A few days ago, Mrs. Garlic looked up from the newspaper and said, “Here’s the story you keep blathering on about.” Liu I-chou 劉義周, head of the Central Election Commission, had said something about the upcoming legislative redistricting. Now, I’ve been chattering about redistricting for months (ok, a few years), so I eagerly picked up the story. My glee quickly turned to horror when I read that Tainan and Hsinchu County would get an additional seat and Kaohsiung and Pingtung would lose a seat each. Um, that’s not what I’ve been telling people for the past few months.

My initial reaction was to contact Dr. Liu, who I know better as a political scientist and my masters thesis advisor, to warn him that he had made a mistake. Hey, I just published one paper on redistricting and another on malapportionment, and I have been through those rules in excruciating detail. If anyone knows the rules, it should be me. However, doubt began to creep in, and I thought maybe I’d better check the rules one more time. So I looked up the documents and found a table (look on p 107) showing exactly how the apportionment had been done.

Well, isn’t this embarrassing. I’ve been doing it wrong. I omitted one step. I shouldn’t have doubted the excellent civil servants at the CEC. I really shouldn’t have doubted Dr. Liu. I guess the student isn’t the master just yet.

Taiwan uses a largest remainders system. You take the total population (minus the indigenous population) and divide by the number of seats to get a quota. In our case, the quota is 22,986,588/73=314,885. (These numbers are from December 2016. The apportionment will be done with August 2017 numbers, but it is highly unlikely that anything will change between now and then.) Every city or county with fewer than 314,885 people automatically gets one seat. There are six such places. Then take the remaining 16 cities and counties and get a new quota. ****This is the step I skipped.**** The new quota is 22088100/67=329673. For each full quota, a city gets one seat. New Taipei City can thus buy 11 full quotas (see column S2). We have now accounted for 66 seats. What about the remaining seven? To apportion those, you take what is left over for each city or county and give the seven largest remainders the last seven seats.


City pop S1 Pop2 S2 Remain S3 S
Total 22986588 6 22088100 60   7 73
新北市 3924326   3924326 11 297922 1 12
台北市 2679523   2679523 8 42138   8
桃園市 2077867   2077867 6 99828   6
台中市 2734190   2734190 8 96805   8
台南市 1878508   1878508 5 230142 1 6
高雄市 2745749   2745749 8 108364   8
宜蘭縣 440708   440708 1 111035   1
新竹縣 526274   526274 1 196601 1 2
苗栗縣 547911   547911 1 218238 1 2
彰化縣 1281569   1281569 3 292550 1 4
南投縣 476289   476289 1 146616 1 2
雲林縣 692532   692532 2 33186   2
嘉義縣 509510   509510 1 179837 1 2
屏東縣 776900   776900 2 117554   2
台東縣 141930 1         1
花蓮縣 238432 1         1
澎湖縣 102789 1         1
基隆市 362819   362819 1 33146   1
新竹市 433425   433425 1 103752   1
嘉義市 268826 1         1
金門縣 134109 1         1
連江縣 12402 1         1


Why did I take you through all that mess with such an emphasis on my stupid mistake? Hold on, there’s a point to this. But first, let’s see what would have happened in my alternate, error-ridden fantasy world. When you don’t calculate new quota but simply use the original quota (314885) to apportion seats, we get a different result. Pingtung, Nantou, and Chiayi County all lose a seat, and Tainan, Taichung, and Hsinchu County all gain a seat. Also, Kaohsiung gets to keep its 9th seat. The difference with the correct reapportionment is that two small counties (Chiayi and Nantou) would have lost a seat while two large cities (Taichung and Kaohsiung) would have gained a seat. Calculating a new, larger quota favors small counties.

Let’s take a moment to appreciate what could have been. (This still isn’t the big point.) I may have told a few Taichung politicians that they should start preparing for a ninth district. I even started drawing up some maps of what might happen. This is my favorite one. It meets all the formal criteria (all legislative districts are within 15% of the mean population and it doesn’t even need to split any administrative districts) and even a few of the evil political calculations. (Check out what it would do to Yen Kuan-heng!) Of course, if you have any local knowledge of Taichung, you will see in an instant that there is no way in hell this plan would ever be adopted. The deputy speaker, for one, might have some objections. (I promise this post wasn’t just a flimsy pretext to show everyone this picture that I spent a lot of time making and will never be able to use again. Well, maybe a little…)

Taichung 9D plan E

So after sulking for a while over my stupid error, I thought I’d go back and see what would have happened in previous elections if they had used my erroneous apportionment method. This is my idea of fun. Don’t judge me. Guess what I found. THEY CHANGED THE METHOD IN 2008!!!! In 2004, they used my method! Using the new method, Taipei County should have had 27 seats and Taoyuan should have had 14. But Taipei County actually got 28 seats and Taoyuan only had 13. My method yields the actual result.

Why did they change the formula? There were all sorts of little indications that the Chen administration had tried to influence the CEC’s decisions, so maybe the CEC was manipulating things for the DPP’s political advantage! Or maybe the CEC was stuffed full of career bureaucrats sympathetic to the KMT. Maybe it was a KMT plot! There’s only one way to find out. Which side benefited from the change? Who would have done better in 2008 using the original formula?


The answer is: no one. The 2008 apportionment would have been exactly the same using the old formula. The change had zero effect. Moreover, it isn’t as though 2008 was an aberration. The two formulae yielded exactly the same results in 1998 and 2001. 2004 was the only year it made a difference, and that difference was modest, to say the least. It’s a big deal if Nantou goes from one seat to two seats – it has doubled its clout. It’s not such a big deal for the largest county to get one more seat and the second largest county to get one less seat. In the old SNTV system, it is impossible to say if that helped the KMT, the DPP, or a small party.

I doubt the CEC made the change in 2006 or 2007 because it could foresee the effects in 2017. A lot has changed in the meantime. It’s hard to predict exactly how fast Hsinchu will grow or how fast Pingtung will lose population. Moreover, they would have had to guess that Kaohsiung, Tainan, and Taichung Cities and Counties would merge. To put it another way, if I were given the opportunity to change the formula now to help one party in 2029, I’m not sure what I would do. Who can even say what the party system will look like then?

So why did they change the rule? My guess is that it was entirely apolitical. Some bureaucrat thought it would be fairer to apportion the last 67 seats according to their population rather than by taking into account the population of the six small counties. That bureaucrat probably had to propose a change, they probably held some meetings in which they discussed fairness and disproportionality, and they eventually rewrote the rule thinking it would probably never matter very much.

Only it has mattered. This year, two rural counties will double their representation. Because every county gets a seat and indigenous voters are given about 2.3 times as many seats as their population would merit, rural and agricultural areas are already overrepresented. This rule change furthers that overrepresentation. Sorry urban residents.


Let’s change gears and think like philosophers about fairness. Scratch that, let’s ask a question that economists would love. Is it fairer to have fixed prices or to allow competitive bidding?

Go back up to the table and look at Pingtung and Nantou. Pingtung has 776900 people, while Nantou has 476289. Even though Pingtung has far more people, both counties will get two legislators. Is that fair? Suppose the country only had these two counties. Should Nantou really get equal representation?

The CEC formula essentially uses fixed prices. Our new country, “Pingtou,” has 1253189 people, so a quota is 313297. Pingtung can afford two full quotas, and Nantou can afford one. After paying those prices, Pingtung has a remainder of 150306, while Nantou has a remainder of 162992. Nantou thus gets the last seat.

However, what if they could bid? Nantou could offer 476289 people for one seat or 238144 each for two seats. Pingtung, however, can offer 258966 each for three seats. Since Pingtung can offer more for the fourth seat, maybe it should get three seats and Nantou should only get one. Wait, now Pingtung gets three times as much power even though it has less than twice Nantou’s population? This is clearly unfair, and I’m not just saying that because I used to live in Nantou and my wife used to live in Pingtung.

I don’t have an answer to which system is fairer. Largest remainders systems, like the CEC method, tend to favor smaller areas. The divisor method used above is called the D’Hondt system, and it favors bigger areas. Before you put on your urban hat and decide that the D’Hondt method is clearly more progressive / pro-industry and therefore more desirable, please remember that these methods are most commonly used for allotting seats to party lists in PR elections, not apportioning seats to different regions. Hey Green Party apologist / Faith and Hope League zealot who can’t stand the sellouts in the establishment, now you probably think the largest remainder system, which is good for your crazy fringe party, is the best way to go.

Since I know you are dying to know, if we used the D’Hondt method to apportion the 73 seats, the big cities would do much better. New Taipei would get a 13th seat, and Kaohsiung, Taichung, and Taipei would all get a 9th seat. The mid-sized cities and counties including Taoyuan (6), Tainan (6), Changhua (4), Yunlin (2), and Pingtung (2) would be unaffected. The rest would only get one seat, which is not good news for Hsinchu County, Miaoli, Chiayi County, or Nantou. Power to the (urban) people!


As you’ve been reading along, I’d be willing to be that in each scenario, you judged whether something was reasonable or not by whether it helped or hurt your side. Maybe you thought about it intentionally or maybe it was just an involuntary reflex, but I’ll bet you did it. We all do. It’s not an accident that my crazy map of Taichung with nine districts shows how well Tsai Ing-wen did in each of them. When I realized that the CEC had changed the apportionment formula, my heart sank. I can’t tell you how relieved I was to be able to conclude that there was no obvious partisan motive behind that change. Whether or not one system is objectively slightly fairer than another is really beside the point. We have one system right now that wasn’t designed with obvious partisan motives. This year, it might advantage one side or the other. However, it matters that it was not intended to produce this result. It matters a lot. It is better to have a slightly imperfect but nonpoliticized electoral system than to chase perfection and risk politicization. This apportionment system is just fine.


Redistricting, on the other hand, is already a problem, and it is probably about to get worse.


Note: This post was written at 37000 feet. If it seems a bit loopy, I’m blaming altitude sickness.

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