Now corrected from its original version (which contained some errors in the Czech data reported). Originally planted 18 July.
In discussing the proposed threshold of 5% of party preference votes to guarantee election from “flexible” lists in Catalonia, I expressed skepticism that this would result in many members being elected by their own votes.
Well, I just happen to have some data that might shed a little ray of light on this question, for those few of you who actually find this kind of stuff interesting. I opened up my merged data set of legislators from several open list systems, and restricting the analysis to districts that are about the size proposed for Catalonia (specifically, districts of 10 to 25 seats), I find that the mean preference vote share (preference votes divided by list votes in the district) of the elected members is .174. That is a lot more than .05, but the standard deviation is almost as big as the mean: .162. The median share is .115, and about 15% of elected candidates in these districts won with under .05.
So, perhaps I turned the old skepticism meter a bit too high when I expressed doubt that many candidates would be elected on their preference votes under a 5% threshold. Still, if the legislators in my data set had needed 5% to be elected, 15% of them would not have been–unless they had a high enough list rank provided by the party to be elected anyway. (Remember, in a flexible list system, seats not filled by preference votes default to the list rank, unlike in an open list, where there is no list rank and thus preference votes alone determine election.)
For larger parties, those that win at least the mean for this set of districts, which is 5 seats, the result is more favorable to my skepticism: Mean prefshare of .097, standard deviation of .10; median of .068; and around 28% elected with less than 5%. Not surprisingly, larger parties divide their votes among more candidates, successful or otherwise, while smaller parties are somewhat more likely to have a single vote-puller.*
However, all the above may overestimate the number of members who would be elected on preference votes if lists were flexible rather than fully open. My (more limited) information on existing flexible-list systems suggests that a very high share of total preference votes in such systems are given to the list head or one of the other top-ranked candidates (in other words to those who would win easily anyway). Of course, the more that voters do that, the smaller the pool of preference votes left to go around for other candidates with lower ranks, and thus the fewer candidates win on “their own” efforts and the more that are elected as if the list were closed.
To probe this further, we can look at data that I have from one flexible-list case in which many legislators are elected in districts of magnitudes ranging from 10 to 25: The Czech Republic (2002 and 2006). There, for winning legislators in these districts, the mean prefshare is only .017, the standard deviation is .022, and the median is .028. How many of those elected had preference shares under 5% of their list’s vote? 71.4%!
A quick check of the data appears to show only 17 of the 374 members elected on their preference votes who would not have been elected based on their party-provided rank. Thus the lists do not prove to be very “flexible” in practice.
The Czech rules in 2002 and 2006 allow the voter to cast up to two candidate preferences and require a 7% threshold of list votes for the candidate to be assured of election (i.e. even if the party has not given a high enough pre-election rank to the candidate).
Surprisingly (to me, anyway), Czech voters do not appear to concentrate their preference votes on a few top-ranked candidates. Even the winners who had the first rank on their list average less than 9% of their list’s votes. Nonetheless, the result is the same as what I expected–lots of candidates getting less than 5% of their list’s votes–even if the way that result came about is quite different from what I expected. (Looks like some research into flexible lists is in order!)
Is any of this relevant to Catalonia? Well, if Catalonian voters vote like Czech voters when it comes to using the preference vote, not very many candidates are going to clear the 5% preference-vote threshold.
Roman Chytilek, a political scientist at the Masarykova University of Brno, reports that for the next Czech elections the intraparty threshold will be reduced to 5% and a voter will be allowed up to four preference votes. (Before 2002, the rules provided for four preference votes and a 10% intraparty threshold.)
*In fact, each additional seat won by a party reduces the estimated prefshare of its winning candidates by .02, and the relationship is highly significant and the R-squared is more than 20%.
Data sample sizes: N=767 for the open-list sample; N=374 for the Czech Republic.
Another data note: In the Czech data, there is a much smaller relationship between the number elected off the list and the prefshare of those who are elected. It is “significant,” but barely more than zero anyway (-.003) and the R–squared is only around 7%.
I thank Joel Johnson for correcting my misreading of the data output and Roman Chytilek for his help in data acquisition as well as interpretation (including his comments in this thread since its original 18 July “plant” date.)