The Greek general election of July, 2019, may have been about as “normal” as they get. After the country’s period of crisis–economic and political–things seem to have settled down. The incumbent party, Syriza (“Radical Left”), which saw the country through the crisis got booted out, and the old conservative New Democracy got voted in.

Of course, around here when we refer to an election as “normal” it means it conforms to the Seat Product Model (SPM). Applying the SPM to an electoral system as complex as that of Greece is not straightforward. However, based on some calculations I did from breaking the system down to its component parts (an approach I always advocate in the face of complexity), it seems we have a result that conforms to a plausible interpretation of its “expectation”.

The basics of the electoral system are as follows: there are 300 seats, of which 50 are an automatic bonus to the party with a plurality of the vote, while the remainder are allocated as if there were one nationwide district. The “as if” is key here. In fact, there are 59 districts. In other words, the district magnitudes in which the election plays out for voters and candidates are quite small. There are 12 seats in a nationwide compensatory tier [EDIT: see below], so we have 288 basic-tier seats for a mean district magnitude of around 4. (I am not going to go into all the further details of this very complex system, as these will suffice for present purposes; Election Resources has a great detailed summary of the oft-changed Greek electoral system.)

To check my understanding that the system is *as if* nationwide PR for 250 seats, plus 50 for the plurality party, I offer the following table based on the official results. Note that there are two columns for percent of seats, one based on 250 and the other based on the full 300. For the largest party, ND, the “% seats out of 250” is based on 108 seats, because we are not including the 50 bonus seats in this column.

Party | % votes | seats | % seats out of 250 | % seats out of 300 |

Nea Dimokratia | 39.9 | 158 | 43.2 | 52.7 |

Syriza | 31.5 | 86 | 34.4 | 28.7 |

Kin.Al | 8.1 | 22 | 8.8 | 7.3 |

KKE | 5.3 | 15 | 6.0 | 5.0 |

Elliniki Lysi | 3.7 | 10 | 4.0 | 3.6 |

Mera25 | 3.4 | 9 | 3.6 | 3.0 |

14 others | 8.1 | 0 | 0.0 | 0.0 |

We can see that the seat percentages out of 250 are close to the vote percentages, as we would expect if the system acts as if it were nationwide PR (not counting the bonus). More to the point, we would expect all parties, even the smallest that win seats, to be over-represented somewhat, due to the nationwide threshold. That is indeed what we see. Over 8% of the votes were wasted on parties that failed to clear the threshold. The largest of these, Laikos Syndesmos, had 2.93%. The threshold is 3%. No other party had even 1.5%.

It is clear that the system has worked in this election exactly as intended. The largest party has a majority of seats, due to the bonus, but even the percentages out of 300 are close to proportionality–far more than they would be if Greece tried to “manufacture” majorities via FPTP or two-round majority instead of “bonus-adjusted PR”.

The effective number of seat-winning parties (N_{S}) is **2.70**. It would have been 3.13 based on the indicated parties’ percentages of seats out of 250. So the bonus provision has reduced N_{S} by 13.7%. (The effective number of vote-earning parties, N_{V}, is 3.68, calculated on all the separate parties’ actual vote shares.)

But what about the SPM? With 288 seats in districts and 12 nationwide, we technically have a basic-tier seat product of 288 x 4 (total seats in the basic tier, times the mean magnitude). However, this includes the 50 bonus seats, which are actually assigned to districts, but clearly not allocated according to the rules that the SPM works on: they are just cream on top, not a product of seat allocation rules in the basic tier and certainly not due to compensation. So, what percentage of seats, excluding the bonus, are allocated in districts? That would be 288/300=0.96, which out of 250 yields a “shadow” basic-tier size of 240 (96% of 250). So our adjusted basic-tier seat product is 240 x 4=960.

In a “simple” system (no compensatory tier as well as no bonus), we would expect, based on the Seat Product Model formula, that the effective number of seat-winning parties would be N_{S}=960^{1/6}=3.14. We would expect the size of the largest party to be s_{1}=960^{–1/8}=0.424. Note that these are already really close to the values we see in the table for the 250-seats, pre-bonus, allocation, which are 3.13 and 0.432. I mean, really, we could hardly get more “normal”.

[Added, 14 July: The following paragraph and calculations are based on a misunderstanding. However, they do not greatly affect the substantive conclusions, as best I can tell. The system is two-tier PR, of the “remainder-pooling” variety. However, the 12 seats referred to as a nationwide tier are not the full number of compensatory seats. With remainder-pooling systems it is not always straightforward to know the precise number of seats that were allocated above the level of the basic tier. Nonetheless, the definition here of the basic tier seems correct to me, even if I got the nationwide portion wrong. Thanks to comments by JD and Manuel for calling my attention to this.]

Nonetheless, there is a nationwide compensation tier, and if we take that into account through the “extended” SPM, we would multiply the above expected values by 2.5^{0.04}=1.037, according to the formula explained in *Votes from Seats*. (The 0.04 is the share of seats in the upper, compensatory, tier; 100–0.96). This is obviously a minor detail in this system, because the upper tier is so small (again, not yet counting the bonus seats). Anyway, with this we get expected values of N_{S}=1.037 x 3.14=3.26. We do not have a formula for the largest seat winning party (s_{1}) in two-tier PR, but one can be determined arithmetically to lead to the following adjustment: s_{1}=0.973 x 0.424=0.413. (This is based on applying to the extended SPM for N_{S }the formula, s_{1}=N_{S}^{–3/4}, as documented in *Votes from Seats* [and its online appendix] as well as Taagepera (2007).) I believe these are the “right” figures for what we should expect the outputs of this system to be, *on average* and without taking election-specific politics into account, given this is not a “simple” (single-tier PR) system even before the bonus seats are taken into account.

Out of 250 seats, 41.3% is 103. The ND actually won 108 pre-bonus seats. The 50 bonus seats then would get the party to an expected 153, which would be** 51.0%**. It actually got 52.7%.

So, as we deconstruct the electoral system into its relatively simpler components, we get an impact on the party system that is expected to result in a bare-majority party. As for N_{S}, values are generally around s_{1}^{–4/3}, which with s_{1}=0.51, would be 2.45, which is somewhat lower than the actually observed 2.70. But perhaps the actual relationship of s_{1} to N_{S} should be something between a “typical” party system with a largest party on 51% of the seats (2.45) and the party system we expect from 250 seats with Greece’s pre-bonus two-tier PR system (3.26). The geometric average of these two figures would be 2.82. The actual election yielded N_{S}=2.70, which is pretty close. OK, so maybe the similarly of this value of N_{S} to our “expectation” came out via luck. But it sure looks like as normal a result as we could expect from this electoral system.

Of course, in 2015, when there were two elections, the country was in crisis and the outcome was rather more fragmented than this. I am not sure when the 50-seat bonus was implemented; it used to be 40. So I am reluctant to go back to the pre-crisis elections and see if outcomes were “normal” before, or if this 2019 result is just a one-off.

For the record, in September, 2015, the largest party had 48.3% and N_{S}=3.24; in January, 2015, the figures were 49.7% and 3.09. These are hardly dramatic differences from the expectations I derived above (51.0% and 2.82), but they are more fragmented (particularly in terms of higher N_{S} albeit only marginally in terms of a lower s_{1}). So, all in all, maybe the Greek electoral system is not as complex as I think it is, and all its elections fall within the range of normal for such a system. But this 2019 election seems normaler than most.

I believe that in the “seats out of 250” column on your table, the result in the row for ‘Elliniki Lysi’ should be 4% rather than 9%, unless I’ve misunderstood something.

The only complicated aspect of the Greek system appears to be the fact that there are districts at all, since they appear to have no relevance or effect on the overall national result.

I was confident there would be an error in transcribing the table. I just was not sure where. Corrected now. Thanks.

As for districts not shaving effect on the overall national result, that is usually the case in two-tier PR systems–if by effect we mean from observed votes to actual seats. However, what the Extended Seat Product Model reveals is that they do still matter: the number of parties would be anticipated to be much greater if it were actually a 250-seat nationwide district than what we get from all these small-magnitude districts in the basic tier. There is an extensive “reality check” on this model in Chapter 15 of

Votes from Seats, and in the on-line appendix.From my reading of the description of the system, I think the 12-seat district might not be compensatory, but parallel.

As I wrote on my website’s Greece page, “under the terms of a 2008 amendment to the electoral law, the majority premium increased to fifty seats in 2012, leaving 250 seats to be allocated by PR;” this was noted as well here on this blog just over seven years ago. Also, on my site’s Greece page there’s a link to an entry on my blog detailing the Allocation of Constituency Seats in the Hellenic Parliament (Vouli), where I wrote that “The twelve nationwide or state mandates are distributed among qualifying parties (that is, those polling at least three percent of the nationwide vote) by the largest remainder method of PR – the same method used for the nationwide allocation of 250 Vouli seats.”

The only significant change in last Sunday’s election was the division of the Athens B and Attica constituencies in three and two smaller constituencies, respectively, which increased the total number of constituencies from fifty-six to fifty-nine. Incidentally, I ran the procedure described on my blog’s entry, and obtained exactly the same constituency-level distribution of seats published on Greece’s Ministry of the Interior’s elections website.

Finally, had the election been carried out by districted D’Hondt with a nationwide 3% threshold, ND would have won an even larger majority of 165 seats, but the four smaller parties would have been reduced to a total of eighteen seats.

Yes, just as Manuel pointed out: there are two PR allocations: one for the 12 seats, and one for the 238 seats. They are made in parallel, and both are nationwide. seats are not allocated to parties in the districts but at the national level, with those seats then allocated to districts along with the 50 bonus seats. If seats had actually been allocated in the districts, the result would have been considerably more majoritarian.

As I’ve understood it, all 250 PR seats are distributed on a nationwide basis, and the 12 nationwide seats are then subtracted from the overall PR distribution, leaving 238 seats to be allocated among the constituencies, along with 50 majority bonus seats. That said, in 2019 the separate nationwide distributions of 238 and 12 seats would have produced together the same seat outcome as the single PR distribution of 250 seats.

At any rate, the data files which feed the Greek Ministry of the Interior’s 2019 general election website report the following seat totals for the twelve nationwide or state mandates:

ND – 5

SYRIZA – 4

KIN.AL. – 1

KKE – 1

ELLINIKI LYSI – 1

MERA25 – 0

For the remaining 288 constituency mandates, the overall distribution of seats was as follows:

ND – 153 (103 + 50 majority bonus)

SYRIZA – 82

KIN.AL. – 21

KKE – 14

ELLINIKI LYSI – 9

MERA25 – 9

An English-language translation of the 2008 amendment to Greece’s electoral law – Law 3636/2008, available in PDF format on ODIHR’s Legislationline website here – states that:

“To determine the seats each party is entitled to, the total votes it accumulated in the State is multiplied by the number 250. The product is divided by the sum of valid votes accumulated in the State by the parties involved in the distribution of seats in accordance with the provisions of Article 5. The seats each party is entitled to in the State is the integral part of the division’s quotient.

If the sum of those integral parts of the quotient is below the number 250, then seats are ceded, in order, up to the achievement of this number, to parties whose quotients have the largest decimal fractions.”

Meanwhile, Article 100 of the 2007 electoral law – also available in English on the Legislationline link furnished above – clearly indicates the twelve nationwide seats are also distributed by the largest remainder method of PR used to allocate the 250 (originally 260) PR seats.

At any rate, I have gone over the results of Greek parliamentary elections from 2007 to 2015, and attempts to carry out separately a nationwide distribution of the 238 constituency seats (248 in 2007 and 2009) from the twelve state mandates resulted in slightly different (and therefore incorrect) seat distributions in every election except 2007.

https://en.m.wikipedia.org/wiki/Elections_in_Greece

This article indicates the allocation of seats, the next election (2023 or earlier) will be by proportionality as the 50 bonus seats have been abolished.

That was noted here previously. As stated in the earlier post, it will be interesting to see if ND repeals the law to remove the bonus seats. But even if they do, I guess the next election will have to be without the bonus (unless a law restoring the bonus adjustment were to get two-thirds support).

Going over the English-language translation (by Google Translate) of Law 4406/2016 – which provides for the distribution by PR of all 300 Vouli seats in the next Greek general election – it would seem the existing mechanism for allocating party seats among constituencies has been retained, albeit with apparently minor changes in the wording of the relevant provisions. However, the translation leaves much to be desired – for one, it repeatedly trips up over the Greek term for “two-seat district” – and I’m by no means fully certain that is indeed the case.

Yes, the electoral law was reformed before this election to go to (essentially) a national proportional system. By law, unless there is a supermajority in favor, changes cannot go into effect for the next election, but the one after that (presumably to stop the parliamentary majority from passing an electoral law to benefit themselves).

ND (who led polling for this election for several years) understandably voted against putting the new law in place for this year’s election. Had it been in place, they would have needed a coalition partner (probably KIDISO, which is essentially a rump PASOK with some intervening centrist movements merged in) to form a working government.

The center-right won a weak plurality, and the vote for the incumbent party dropped slightly, so the election was completely normal. A normal election will see a center-right party win with a plurality in the high 30s or low 40s and a slight drop in support for the incumbent party. Really what changed from last time was the consolidation of the pro-establishment vote around New Democracy.

Very interesting to know (up-thread) that the nationwide seats are non-compensatory. OK, so it just got a little more complex again in my assessment.

As shown in the main entry, it would not make much difference to the calculations if we took it to be a “simple” system (ignoring the small parallel component in the estimates), because the multiplier term from the extended SPM for a compensatory tier this size would be only 1.037.

The interesting finding, for me, is that the districts evidently do matter. As noted, if we considered it to be effectively a 250-seat (or 238-seat) nationwide allocation, we would expect a much more fragmented party system. Somehow, voters and other actors “see” a districted system, the nationwide allocation process notwithstanding.

So this is one of those cases where I do not understand why the SPM works. Maybe it’s just luck. But it works, as long as we take the districts seriously as a constraining feature of the system–as the process by which votes come from seats.

So I am still unsure if the 12 nationwide seats are compensatory or parallel.

There is a page at Manuel’s site (that I had missed before) that sates, referring to the 12 seats, “These are then deducted from the parties’ nationwide PR seat totals to obtain their corresponding constituency mandate totals.” Unless I am misunderstanding, this seems to describe a compensatory feature.

Also, an earlier comment by Manuel at this thread also leaves me thinking they might be compensatory.

On the other hand, it is clear that the process involves more seats being allocated based on extra-district votes, i.e., in a remainder-pooling system, than just these 12 fixed nationwide seats. Therefore, the multiplier in the Extended Seat Product would be higher than the 1.037 reported in the post. It would not appear possible to determine how much higher without a full accounting of which seats in the basic-tier districts were actually allocated to a party via the remainder pool. The bottom line would be that the “expected” values from the SPM would be higher for Ns and lower for s1 than I reported above.

I wouldn’t consider the 12 nationwide seats compensatory, at least insofar as the PR portion of the electoral system is concerned, because they are distributed by the same method as all 250 PR seats, namely Hare/largest remainder, and the resulting percentage differences between the overall distributions of the 250 seats and the 238 constituency seats are insignificant. For example, in this year’s general election ND won 43.4% of the votes cast for qualifying parties i.e. above the nationwide 3% threshold, which entitled the party to 108 of 250 PR seats (43.2%), and 5 of 12 nationwide seats (41.7%). After deducting the latter, ND was entitled to 103 of 238 constituency PR seats, or 43.3% of the total.

Excluding the fifty majority bonus seats for ND, the overall distribution of the 238 constituency seats was as follows:

ND – 103

SYRIZA – 82

KIN.AL. – 21

KKE – 14

ELLINIKI LYSI – 9

MERA25 – 9

After allocating seats in single-member districts to the largest qualifying party; seats in two- and three-member constituencies by Hare/largest remainder; and seats in constituencies with more than three seats by full Hare quotas – the Hare quota in each constituency being calculated by dividing all valid votes cast (i.e. including votes for below-threshold parties) by its number of seats – the distribution of constituency PR seats stood as follows:

ND – 99

SYRIZA – 79

KIN.AL. – 11

KKE – 2

ELLINIKI LYSI – 0

MERA25 – 0

Therefore, qualifying parties had the following unfilled PR constituency seat totals:

ND – 4

SYRIZA – 3

KIN.AL. – 10

KKE – 12

ELLINIKI LYSI – 9

MERA25 – 9

These unfilled seats were allocated on a party-by-party basis, starting with the qualifying party with the smallest nationwide vote total, then the second smallest qualifying party, and so on until there were no parties with PR constituency seats to be filled. For each party its largest vote remainders in constituencies where mandates remained available were assigned one seat each, until the party reached its PR constituency seat total.

The only instance in which a remainder had to be skipped because there were no further seats available was in nine-seat Thessaloniki B, where ND – the last party to have its unfilled seats allocated – initially obtained three seats by full Hare quotas, while SYRIZA secured two. The party-by-party allocation of unfilled seats by largest vote remainders gave one seat each to the remaining four qualifying parties; however, when ND’s four unfilled seats were allocated, its second largest remainder in Thessaloniki B, was disregarded, since by that point the constituency had no unfilled seats. The party’s fourth and final unfilled mandate was assigned instead to its fifth largest remainder in Ioannina, where ND and SYRIZA had been initially assigned a seat each by full Hare quotas and three seats remained unfilled.

Finally, the fifty majority bonus seats were allocated to ND – the winning party – from the remaining unfilled seats (50 out of 288) in the multi-member constituencies, including the two unfilled seats in Ioannina.