Coordination failures in City Council races

Consider the city council election in New Taipei District 5. This is the Zhonghe 中和區 district, traditionally a KMT stronghold. It elected 6 seats this year. Here are the results.

votes party Win
江永昌 Chiang 38,503 DPP Y
邱烽堯 Chiu 28,764 KMT Y
陳錦錠 Chen 26,290 KMT Y
游輝宂 You 24,703 Ind Y
張瑞山 Chang 21,768 DPP Y
林秀惠 Lin HH 21,678 DPP Y
金瑞龍 Chin 21,159 KMT
戴德成 Tai 13,965 New
林朝鑫 Lin CH 8,788 Ind

The DPP won half the seats with only 39.9% of the vote. (They actually won more votes than the KMT, though that isn’t as impressive as it sounds. Both of the independent and the New Party candidate are from the blue camp, so the district is basically 60-40 in favor of the blue camp.)

The KMT nominated three candidates, but it only won two seats. Could it have won all three seats? It certainly looks like it could have. The third KMT candidate (Chin) lost the last seat by only about 500 votes. If the KMT had been able to shift a thousand votes from their top candidate (Chiu) to Chin, they would have won the last seat. This is what we call a coordination failure. If the KMT had coordinated their electoral strategy more successfully, they might have won another seat.

But wait, you say. The DPP could play that game too. The top DPP candidate had lots of extra votes. If we imagine the KMT could have rearranged its votes, why don’t we assume that the DPP could have as well? In fact, if you allow both parties to distribute their votes perfectly, the DPP comes out on top. The DPP had 81949 votes, so each of its three candidates could have won 27316. The KMT only had 76213, or 25404 for each candidate. But wait (again!). The independent candidate (You) won with only 24703 votes. If both parties had rationed their votes perfectly, the DPP would have won the first three seats, the KMT would have won seats four through six, and the independent candidate would have lost. So the KMT really could have won three seats with better coordination.

Of course, we are knee-deep in questionable assumptions. Most importantly, many of the KMT’s (and DPP’s) votes are personal, not partisan. A person might like Chen because Chen did some constituency service for her or because Chen was her elementary school classmate, and that voter’s second favorite candidate might not be another KMT nominee. Still, it is probably safe to assume that there is a pool of KMT supporters who would be willing to switch to any KMT candidate if that helped to produce more KMT winners. It is not entirely unrealistic to think about moving votes around.


Coordination failures are at the heart of the Single Non-transferable Vote (SNTV) electoral system. Like in every system, the most important thing is winning popular support. However, votes must be turned into seats, and this is particularly convoluted in SNTV. Some systems are proportional, such as the party list system used in Taiwan’s legislative elections. If a party gets 35% of the votes, they should get 35% of the party list seats. Some systems are majoritarian, such as the geographical seats in Taiwan’s legislative elections. If a party gets 35% of the votes, it might end up with a very low seat share (if it is opposed by one large party) or a very high seat share (if the other 65% of the votes are fragmented among many smaller parties. SNTV is generally considered to be a semi-proportional electoral system, since parties usually win roughly similar proportions of votes and seats. However, there are no guarantees of proportionality, and a party that suffers too many coordination failures can win a far lower seat share than one might expect.

There are three ways to mess up. A party can nominate too few candidates, it can nominate too many candidates, or it can fail to distribute its votes appropriately among its nominees. In the above example, the DPP had enough votes for three seats. It could have messed up by nominating only two candidates. That doesn’t happen very often. It generally only happens when a party does unexpectedly well at the polls. More commonly, a party will nominate too many candidates. Sometimes this happens because the party’s support is shrinking. Usually, there simply are too many people who want to run, and none of them are willing to step aside. In the last two election cycles, the KMT has suffered both of these. The 2010 Taichung city council race was a particularly stark example. In the old Taichung County, the KMT’s vote share fell from 45% in 2005 to 35%, while the reduction in total seats meant that there were lots of incumbents who were unwilling to step aside. The result was too many candidates chasing too few votes and a KMT bloodbath. The third failure is the one we saw in 2014 New Taipei 5, the failure to ration votes evenly to each nominee. This is the most common error.

One of the big questions in the academic literature is whether SNTV is good for small parties or for big parties. The initial answer was that it must be good for small parties. Small parties face much simpler coordination problems. It is much easier for small parties to figure out how many people to nominate. The answer is almost always one. With only one candidate, vote rationing is not a problem. Supporters simply vote for the only party nominee on the ballot. If there are enough votes for two seats, things get more difficult. The small party might nominate incorrectly, not believing it really has that much support. More importantly, with two candidates, vote rationing becomes a challenge. It is hard to ensure that both candidates will get the same number of votes. If two is hard, three is harder. Compared with four, three is a breeze. In general, the more seats a party can win in a given district, the harder it is to turn those votes into the full number of seats. If this is correct, it should be very hard to hold big parties together, since the electoral system rewards smallness.

That logic seems sound, but observers noticed that big parties always seemed to win a seat bonus. For example, in the 1992 Legislative Yuan elections, the KMT won 53% of the votes but 59% of the seats. How could this be? There are two answers. First, in the absence of any coordination failures, SNTV will produce results exactly equal to the D’Hondt system of proportional representation. Among all the PR systems, D’Hondt is the friendliest to big parties. (I’ll explain this later on.) Second, some big parties are governing parties. Governing parties can use their control of state resources to mitigate coordination problems. If too many people want to run, a governing party might convince one of them to withdraw by offering her a position in the cabinet, by promising a big bank loan to the candidate’s company through a state-run bank, by threatening to start inspecting the candidate’s food oil company every month, or by using the judicial system to investigate unethical financial practices. Governing parties might also be better at figuring out how many nominees are appropriate, since they can draw on information about economic development, the popularity of various government programs, and other national trends from their control of the government bureaucracy. Finally, they should be better at vote rationing. If one candidate is weaker than other nominees, they can shift state resources to that candidate. For example, the government could suddenly pave a lot of roads in the candidate’s home area. (Note: Before you start screaming at your computer about how this is blatant abuse of power and the goddamn KMT cheats like hell and the playing field isn’t level and that is Taiwan’s democratic birth defect, please be aware that this literature was all developed by scholars studying Japan, not Taiwan. Taiwan was merely a corroborating case.)

So who made more errors this year, the KMT or the DPP? On the one hand, the KMT was the governing party, so we should expect it to do better. (National governing power has generally been a better indicator than local governing power.) On the other hand, the KMT had a surprisingly awful election in terms of winning votes. It is always harder to shrink than to grow, so we might expect that the KMT overnominated in too many places.

Measuring coordination failures is a subjective matter. Some people insist that we should judge whether the KMT erred based on the actual performance of all the other candidates. In the Zhonghe example, the KMT should have known that its candidates each needed at least 21679 votes (since the last wining non-KMT candidate got 21678), so it failed. I think this demands too much, since it assumes the KMT could estimate how many votes each individual candidate would get (after the other parties rationed their votes) and then ration its own votes appropriately. I prefer to assume simply that the parties can estimate how many votes each party will get, but not how many votes each individual candidate will get. We can then assess how many seats each party “should have” won (with no errors) and how many it actually won.

If no one makes any errors, SNTV becomes equivalent to the D’Hondt system. D’Hondt is a system of divisors which essentially asks how many votes you can pay for each seat. Take all the parties’ vote totals, and give the first seat to the highest number. So the DPP wins the first seat. Then divide that party’s vote by two. The next seat goes to the new highest number, so the KMT wins the second seat. After that, the DPP wins the third seat, and now the DPP’s vote total is divided by 3. Eventually, the KMT and DPP both win three seats. Given the KMT’s 76213 votes, it can give three candidates 25404 each. The DPP can’t take away and of those seats. If it tried to nominate four candidates, it could only give each one 20487. This would put them behind not just the KMT’s three candidates, but also behind You. Thus, my expectation for this district is that the KMT and DPP should both win three seats.

votes 2 3 4
KMT 76213 (2) 38107 (4) 25404 (6) 19053
DPP 81949 (1) 40975 (3) 27316 (5) 20487
New 13965
You 24703
Lin CH 8788

In the actual election, the DPP won three seats, so they did not suffer a coordination failure. The KMT only won two seats, so they failed. (Note that this can seem a little unfair. The KMT’s three candidates were more closely bunched together than the DPP’s three, but because the DPP had more overall votes it had a larger margin for error. In the end, winning seats is what matters.)

You will notice that in this example, when a coordination failure occurs, it costs a big party a seat and a little party (in this case, an independent) benefits. This is not unusual. Little parties often depend on big parties making mistakes. Little parties might not have enough votes to be assured of winning a seat, but they might have just enough to be able to sneak in whenever a big party messes up.


I looked at the city council races for all 375 seats in 83 districts in the six metro city council elections this year. There were a total of 33 errors. The KMT made 18 mistakes, the DPP made 14, and the New Party made one. Most of those seats went to independents and small parties. Independents won 18, the TSU gained 3, the PFP got 2, and the New Party got 1. The two big parties did get a few, with the KMT taking 6 and the DPP winning 3. Here is how this affected seat shares:

votes seats seats
SNTV D’Hondt
actual no errors
KMT 36.5 40.3 43.2
DPP 41.6 44.5 47.7
New 1.6 0.5 0.5
PFP 2.0 1.3 0.8
TSU 2.3 1.3 0.5
Green/Tree 1.1 0.3 0.3
Independents 14.9 11.7 6.9

The KMT won 36.5% of the votes and had a potential seat bonus of 6.7%. However, it only managed to realize part of that and had to settle for 40.3% of the seats, a seat bonus of 3.8%. The DPP’s potential seat bonus was a bit smaller (5.9%) as was its actual seat bonus (2.9%). Overall, I think the two parties both did quite well. They both had numerous districts with four, five, or more nominees, and these are extremely difficult to get right. Both big parties are getting quite good at playing this game.

There are people who think that this need for appropriate nomination and vote rationing strategies is an argument for abolishing the SNTV system. Sometimes more seats can go to parties that have won fewer votes, and that is a basic failure for any electoral system. However, the more I think about it, the more I like it. SNTV rewards parties for developing the capacity to act collectively. If you want to be big enough to win governing power, you need to be able to resolve your internal differences. Parties that can overcome these coordination challenges are rewarded with more seats. There are always temptations to break ranks, but parties that can effectively cooperate will reap an electoral reward.


Just for fun, let’s try something else. Remember that I said the D’Hondt system was the friendliest PR system for big parties? Note that in the above table, small parties and independents (who are simply single person parties) are dramatically underrepresented. What would produce a more proportional result?

There is already a much more proportional system in use in Taiwan. The Central Election Commission uses a quota formula used to determine party list seats in the legislature and also to apportion legislative or city council seats to various districts. Again, start with the party totals in Zhonghe. Calculate the quota by dividing the total number of votes by the number of seats. Quota=205618/6 = 34269. Divide each party’s vote total by the quota to determine how many complete quotas each party gets. In this example, the KMT and DPP both have enough votes for two full quotas. However, that is only four seats, and this district has six. The last two seats are determined by comparing the remainders. In this case the largest two remainders belong to You and the New Party.

votes quotas Remainder Largest? total
KMT 76213 2 7675 2
DPP 81949 2 13411 2
New 13965 0 13965 1 1
You 24703 0 24703 1 1
Lin CH 8788 0 8788 0

This formula is clearly more favorable to small parties. The DPP has 5.8 times as many votes as the New Party, but it only wins twice as many seats. Whether you think that is reasonable probably depends on how you feel about small parties.

The difference between the two systems is roughly the difference between preset prices and haggling. In the quota system, the price of each seat is fixed. If you have a quota, you can buy a seat. In D’Hondt, you can bargain. Ok, I’ll give you x votes for 2 seats or y votes for three seats. The critical difference is that the price for a full seat is lower in D’Hondt. Big parties buying multiple seats at full price can thus buy more seats. If the price of a quota is higher, why do small parties do better in a quota system? They don’t pay full price! The last seat a party wins can come at a discount. For small parties, the last seat is the first seat. Thus the New Party was able to win a seat with only 40% of a quota.

These extremely cheap first seats can cause major problems. While they help ensure a voice for small parties, they also create a strong incentive for big parties to splinter. Remember, if the DPP breaks into three parties called Chiang, Lin, and Chang, it can win three seats instead of two. The DPP is actually penalized for presenting a common name and a common platform. It should split up into lots of small parties. If you think this sounds far-fetched, it is actually an accurate description of what happened in Colombia. After several election cycles, the politicians figured out how to work the system and eventually every party list elected only one person. In other words, they turned a quota system into SNTV. This eventually led to electoral reform to a German-style mixed electoral system.

These problems haven’t cropped up in Taiwan for two separate reasons. In seat apportionment, each district is guaranteed one seat regardless of size, so the various districts are only competing for full quotas. Anyway, cities and counties aren’t really strategic actors that can split up or merge for electoral gain. In the legislative elections, the 5% threshold ensures that parties cannot win one cheap seat. Any party that gets at least 5% will win at least two seats, so all additional seats require a full quota.

What happens if we use the quota rule on the 375 municipal council seats?

votes seats seats seats
SNTV D’Hondt Quota
actual no errors CEC rule
KMT 36.5 40.3 43.2 37.9
DPP 41.6 44.5 47.7 41.1
New 1.6 0.5 0.5 1.3
PFP 2.0 1.3 0.8 1.1
TSU 2.3 1.3 0.5 1.6
Green/Tree 1.1 0.3 0.3 0.5
Independents 14.9 11.7 6.9 16.5

This is a much more proportional result. The two big parties get roughly the same seat share as their vote share. The four small parties also do much better, though they still don’t get quite as many seats as votes.

Anyway, this little exercise was just for my fun. Some people like to think about how to get more votes. I like to think about how to turn the votes you already have into more seats. I’m just a nerd that way.


8 Responses to “Coordination failures in City Council races”

  1. Rob Says:

    Fascinating analysis. This question might be over my head (I feel like a middle school dropout asking Stephen Hawkings about physics), but I want to ask you anyways: I think I remember you saying a few years ago (when Taiwan changed their legislative elections from its former Japanese-like proportional system to its current system) that you personally thought this was not a good idea. Plus, you thought that Taiwan’s legislature had too few members. I’m wondering what your opinion is now. Or is this question not relevant (because we’re currently in local mayor/township elections and not national legislative elections)? Thanks.

    • frozengarlic Says:

      I still think the electoral system needs to be changed. There are a lot of reasons for this. These local elections illustrate one of the (less important) problems. Why didn’t the KMT have any good candidates to run in Tainan, Kaohisung, Pingtung, or Yilan? Why couldn’t the DPP find a reasonable candidate for Hualien or Hsinchu County? A generation ago, they would have had an incumbent legislator in those places who could provide a credible challenge for mayor. Now, with fewer seats and single member districts, parties are wiped out in places where they are the second party, so the mayoral races are not as competitive as they should be. Democracy needs vigorous competition. Again, this is only about the 12th worst thing about the current system. It needs to be replaced.

    • Rob Says:

      You’ve said before that Taiwan is a country that faces basic existential issues (since China is intent on absorbing Taiwan). The old system allowed “fringe” parties to have representation as opposed to the current system which brings more mainstream parties/ideas to the legislature. I realize that in a theoretical/ideal country, you’d want “vigorous competition.” But given China’s constant threat, do you think a country like Taiwan can afford a democracy with “vigorous competition”?

    • frozengarlic Says:

      I am not that afraid of fringe parties. There are two cases that everyone brings up: Weimar Germany and modern Israel. Weimar Germany was not killed by fringe parties. In the critical July 1932 elections, the Nazi Party won 37% and the Communist Party won 14%. These were mainstream extremist parties created by the society, not by the electoral system. There are also no equivalents to either extremist party in current Taiwan (the TSU doesn’t advocate exterminating all Mainlanders, and the New Party doesn’t advocate overthrowing the democratic regime). Modern Israel is famous for tiny fringe parties that blackmail the cabinet into accepting their religious extremist positions. This will not happen in Taiwan for a couple of reasons. First, the Israeli electoral system is the friendliest system in the world to small parties. Under either Taiwan’s current law or any alternative on the table, small parties will have to climb over a much higher hurdle to win seats in the Taiwanese legislature. Second, Taiwan has a presidential system, not a parliamentary system. This not only means that small parties cannot blackmail the governing coalition as readily, it also provides a strong incentive for politicians to coalesce into two large alliances in order to contest the presidential election.

      Look, if a voice has significant support in society, it needs to be heard. Germany has constitutionally prohibited Neo-Nazi parties, but that hasn’t stopped Neo-Nazis from existing. It is far better to let them make their stupid arguments in the full light of day, where everyone can hear them and ridicule them as stupid and useless.

      There is no question of being able to afford vigorous competition. Vigorous competition is the essence of democracy. Without the constant innovation and evolution that competition demands, the system hardens and rots. Venezuela in the 1980s and 1990s is a perfect example of a democracy without much real competition. It is not a coincidence that Venezuela no longer has a democracy at all.

    • Rob Says:

      Thanks. In that case, which country’s political system do you think would be ideal for Taiwan?

      • frozengarlic Says:

        Each country’s political system has to be adjusted to the unique features of that country. The cases in which a country has tried to copy everything from another country have almost always ended in disaster.

  2. Irwin Says:

    The problem with the legislative election is not necessary the system of election (although it’s fun to debate that). I believe the issue is the size of districts. They are just too big (another way of saying not enough members), and they are not equally proportioned to the population (a lot of KMT gerrymandering happened).

    In the US, there is at least some mechanism for redistricting every so often (usually once every 10 years after the census). I’m not sure if there is a redistricting mechanism build into Taiwan’s electoral system (at all levels).

    • frozengarlic Says:

      Malapportionment and gerrymandering are different things. Malapportionment involves the number of seats given to each city or county. If a city or county has multiple seats, gerrymandering is possible. Gerrymandering refers to drawing the district lines to favor a certain political party. Both of these occur in Taiwan, though malapportionment is by far the more important. Malapportionment in Taiwan is well above the global average. About 8% of the seats are apportioned to districts that would not receive those seats given perfect proportionality. This produces a small geographic bias toward rural areas and a partisan bias of about 3% toward the KMT. Malapportionment would be cut by more than half if the legislature were simply returned to its former 225 seats. A change to a German-style MMP system would not affect the geographic bias, but it would eliminate the partisan bias.

      Currently, reapportionment is to be conducted every ten years. That means that the seats will be redistributed for the 2020 election. However, without electoral reform, the current level of malapportionment will not change significantly.

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