seats. Muenchen-Nord and Nuernberg-Nord are most likely to fall to the SPD. But the others are not certain.

So the CSU could still end up with 42-44 seats, on just 28% of the vote, or 31% if we remove votes for parties that do not get into the Bundestag.

14/ By my calculations, that would mean Bavaria’s seat share increases to 129 seats from their current 108 (and their nominal allocation of 93).

Once other states are compensated, that would get us to possibly 840 seats. 

15/ A few changes have been made, which I have taken into account – the first three overhang seats will not be compensated, which would keep Bavaria’s share at 129 rather than 135 under 2017 rules.

16/ And overhangs can also be compensated against a party’s list seats in other states. But I don’t think that applies to the CSU. They won’t take CDU seats away in other states to compensate for CSU over-representations.

17/ So one such lop-sided result, under increasing fragmentation – where suddenly 28% of the vote share allow a party to win almost all constituencies – can have incredible effects on the size of the Bundestag.

18/ The nominal size of the Bundestag is 598. This one result in Bavaria could increase the size of parliament by 40%.

“Effective Seat Product” for two-tier PR (including MMP) and MMM

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[Update, late April, 2022: I have continued to refine this method, and the specific values mentioned below no longer hold (due a revision of the estimation of the exponent in the model for two-tier systems), although the basic framework remains the same. User beware! This also means that the datasets linked at the end of this post are not accurate. I will upload corrected ones at some point.]

The seat product for a simple electoral system is its assembly size (S) times its mean district magnitude (M) (Taagepera 2007). From this product, MS, the various formulas of the Seat Product Model (SPM) allow us to estimate the effective number of parties, size of the largest, disproportionality, and other election indicators. For each output tested in Shugart and Taagepera (2017), Votes from Seats, we find that the SPM explains about 60% of the variance. This means that these two institutional inputs (M and S) alone account for three fifths of the cross-national differences in party system indicators, while leaving plenty for country-specific or election-specific factors to explain as well (i.e., the other 40% of the variance).

The SPM, based on the simple seat product, is fine if you have a single-tier electoral system. (In the book, we show it works reasonably well, at least on seat outputs, in “complex” but still single-tier systems like AV in Australia, majority-plurality in France, and STV in Ireland.) But what about systems with complex districting, such as two-tier PR? For these systems, Shugart and Taagepera (2017) propose an “extended seat product model”. This takes into account the basic-tier size and average district magnitude as well as the percentage of the entire assembly that is allocated in an upper tier, assumed to be compensatory. For estimating the expected effective number of seat-winning parties (NS), the extended SPM formula (Shugart and Taagepera, 2017: 263) is:

NS=2.5t(MB)1/6,

where MB is the basic-tier seat product, defined as the number of seats allocated in the basic tier (i.e., assembly size, minus seats in the upper tier), and t is the tier ratio, i.e., the share of all assembly seats allocated in the upper tier. If the electoral system is simple (single tier), the equation reduces to the “regular” seat product model, in which MS=MB and t=0.

(Added note: in the book we use MSB to refer to what I am calling here MB. No good reason for the change, other than blogger laziness.)

We show in the book that the extended seat product is reasonably accurate for two-tier PR, including mixed-member proportional (MMP). We also show that the logic on which it is based checks out, in that the basic tier NS (i.e., before taking account of the upper tier) is well explained by (MB)1/6, while the multiplier term, 2.5t, captures on average how much the compensation mechanism increases NS. Perhaps most importantly of all, the extended seat product model’s prediction is closer to actually observed nationwide NS, on average, than would be an estimate of NS derived from the simple seat product. In other words, for a two-tier system, do not just take the basic-tier mean M and multiply by S and expect it to work!

While the extended seat product works quite well for two-tier PR (including MMP), it is not convenient if one wants to scale such systems along with simple systems. For instance, as I did in my recent planting on polling errors. For this we need an “effective seat product” that exists on the same scale as the simple seat product, but is consistent with the effect of the two-tier system on the effective number of parties (or other outputs).

We did not attempt to develop such an effective seat product in Shugart and Taagepera (2017), but it is pretty straightforward how to do it. And if we can do this, we can also derive an “effective magnitude” of such systems. In this way, we can have a ready indicator of what simple (hypothetical) design comes closest to expressing the impact of the (actual) complex design on the party system.

The derivation of effective seat product is pretty simple, actually. Just take, for the system parameters, the predicted effective number of seat-winning parties, NS, and raise it to the power, 6. That is, if NS=(MS)1/6, it must be that MS=NS6. (Taagepera 2007 proposes something similar, but based on actual output, rather than expected, as there was not to be a form of the seat product model for two-tier systems for almost another decade, till an initial proposal by Li and Shugart (2016).)

Once we do this, we can arrive at effective seat products for all these systems. Examples of resulting values are approximately 5,000 for Germany (MMP) in 2009 and 6,600 for Denmark (two-tier PR) in 2007. How do these compare to simple systems? There are actual few simple systems with these seat products in this range. This might be a feature of two-tier PR (of which MMP could be considered a subtype), as it allows a system to have a low or moderate basic-tier district magnitude combined with a high degree of overall proportionality (and small-party permissiveness). The only simple, single-tier, systems with similar seat products are Poland (5,161), with the next highest being Brazil (9,747) and Netherlands before 1956 (10,000). The implication here is that Germany and Denmark have systems roughly equivalent in their impact on the party system–i.e., on the 60% of variance mentioned above, not the country-specific 40%–as the simple districted PR system of Poland (S=460, M=11) but not as permissive as Brazil (S=513, M=19) or pre-1956 Netherlands (M=S=100). Note that each of these systems has a much higher magnitude than the basic-tier M of Germany (1) or larger assembly than Denmark (S=179; M=13.5). Yet their impact on the nationwide party system should be fairly similar.

Now, suppose you are more interested in “effective district magnitude” than in the seat product. I mean, you should be interested in the seat product, because it tells you more about a system’s impact on the party system than does magnitude alone! But there may be value in knowing the input parameters separately. You can find S easily enough, even for a complex system. But what about (effective) M? This is easy, too! Just take the effective seat product and divide it by the assembly size.

Thus we have an effective M for Germany in 2009 of 7.9 and for Denmark in 2007 of 36.9. These values give us an idea of how, for their given assembly sizes, their compensatory PR systems make district magnitude “effectively”–i.e., in terms of impact on the inter-party dimension–much larger than the basic-tier districts actually are. If we think low M is desirable for generating local representation–a key aspect of the intra-party dimension–we might conclude that Germany gets the advantages M=1 in local representation while also getting the advantages of the proportionality of 8-seat districts. (Best of both worlds?) By comparison, simple districted PR systems with average M around 8 seats include Switzerland and Costa Rica. (The Swiss system is complex in various ways, but not in its districting.) Eight is also the minimum magnitude in Brazil. Denmark gets whatever local representation advantages might come from an actual mean M of 13.5, yet the proportionality, for its assembly size, as if those districts elected, on average, 37 members. Actual districts of about this magnitude occur only in a relatively few districts within simple systems. For instance, the district for Madrid in Spain has M in the mid-30s, but that system’s overall average is only 6.7 (i.e., somewhat smaller than Germany’s effective M).

Now, what about mixed-member majoritarian (MMM) systems. Unlike MMP, these are not designed with a compensatory upper tier. In Votes from Seats, Taagepera and I basically conclude that we are unable to generalize about them. Each MMM system is sui generis. Maybe we gave up too soon! I will describe a procedure for estimating an effective seat product and effective magnitude for MMM systems, in which the basic tier normally has M=1, and there is a list-PR component that is allocated in “parallel” rather than to compensate for deviations from proportionality arising out of the basic tier.

The most straightforward means of estimating the effective seat product is to treat the system as a halfway house between MMP and FPTP. That is, they have some commonality with MMP, in having both M=1 and a list-PR component (not actually a “tier” as Gallagher and Mitchell (2005) explain). But they also have commonality with FPTP, where all seats are M=1 plurality, in that they reward a party that is able to win many of the basic seats in a way that MMP does not. If we take the geometric average of the effective seat product derived as if it were MMP and the effective seat product as if it were FPTP, we might have a reasonable estimate for MMM.

In doing this, I played with both an “effective FPTP seat product” from the basic tier alone and an effective FPTP seat product based on assuming the actual assembly size. The latter works better (in the sense of “predicting,” on average for a set of MMM systems, what their actual NS is), and I think it makes more logical sense. After all, the system should be more permissive than if were a FPTP system in which all those list-PR component seats did not exist. So we are taking the geometric average of (1) a hypothetical system in which the entire assembly is divided into a number of single-seat electoral districts (Eeff) that is Eeff = EB+tS, where EB is the actual number of single-seat districts in the basic tier and S and t are as defined before, and (2) a hypothetical system that is MMP instead of MMM but otherwise identical.

When we do this, we get the following based on a couple sample MMM systems. In Japan, the effective seat product becomes approximately 1,070, roughly equivalent to moderate-M simple districted PR systems in the Dominican Republic or pre-1965 Norway. For South Korea, we would have an effective seat product of 458, or very roughly the same as the US House, and also close to the districted PR system of Costa Rica.

Here is how those are derived, using the example of Japan. We have S=480, with 300 single-seat districts and 180 list-PR seats. Thus t=0.375. If it were two-tier PR (specifically, MMP), the extended seat product would expect NS=3.65, from which we would derive an effective seat product, (MS)eff=3.666 =2,400. But it is MMM. So let’s calculate an effective FPTP seat product. Eeff = EB+tS=300+180=480 (from which we would expect NS=2.80). We just take the geometric mean of these two seat-product estimates: (2400*480)1/2=1,070. This leads to an expected NS=3.19, letting us see just how much the non-compensatory feature reduces expected party-system fragmentation relative to MMP as well as how much more permissive it is than if it were FPTP.

How does this work out in practice? Well, for Japan it is accurate for the 2000 election (NS=3.17), but several other elections have had NS much lower. That is perhaps due to election-specific factors (producing huge swings in 2005 and 2009, for example). As I alluded to above already, over the wider set of MMM systems, this method is pretty good on average. For 40 elections in 17 countries, a ratio of actual NS to that predicted from this method is 1.0075 (median 0.925). The worst-predicted is Italy (1994-2001), but that is mainly because the blocs that formed to cope with MMM contained many parties (plus Italy’s system had a partial-compensation feature). If I drop Italy, I get a mean of 1.0024 (but a median of only 0.894) on 37 elections.

If we want an effective magnitude for MMM, we can again use the simple formula, Meff=(MS)eff/S. For Japan, this would give us Meff=2.25; for Korea Meff=1.5. Intuitively, these make sense. In terms of districting, these systems are more similar to FPTP than they are to MMP, or even to districted PR. That is, they put a strong premium on the plurality party, while also giving the runner-up party a considerable incentive to attend to district interests in the hopes of swinging the actual district seat their way next time (because the system puts a high premium on M=1 wins, unlike MMP). This is, by the way, a theme of the forthcoming Party Personnel book of which I am a coauthor.

(A quirk here is that Thailand’s system of 2001 and 2005 gets an effective magnitude of 0.92! This is strange, given that magnitude–the real kind–obviously has a lower limit of 1.0, but it is perhaps tolerable inasmuch as it signals that Thailand’s MMM was really strongly majoritarian, given only 100 list seats out of 500, which means most list seats would also be won by any party that performed very well in the M=1 seats, which is indeed very much what happened in 2005. The concept of an “effective” magnitude less than 1.0 implies a degree of majoritarianism that one might get from multi-seat plurality of the MNTV or list-plurality kind.)

In this planting, I have shown that it is possible to develop an “effective seat product” for two-tier PR systems that allows such systems to be scaled along with simple, single-tier systems. The exercise allows us to say what sort of simple system an actual two-tier system most resembles in its institutional impact on inter-party variables, like the effective number of seat-winning parties, size of the largest party, and disproportionality (using formulas of the Seat Product Model). From the effective seat product, we can also determine an “effective magnitude” by simply dividing the calculated effective seat product by actual assembly size. This derivation lets us understand how the upper tier makes the individual district effectively more proportional while retaining an actual (basic-tier) magnitude that facilitates a more localized representation. Further, I have shown that MMM systems can be treated as intermediary between a hypothetical MMP (with the same basic-tier and upper-tier structure) and a hypothetical FPTP in which the entire assembly consists of single-seat districts. Again, this procedure can be extended to derive an effective magnitude. For actual MMP systems in Germany and also New Zealand, we end up with an effective magnitude in the 6–8 range. For actual MMM systems, we typically get an effective magnitude in the 1.5–3 range.

I will post files that have these summary statistics for a wide range of systems in case they may be of use to researchers or other interested readers. These are separate files for MMM, MMP, and two-tier PR (i.e, those that also use PR in their basic tiers), along with a codebook. (Links go to Dropbox (account not required); the first three files are .CSV and the codebook is .RTF.) [As noted at the top of this article, these files should no longer be used. At some point I will upload corrections. Sorry for the inconvenience.]

Added note: In the spreadsheets, the values of basic-tier seat product (MB) and tier ratio (t) are not election-specific, but are system averages. We used a definition of “system” that is based on how Lijphart (1994) defines criteria for a “change” in system. This is important only because it means the values may not exactly match what you would calculate from the raw values at a given election, if there have been small tweaks to magnitude or other variables during an otherwise steady-state “system”. These should make for only very minor differences and only for some countries.

MMP in NZ: An example of “best of both worlds” in action

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In Shugart and Wattenberg (2001) we ask if mixed-member systems offer a “best of both worlds.” That is, do they allow simultaneously for the benefits of local representation and individual-member accountability that are the (supposed) advantages of single-seat plurality (FPTP) and the representation of smaller national parties that might struggle to win districts but would be represented under proportional representation (PR).

There was a question mark in the book’s subtitle. Over time, I have come to believe that indeed the proportional type (MMP) does have a strong tendency to offer the best of both worlds. The reason is that members elected in districts have incentives to behave as local representatives at the time that there is close approximation between party vote and seat shares (assuming compensation is carried out nationwide or in large regions). The majoritarian type (MMM, as in Japan and Taiwan) probably does not; it is much closer in its overall incentive structure to FPTP, even though it does indeed permit smaller national parties to win seats.

For MMP, the “best of both worlds” argument assumes that parties nominate dually–meaning many elected members will have run in a district and had a (realistically electable) list position simultaneously. If they do, then even the list-elected members will have a local base, and should have incentives to act as the local “face” of the party, including possibly by offering constituent services. Both prior anecdotes I have shared from New Zealand (e.g., “shadow MPs” who win from the list and maintain a local office) and my forthcoming coauthored book, Party Personnel, offer further evidence that MMP does indeed work in this way.

Now comes a terrific anecdote from New Zealand’s 2020 election. In this election, Labour won a majority of seats (64/120) with 49.1% of the nationwide party list vote. In the nominal tier of single-seat districts (electorates) it won 43 of the 72 available seats. Its win included some districts that are normally strongholds of the center-right National Party (which won 35 seats overall and just 26 districts).

Commenting on some of the Labour wins in mostly rural districts, Federated Farmers president Andrew Hoggard said:

in some “flipped” electorates Labour list MPs had worked hard to raise their profile and get involved with the community and this had paid off when they campaigned for the electorate.

This is an ideal description of how the “best of both worlds” argument works: list-elected members have incentives to attend to local needs of the district in which they ran for the nominal seat (but “lost”) in hopes of capturing the local plurality in the next election.

Of course, there were other factors at work as well. I will offer another planting about one of those factors separately. There is also some uncertainty at this stage just exactly the degree to which rural voters flipped, as the wins may have come in significant part from very large swings in the town areas within districts that also include large rural areas. Regardless, MMP offers the key advantage of giving most elected members, if dually nominated, a tie to a local constituency while ensuring close approximation of overall seat totals to party-list votes.

South Korea 2020

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South Korea had its assembly election on 15 April, with various covid-19 precautions in place. The Democratic Party of President Moon Jae-in (elected in 2017) won a majority of seats.

As discussed previously at F&V, the electoral system was changed from mixed-member majoritarian (MMM) to, at least partially, mixed-member proportional (MMP) prior to this election. It is only partially MMP not mainly because the number of compensatory list seats is so small (30 out of 300 total), but because there remain 17 seats that are, apparently, allocated in parallel (i.e., as if it were MMM).

There was some discussion in various media accounts (and in the previous thread) of the major parties setting up “satellite” parties to “game” the MMP aspect of the system. Under such a situation, a big party will contest the nominal tier seats and use a separate list to attract list votes and seats. By not linking its victorious nominal candidates with a same-party list, a party can gain extra seats, vitiating the compensation mechanism that defines MMP. This is what happened in Lesotho in 2007, for example. (That thread has an interesting series of comments about the issue, including why German parties do not do this in their MMP system.)

The Democratic Party set up a Together Citizens Party to compete for list seats and the main opposition United Future Party set up a Future Korea Party to do the same.

However, if I understand the results correctly (at Wiki), it seems the satellite was not necessary for the Democratic Party to win its seat majority. The Democrats won 163 constituency seats on 49.9% of the (nominal) vote; with 300 total seats, this is a majority no matter what happens with the list seats. Their satellite won 17 seats on 33.4% of the list votes. The United Future won 84 nominal seats on 41.5% of the nominal vote; their satellite won 19 seats on 33.8% of the list votes. I am finding these numbers hard to understand! Maybe someone else can figure this out for us.

South Korea moving to MMP?

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South Korea’s National Assembly appears close to passing an electoral reform bill. It seems that it would change the existing mixed-member majoritarian (MMM) system to mixed-member proportional (MMP).

I always take media reports about important details of electoral systems with caution, but it seems the list seats will be made compensatory: “Under MMP, parliamentary seats are tied to the percentage of voters’ support for political parties.”

The current system (as of 2016) has 47 non-compensatory list seats, in a 300-member assembly.

However, there is a catch. The article says, “The number of PR posts to be allocated under the MMP representation scheme will be capped at 30.” Yet there are to remain 47 list seats; how are the other 17 allocated? To the largest party, or based on vote shares without taking district wins into account (as under MMM)? I wish it were clear, as such details would make quite a difference.

Regardless, proportionality will be quite limited.

An earlier provision of the reform bill that would have provided for 75 list seats was turned down.

Maybe we can call the new system MMp. Maybe.

Thanks to FairVote Vancouver and Kharis Templeman for the tip.

Lesotho (MMP) & Malta (STV) hold early elections on the same day

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Lesotho and Malta will hold early elections this Saturday, June 3rd. Both have parliamentary systems and each one uses a different (and interesting!) type of proportional representation – each having a certain following among readers of this blog.

Lesotho uses a one-vote variant of MMP, with 80 single-seat districts in the nominal tier and 40 in the list tier. There is no threshold, and no seats are added in case of overhang, so a party can win a majority by taking more than 60 districts.

Malta uses STV, with a twist: if I understand correctly, in case one party receives an absolute majority of first-preference votes, seats are added to ensure that party has a majority, and that the majority is in proportion to its majority of the vote.

The elections were also called in different ways. Lesotho’s parliament (election not required before February 2020) was dissolved after the government lost a confidence vote in March – the prime minister could have handed over power to the coalition that ousted him, but chose instead to ask the king for an early election. Malta’s early election (originally not due until March 2018) was called by the prime minister.

New Zealand split-vote results released

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The New Zealand Electoral Commission has released the split-voting statistics from the 2014 general election.

This is a great service provided by the Electoral Commission, showing in each electorate (district) what percentage of voters for each party list cast their vote for that party’s candidate or any other candidate in the electorate. To make it even better for those who like analyzing voting statistics, they offer CSV files.

The NZ Herald offers a summary of key electorates.

Piggyback MPs, part 2

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With apologies to New Zealanders’ somewhat complicated memory of Robert Muldoon, I am sticking to my “piggyback MPs” as a preferred term for members elected under MMP via an alternative threshold to the one based on party-list votes.

Here I want to address briefly the question of whether allowing an alternative threshold, by which a party qualifies for list seats through the winning of one (or more) district seats, is itself a problem in electoral-system design. I have been wanting to address this issue for some time, and some of my thoughts are anticipated by a comment left by Rob at the previous thread.

Up front, let me state that I see no problem with the principle of an alternative threshold. If mixed-member proportional systems are to have a chance of delivering on the “best of both worlds” promise, then one really should allow both worlds to coexist simultaneously. One of those worlds is one in which local concentrations of support for particular parties or candidates are able to attain representation. The other world is one in which only nationwide levels of support for particular parties are worthy of representation. Any one of us might prefer one conception of representation over the other, but MMP is explicitly designed to promote both.

Now, one might respond that one need not have the alternative threshold in oder to obtain both of these worlds. Parties could still exist to target one or a few district seats, and earn their representation that way, without being entitled to any list seats.* I concede that this is a perfectly valid argument, and it seems to be the position taken by the New Zealand Electoral Commission in its MMP Review. That is fine; they have thought much more about these issues, and the needs of New Zealand society, than I ever can do.

However, I think it is a perfectly valid “best of both worlds” provision to say that we want to give incentives to smaller parties to attract support outside their district-based strongholds, while still being able to win representation based on their regional concentration. A very small party may have supporters around the country, but be concentrated in one area. Voters outside the areas of strength have little reason to vote for the list of such a party if it won’t win seats; by the same token, voters in a single district where the party has local strength may have little reason to vote for the party if it lacks any chance to win further seats via list votes obtained elsewhere. (If one seat is expected to affect the balance of power, the second consideration vanishes, of course.)

It seems to me that the decision whether to abolish the alternative threshold should be made not on the basis of disliking particular parties that take advantage of it. (Search on “Key cup of tea” if you are unfamiliar with the debate.) Rather, it should be taken after considering what minimal size of party is considered optimal in a given country’s proportional system. (One can never squeeze out all one-seat parties, as they are at least a latent possibility in any system that has single-seat districts, including mixed-member PR, but one can eliminated the opportunity for such parties to exist to seek additional seats via the list.)

What is the optimal minimum size for parties that win more than just a given district (or two or more), but also win list seats? Continue reading →

MMP and dual candidacy in Wales

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The question of dual candidacy in the Welsh Assembly mixed-member proportional (MMP)* system is being debated again. “Dual candidacy” refers to a provision permitting candidates to run simultaneously in a nominal (district) race and on their party’s list for the proportional component of the system.

Roger Scully offers an overview of the history and debate.

Wales permitted dual candidacy in 1999 and 2003 and banned it for elections of 2007 and 2011. Now a bill is in the House of Commons (yes, this decision is taken in London) to ban dual candidacy again.

Scully mentions various other reforms that have been debated, including an increase in the size of the assembly, from 60 to 80 or 100. As he notes, such an increase would have an impact on the proportionality of the system (independent of dual candidacy).

For instance: the easiest way to change from 60 to 80 AMs would be to raise the number of list AMs in each region (from 4 to 8). But with list AMs now comprising half of the Assembly’s membership, rather than one-third, the proportionality of the electoral system would be changed substantially. An 80-seat Assembly where 40 members came each from the constituency and list ballots would be more-or-less a fully proportional system, rather than the semi-proportional system we have at present.

This is an important point. Because the compensation in the Welsh MMP is carried out in regions instead of Wales-wide, and because the number of seats per region is relatively low, the proportionality is indeed modest. Michael Gallagher‘s Election Indices shows values on the Least Squares (Gallagher) index of disproportionality in the four elections of 8.61, 10.39, 11.36, and 10.47. By contrast, New Zealand, with nationwide proportionality in its MMP system and a 5% threshold, has had index values ranging from 1.13 to 3.84. The UK, with only single-seat districts, has averaged 16.53 on the index over the elections of the same period.

Alternatively, the number of constituencies for the nominal tier could be increased. To keep the same ratio between tiers as is current practice would require 53 constituencies, which “would require the drawing of new constituency boundaries, and losing ‘co-terminosity’ between Westminster and Assembly constituencies.”**

Scully’s preference is for STV, which would resolve the dual candidacy question by reverting to a single tier, while keeping the level of proportionality about the same (potentially). A commission proposed STV a decade ago. Scully notes that there have been two main proposals: grouping the current 40 constituencies into 20 pairs that each elect 4 assembly members or using local authority boundaries as districts (which, I assume, would mean district magnitude varying by municipality population).

As for the dual-candidacy issue, many readers of this blog will know my position. Dual candidacy is an essential feature of mixed-member systems, especially MMP systems, without which many of the main benefits of the system are unrealized. Sure, it does not affect proportionality, but the system also delivers benefits on the intra-party dimension, by encouraging more constituency focus of members elected from party lists than would be the case under pure PR.*** This benefit is likely lost if parties refrain from nominating their best personnel in districts where they are unsure of victory and instead nominate them only on the list. Thus the “legitimacy” problem of list members that underlies the charge against dual candidacy (“entering through the back door,” “zombies”, etc.) is actually made worse by eliminating dual candidacy and thus severing the constituency link of list candidates. The MMP Review in New Zealand extensively commented on this issue and came clearly down in favor of retaining the right to dual candidacy. Wales should do the same–if it retains MMP.

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* In Wales it is called the Additional Member System (AMS). I very much dislike this name, as it treats the list-elected members as mere add-ons, rather than an integral (in fact, the decisive) component of the system. In fact, the name would fit better for the other main category, MMM (mixed-member majoritarian).

** I think “co-terminosity” is a new word for me. I like it.

*** And also without the direct intra-party competition of STV or OLPR, or the partisan incentive for “vote management” and “friends and family” voting/clientelism concerns that STV is especially prone to.