In a comment in the previous thread on potential political reform in Israel, Ed raised the point that the country’s party-system fragmentation is at least as much a product of Israel’s social diversity as it is of the electoral system. It is a sensible argument, inasmuch as the party system has grown steadily more fragmented over time, while the most important features of the Knesset electoral system have been unchanged. (The 1996-2001 period of direct election, also discussed in the comments to the previous thread, was quite likely a contributor to fragmentation in the 1990s, but fragmentation has not declined since the return to a pure parliamentary system.)

In the past two decades, Israeli society has become more plural than ever, as immigrants from the former Soviet Union have created a new cleavage that has seen the rise of a significant new party, Yisrael Beiteinu (Israel is Our Home¹ ), led by current Foreign Minister, Avigdor Lieberman. And while there is no single party that represents the Sephardi/Mizrahi Jewish population (those whose disaporic roots are in other Middle Eastern countries), the Shas party, which draws a significant share of this community’s votes, has been growing since the early 1990s. So these developments seem to support the social-origins argument for Israeli party-system fragmentation over the electoral-system argument.

On the other hand, no clear social cleavage precipitated the creation of the Kadima Party, the launch of which by then-PM Ariel Sharon prior to the 2006 election was an even bigger contributor to the recent fragmentation than the growth of either Yisrael Beiteinu or Shas. And no new cleavage is clearly behind the stated intention of TV newsman Yair Lapid to form his own new party.²

Lkely none of these parties would have been as viable in the short run without such an extreme proportional system. Yet thanks to the seamlessness with which electoral support guarantees Knesset seats, Yisrael Beiteinu has grown from 2.6% of the vote in 1999 to 11.7% in 2009 and Kadima won 22% in its first election.³ Polls immediately suggested Lapid’s party could earn 15-20 seats, which would place it among the three largest parties in the country.

An extreme proportional system does not guarantee a proliferation of parties, but it makes proliferation feasible, whether due to new social groups mobilizing behind new parties or to existing public figures creating new electoral vehicles for themselves and their associates.

In fact, we can use a purely institutional theory to account for the degree of fragmentation facilitated by the electoral system. We can then attribute any deviation from the predicted value of fragmentation to other social or political factors. For example, in Predicting Party Sizes (Oxford University Press, 2007), Rein Taagepera derives the following equation:

N=(MS)^1/6

Where N is the “effective” number of seat-winning parties, which is by now the standard measure of party-system fragmentation in the political science literature, M is the average district magnitude, and S is the assembly size. The product of the latter two indicators is what Taaepera defines as the Seat Product.

The equation is derived deductively. (That is, it is not a “post-dictive” regression equation, but rather is built as a “logical model” from sparse assumptions about how district magnitude and assembly size “should” affect the outcome variable of interest.)

The graph of this equation against the data (on p. 153 of the book) from two dozen long-term democracies shows a very strong fit to this model. However, it is important to note that the value of N that is plotted for any given country is its average value over several decades of elections, and not the snapshot of any one election, or a recent sequence of elections. Because Israel elects the Knesset from a single 120-seat district, M=S=120, and MS=14,400. Raising this to the exponent, 1/6, yields 4.93. The data point for Israel is almost precisely on line representing the equation reproduced above. Slightly below it, in fact.⁴

So the Seat Product equation tells us that Israel, known for decades as a diverse polity with numerous parties, has experienced just about the precise degree of party-system fragmentation that we should expect it to have, given its Seat Product. The implication of this finding is that changing the Seat Product, for instance by reducing the district magnitude, could be expected to reduce party-system fragmentation.

As noted above, Israeli fragmentation has been growing recently. In fact, the last three elections–those since the abolition of the brief phase of direct prime-ministerial elections–have had an average N=6.93. That is above the predicted value (which is close to the actual longer-term average, as noted) of 4.93. The recent elections exceed the Seat Product by just over 40%. This suggests that recent factors driving the formation of new parties are accounting for the extra “two parties” that the party system now “effectively” supports.⁵

What impact might electoral reform have? And here I mean serious electoral reform, but one that remains firmly within the proportional family. Not a small rise in the threshold, but also not a move to (or towards) a majoritarian system. Let’s suppose Israel adopted a system of districts, as a means to cut its Seat Product.

If the average magnitude of the districts were to be 30, which would still mean the average district in Israel would be around the size of the largest district used by some of Europe’s other fragmented party systems⁶, the resulting Seat Product would be 3,600. Plug that into the equation and you would have an estimate of 3.91–effectively one party less than Israel’s long-term average. However, if the current three-election average is 40% higher than the Seat Product prediction, we might realistically expect it to remain so even with a change to M=30. If so, then it might be at N=5.48–still a substantial reduction from where it is now.⁷

What if Israel went to an average magnitude of 10, which would result from carving the country into twelve electoral districts? Then we have a Seat Product of 1,440. This yields a prediction of N=3.36, and if Israel’s actual system remained 40% over, it might be around N=4.70.

Could the social divisions of Israel be so great that they would resist even a 90% reduction of the Seat Product, through the adoption of twelve districts? Perhaps, but if the effective number of seat-winning parties remained at its recent 6.93, that would be 106% over the predicted value. Only one country in Taagepera’s graph is anywhere near such an excess relative to prediction: Papua New Guinea. And I submit that PNG is a good deal more fragmented than Israel.⁸

Clearly social and political factors outside of the electoral system are responsible for the recent rise in Israeli party-system fragmentation. Yet the fact that the longer-term average for Israel–which it should be stressed already placed it among the more fragmented systems!–almost perfectly matches what Taagepera’s Seat Product predicts suggests that electoral reform could make an impact. Perhaps Israel has finally outgrown its 120-seat district, and it is time for a more modest proportional system.⁹

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1. Yes, Israel Is Our Home; I regularly see news stories that translate the party’s name as “Israel Our Home”, which of course makes no sense in English. There is no linking verb in the Hebrew expression. [↩]
2. He is likely simply to compete for the same basic voting bloc that helped the rise of the new leader of the Labor Party and that which votes for Kadima. [↩]
3. See the Israeli Knesset pages for past election results. [↩]
4. Only Papua New Guinea has an effective number of parties far higher than predicted from its Seat Product, while Botswana, the U.K., and Spain are among the countries clearly on the low side (though not by large differences). [↩]
5. The “effective” number tells us how many hypothetical equal-sized parties would fragment the party system as much as the actual unequal-sized parties do. Thus it is incorrect to say, as some do even in the published literature–that it is a measure of how many “effective parties” there are. It is the number, not the parties it counts, that is “effective”. [↩]
6. E.g. Finland and Switzerland. [↩]
7. This assumes no supra-district allocation; if there were such a compensatory procedure in place even after districting, it would really not be any different from the status quo, as allocation would be “as if” there were still one 120-seat district. [↩]
8. Plus, PNG’s fragmentation is localized, and hence capable of finding expression through the single-seat districts that PNG uses, and that make its Seat Product equivalent to its assembly size of 109. [↩]
9. By the way, the same argument could be made for the Netherlands, where N over the long term is likewise almost precisely where its high Seat Product says it “should be”, but where there has been a marked upward trend in N recently. [↩]