This question that James raised in the comments to the previous planting on Turkey is a good one: how “friendly” or not is Turkey’s threshold to small parties, relative to a first-past-the-post (or plurality) system in single-seat districts?
The question can be addressed using Rein Taagepera’s “seat product.”
If all the mathematics that follow are not of interest, the reader can be advised that the conclusion of the exercise is that Turkey’s electoral system restricts the smallest party to around 50 seats at a minimum (not counting independents–addressed below). Thus it is extremely unfriendly to small parties. On the other hand, with a plurality system and the same size assembly, the smallest party could easily have one seat, and it would be a surprise if the smallest party did not have less than 10 seats. So the Turkish system is somewhere between 5 and 50 times more unfriendly to small parties than is an otherwise comparable plurality system.1
OK, on to the estimates…
For reasons Taagepera explains in his 2007 Oxford University Press book, Predicting Party Sizes, we can derive the expected number of parties winning at least one seat by taking the size of the assembly (S), multiplying it by the magnitude of the average district (M), and then taking the fourth root of the product.
p=(MS).25.
As also explained in Taagepera (2007) we can expect the seat share of the largest party to be, on average:
s1 = (MS)-.125 (s1 as decimal share).
Turkey has S=550 in 85 districts, resulting in average M=6.5, approximately.
With no threshold, we would then expect 7.7 parties to win at least one seat, on average. This suggests that the “average” party would have around 71 seats (550 seats divided among 7.7 parties).
The second equation suggests that the largest party would be expected to win about 36% , or 128, seats. Many parties might have 1 or a few seats only, thereby explaining an average that is well below the expected largest share.2
However, the 10% nationwide threshold keeps any party from winning fewer than about 50 seats. (10% of 550 is obviously 55, but because only the threshold is national, not the actual seat allocation, it is impossible to specify precisely what the smallest possible party size is. It would depend on how a 10% party’s votes were distributed across districts. So we can use 50 as a round estimate.)
So if the minumum number of possible seats for any party is around 50, we can take the geometric average of this figure and the theoretical maximum of 550 (when one party wins all seats), and we get an expected average number of seats of 166. Note this is about 2.3 times the size of the expected average under no threshold (71).
This suggests that, with Turkey’s 10% threshold, the average number of parties would only be around 3 (550/166=3.31). This can be double-checked by going back to the likely minimum party size, 50, and recognizing that at most 11 parties could win if all had the minimum size. The geometric average of the theoretical range from 1 party to 11 parties is 3.32. So our math checks out.
How does this check out in reality? Consider the actual number of parties winning at least one seat (p), the seat total of the largest party (s1), and the number of seats won by the smallest party (s-small), in each of the four most recent Turkish general elections.
year, p, s1, s-small
2007, 3, 341, 70
2002, 2, 363, 178
1999, 5, 136, 85
1995, 5, 158, 49
_______________________
avg, 3.75, 259.5, 95.5
exp, 3.3, 273, 913
Pretty well!
Note that I am excluding independents here. In Turkey in 2007, although not in previous elections, there were many candidates who won without formal party endorsement, but with informal support. There were 28 of them in 2007 (5.1% of all seats), a huge increase over the 9 (1.6%) that won in 2002. This is an obvious loophole of the system that makes analyzing it more challenging. But the question at hand here was how unfriendly the 10% party threshold is. Parties that can’t hope to break 10% nationally are forced to play a different game, almost as if the system were SNTV.4 Choosing to run candidates as “independents” makes it hard for a party to win more than 1 seat per (multi-seat) district–because it must practice vote division among its candidates–even where it would be quite strong if it could compete on a level playing field with the major national parties. It is interesting that the recent trend appears to be towards a larger-than-expected largest party, and more seats won by independents, many of whom are de-facto small parties using the loophole in the threshold. It may be that the system is genuinely bifurcating into two classes of parties–a hegemonic ruling party and an increasingly fragmented and personalized opposition.5
Now contrast our expectations and results of the Turkish system with a FPTP system. The seat product when M=1 is obviously equivalent to the assembly size, S. So take the fourth root of 550 and get 4.8 expected average number of seat-winning parties. With 4.8 parties dividing 550 seats, the average per party has 115 seats. This is the largest any party could be in the extremely unlikely event that all “4.8″ parties had equal seat totals. The geometric average of the range of 1 to 115 is 10.7, which is where I dervied the estimate mentioned above of a smallest party in a 550-seat FPTP system of around 10 maximum, in contrast with 50 seats minimum (not an average, but a minimum number, for the smallest).
In fact, in plurality, single-seat districted systems of 400+ seats, the average number of seat-winning parties tends to exceed the estimate derived from the seat product appreciably. There have been at least 10 parties represented in each UK election since 1997, and obviously many more in the similarly sized Indian parliament. Canada almost nails its seat-product estimate, with 308 seats leading to an estimated 4.2 parties, and actually having had 4 parties in each recent parliament (and 5 in the one just elected).6 This fact only further underscores how much more favorable FPTP is to small parties than is Turkey’s system.
(Note: Minor editing and a couple of new footnotes added since original planting.)
- The consideration of the smallest size of a party is important. As recent elections in the UK, Canada, and Australian first chambers show, a small party can concentrate its efforts on a few districts or even just one and thereby break into the system, as Greens have done in each country’s most recent election. However, in Turkey, to get to 10% nationally would require effort, and some measure of vote-winning success, in numerous districts. [↩]
- as almost always is the case, under any electoral system, for the obvious reason that parties vary in size. [↩]
- I derived the expectations on s1 and s-small under Turkey’s thresholds as follows…
-
s1 if there are 3.3 parties has to be at least the average (166) and at most around S-(2*s) where s is the smallest share, expected to be 50. That makes the maximum 450, and the geometric average of 166 and 450 is 273.
s for the smallest is expected to be 50 at a minimum and has to be no more than 166 (for 3.3 parties). The geometric average for this range is 91.[↩]
- That is, single non-transferable vote, in which the M seats go to the highest vote-winning candidates, regardless of party affiliation, if any. In Turkey, candidates running independently of a party list are in direct competition with (closed) party lists for a district’s seats, making it sort of like having SNTV and list-PR systems running concurrently in any district in which there is at least one party that has two or more candidates running as “independents”). [↩]
- With a maximum of 5% of seats won by “independents” so far, we should not exaggerate this trend, but given that 13.8% of votes in 2007 were cast for party lists that fell below the national threshold, we might expect these parties to turn towards playing the “independents”/SNTV game instead of risking winning nothing. [↩]
- The USA is most certainly not typical! [↩]
I’d contest the concentration idea.
Obviously parties throw most resources where they can win, but in the 2 recent elections, the federal election of 2010 and the NSW election of 2011 I know most about the Greens did not focus exclusively on the seats where they were successful.
In both cases the Greens gave at least equal attention to winning upper house seats, federally each state and territory is a single electorate and in NSW the whole state is a single electorate.
The Greens won the balance of power in the federal senate and expanded their representation in the NSW legislative council. Both require statewide campaigning. Focusing on one or 2 lower house SMDs would be suicidal under this system. Indeed in NSW there was a greater effort in the seat of Marrickville where the deputy premier had a close fight to retain her seat. (She did not, of course, retain the deputy premiership because of the change of government)
The parliamentary library comments:
The two party preferred vote there was ALP 50.9%/Green 49.1%. The Greens actually had a higher primary vote 35.9% in Marrickville against 30.7% in Balmain.
Seed planted by Alan — 10 June 2011 @ 19:52
I defer to Alan’s knowledge of Australian campaigns. The presence of other, multiseat constituencies, in Australia makes a difference. So presumably does the fact that Green preferences can affect contests in non-winnable (for the Greens themselves) single-seat districts due to AV.
I’d be surprised if there was not considerable energy focused on that district in Melbourne, in order to win one House seat. But I was not there, and have not researched the matter.
In any case, the argument I was making about Turkey, relative to plurality or majority systems, does not depend on the actual resource effort of the Australian Greens.
(Alan might have zinged me on the fact that the Australian Greens in 2010 actually won over 10% of the vote, so if Australia used Turkey’s system, they might have won 15 seats instead of 1! But fortunately he did not.)
Seed planted by MSS — 10 June 2011 @ 21:01
Dyscalculia is hell)
Seed planted by Alan — 10 June 2011 @ 22:47
Two decades ago, before the Greens, the Australian Democrats likewise tried to win single-member seats by concentrating their resources on high-profile candidates – first Senator Janine Haines in Kingston, 1987 and then John Schumann in Mayo, 1998. Both seats were in South Australia (the ADs’ stronghold). Haines was the first female leader of a federal parliamentary party in Australia, and Schumann was lead singer for political folk group Redgum, who’d topped Australian charts in 1982 with their anti-Vietnam War ballad “I Was Only Nineteen”. However, both failed narrowly. Haines ran third, with 26% of the first preferences to the Liberal’s 33% – a 3.5% swing may have made her a Condorcet winner. Schumann ended up second but lost 52-48%.
As Alan noted, campaigning incentives are different for Greens (and other minor parties) in Australia than under FPTP elsewhere. Over-focusing on one district may mean you lose Upper House PR seats, and lose influence via lower house preferences, everywhere else. Whereas if Elizabeth May and Caroline Lucas don’t break through in that particular constituency, their Green Parties end up with no other seats and no other political clout.
(Ironically, two other AD leaders have held single-member seats, although in both cases it was when they belonged to other parties – Don Chipp for Higinbotham as a Liberal before he quit to form the ADs, Cheryl Kernot for the cursed seat http://tinyurl.com/4yfulda of Dickson after she quit to join the Labor Party.)
Seed planted by Tom Round — 11 June 2011 @ 04:27
Aaargh. Haines in Kingston was 1990, not 1987.
Seed planted by Tom Round — 11 June 2011 @ 08:53
Mixing Instant Runoff Voting with pre-electoral coalitions would be very interesting!
Seed planted by Derek — 11 June 2011 @ 16:54
One nitpick, the 10% requirement in Turkey isn’t really a “loophole”, a better term would be “constraint”.
Seed planted by Ed — 12 June 2011 @ 01:11
Tom: Whereas if Elizabeth May and Caroline Lucas don’t break through in that particular constituency, their Green Parties end up with no other seats and no other political clout.
That’s not entirely true in the UK. The Greens would still have representation in the Scottish and Northern Irish devolved assemblies, in the European Parliament, as well as in the partisan local elections. (I choose to ignore for the moment that technically the Scottish Greens and the English Greens are different parties.) If the House of Lords reform ever actually occurs, it will probably involve some sort of PR, and the Greens could win seats there too.
For whatever reason, the Canadian Greens do rather badly in provincial elections except in BC, and have yet to win a seat in a provincial legislature. Canada is not part of any supra-national organization that deigns to elect its members. Municipal governments have little power, and are either non-partisan or have one-off parties unaffiliated with national or provincial parties. (There’s apparently a tiny Green party in Vancouver, and Projet Montréal is about as green as you can get without being Green.) We’ll see what Senate reform brings, but so far the only province that elects senators, Alberta, uses the block vote. Ew.
Seed planted by Vasi — 12 June 2011 @ 02:14
Vasi – excellent point and I stand corrected. I was thinking of an election for a single legislature alone (albeit both chambers at once), since in Australia the same jurisdiction never votes for two or more different legislatures on the same day. (Federal statute actually bans state polls – including local polls – on the same day as a federal poll without the Cabinet’s permission). The closest we get to a “super Tuesday” downunder is different States holding their elections on the same day, which apparently seems to be the pattern for Tasmania and SA these days (creating an urgent necessity to clone or teleport Antony Green!). Whereas the USA almost always, and the UK often, holds national, regional and local elections (or two of these) concurrently.
Seed planted by Tom Round — 12 June 2011 @ 09:05
The “loophole” is not the 10% threshold, but the fact that a party can run its candidates as “independents” and then they will win if they get one or more candidates sufficient personal votes in a district. But if they run under the party banner, they must win 10% nationwide to get a seat, even if they were to get 100% in some district.
Seed planted by MSS — 12 June 2011 @ 16:39
So reports Al Jazeera, in its Turkish election blog.
If this proves correct, it would mean a third term for the AKP, but also the second consecutive election in which it declined in seats. It would also mean the party fell well short of a two-thirds majority.
Note the further growth of independents.
Seed planted by MSS — 12 June 2011 @ 21:34
I wonder if the success of the independents (who I think are predominantly, though not exclusively, Kurdish nationalists) is the reason for the steady decline in the AKs seat totals in the last few elections. The seat harvest the largest party in the country should expect, when the Kurdish parties are excluded in their heartlands, is substantially reduced when the independents soak up some of that otherwise wasted vote.
Daily Hurriyet in English has a good results page:
http://www.hurriyet.com.tr/english/election2011/election.html
Seed planted by DC — 13 June 2011 @ 06:53