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 more 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.
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.
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. (This is almost always is the case, under any electoral system, for the obvious reason that parties vary in size.)
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, 91**
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.*** 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.****
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). (The USA is most certainly not typical!) This fact only further underscores how much more favorable FPTP is to small parties than is Turkey’s system.
* 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.
** 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.
Seat share 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.