The DPP is determining its nominations for this year’s city council elections by telephone surveys. This is, to my knowledge, unique worldwide. Here in Taiwan, the KMT sometimes claims to also use surveys, but they have not institutionalized their procedures to the extent that the DPP has, and the KMT always reserves (and occasionally employs) the right to ignore the surveys and do something else. As such, I view the KMT’s surveys as simply playing an advisory role. Lots of parties around the world do this. In contrast, the DPP takes its survey results as binding. If you win the survey, you win the nomination.
This is interesting in and of itself, but there is more. The electoral system the DPP uses in its surveys is quite esoteric. Taiwan’s multimember districts use the SNTV system, but the DPP surveys use something just a little different. In fact, I’m not quite sure exactly how to classify this system.
Here are the important rules. There are two conditions, and each uses a different set of rules. If there is only one nomination or if there are three or fewer candidates, survey respondents will only be allowed to express support for one candidate. (OK, this part is easy to understand: it’s just a simple survey and plurality wins.) If there are four or more candidate contesting two or more nominations the following rules will be used.
- Each respondent is asked for his first and second preference. The first preference is given 2 points, and the second preference is given 1 point.
- If, when asked for his first preference, the respondent insists that he cannot differentiate between his two top choices, each will be given 1.5 points. If the respondent cannot differentiate among three or more choices, his answer is coded as “don’t know” and no one is given any points.
- If, when asked for his second preference, the respondent cannot give a clear answer, refuses to choose another candidate, or indicates that he only supports his first choice, the first preference is given 3 points.
The DPP does three separate surveys with at least a sample size of 1068 for each race. The results of each survey are averaged and calculated out to the fourth decimal place to get the final result. (Note: in previous elections, the DPP required a sample size of 3000. They also have used a filter question in the past to disqualify respondents who support the KMT.)
The source for this is this document:
I am looking primarily at pp 20-25, 43-49.
So each respondent has three votes that he can cast in the following ways:
- A: 3
- A: 2, B: 1
- A: 1.5, B: 1.5
Since it is impossible to cast any number other than three total votes, we could normalize the three votes to one vote, which is what the DPP does when they report the results.
This fits somewhere in the family of limited votes. To review, the limited vote has districts with m seats, where m≧1, and each voter casts somewhere between 1 and m-1 votes. The top m vote-getters win the seat. Standard plurality elections are part of this family. M=1, and each voter casts one vote. SNTV is also part of this family. M>1, and each voter casts exactly one vote. However, here we have a case of voters casting more than one vote, and they can either spread their support among two candidates or concentrate it on one candidate.
I think this counts as limited vote with cumulation, except that cumulation is required, not simply allowed. You are not allowed to give one vote to three separate candidates.
Research on limited vote systems is very sparse (except for the SMP and SNTV variants). I need to go and look up the article, but I think I remember reading about a limited vote system for the London city council in the Victorian era. The upshot was that everyone cumulated their votes on the local candidate, so the election essentially turned into SNTV. That is what candidates in Taiwan seem to be trying to do. Every banner, ad, and billboard asks people to express exclusive support for them. However, I’m dying to know if this is actually what happens. Are there successful candidates who get large shares of their support from second preferences? Is there any pattern to whether a voter splits his support or not?
Another interesting question about these surveys has to do with sampling error. In short, there is no concession made to sampling error. If A gets a higher score than B, then A beats B no matter how small the difference is. This, of course, is just the type of thing that drives statisticians crazy. To simplify, the sampling error for a survey is roughly 1/Ön, where n is the sample size. Each survey has a sample size of n=1068, so the error for each survey is .03, or 3%. So when you do one survey, you get one answer. If you do the same survey 1000 more times, you’ll get 1000 more answers, all slightly different. However, 950 of those answers should be within 3% of the actual value in the population (which is what we are trying to measure).
Remember, however, that in these multimember districts, 10% or 15% support can often win the last spot. If one person gets 13% (or more accurately, somewhere between 10% and 16%) while another gets 12% (really 9%-15%), you simply can’t be sure that the former is really stronger than the latter. Doing three surveys helps a bit, but the answer isn’t three times better. The error is roughly 1/Ö3204, or 1.77%. There are going to be lots of instances in which the difference between the last winner and the first loser is more than twice that, which is roughly what it would take to say that the former is more popular than the latter in a statistical sense. I haven’t looked at it, but it wouldn’t surprise me if the last winner and first loser were not statistically significantly different in a majority of races. However, the DPP makes no allowance for this. If you get a lower value, you lose.
(Note: In previous elections, the DPP required each survey to have a sample size of at least n=3000. 1/Ö9000 is 1.05%. Better, but still not necessarily conclusive. And very expensive.)
Of course, you now expect me to conclude that the DPP’s system is unreasonable. Nope. The purpose of a primary system is not to choose the most popular candidates. It is to persuade the losers to stand down so that the party can succeed in the general election. Think about this from the loser’s perspective. There was a fair criterion that was well understood in advance. The loser might not be less popular than the winner, but there is very little reason to believe that he is more popular. Moreover, in the general election, the party nominees will enjoy the benefits of the party label. If the loser ran as an independent, he would probably lose much of his support (since most of his supporters are also DPP supporters and would want to vote for a DPP candidate). In other words, if you couldn’t win the primary, chances are pretty dim that you might be able to win the general election, even if you think you really had more support in the general population than the winner and just got an unlucky sample. If the losers stand down, then this system works.
(Yes, I will be paying attention to what happens next. This is one of the reasons that I’m so excited to get data on people contesting the nominations.)