Sixty Cities, 106.9% of a Country: What Counts as a City

We built a list of 60 Taiwanese cities with population weights. Then we added the weights up.

The sum was 25,005,363. Taiwan's population is about 23.4 million. Our sixty cities contained 106.9% of the country.

That is not an approximation problem or a rounding problem. It is physically impossible, and it took one line of arithmetic to find. This article is about the class of defect that check catches, which is not "wrong numbers" but wrong units — and about why "how many people live in city X" has no answer until you say what you mean by "city."

What was actually in the Taiwanese file

Taiwan has six 直轄市 — special municipalities. They are called cities and they are administratively equivalent to provinces. 新北市 (New Taipei) has 4,044,831 residents; 高雄市 (Kaohsiung) has 2,718,545. Between them the six hold 16,278,931 people, roughly 70% of the country.

Our list contained all six. It also contained 23 rows that are districts inside those same six municipalities — 板橋區 at 549,762, 三重區 at 382,778, 中和區 at 403,791, each listed with 新北市 as its region.

So New Taipei was counted once as a municipality of four million, and then several of its districts were counted again as cities in their own right. The arithmetic:

Every single number in that file was correct. 板橋區 really does have 549,762 people. The defect was that the list mixed two levels of a hierarchy in one column and then treated them as siblings.

Note also what the corrected figure looks like: 84.5%. Still not obviously wrong — a country can plausibly have 84.5% of its people in its 60 largest settlements. Which is exactly the problem with using 100% as the threshold, and we will come back to it.

The same defect, quieter: Norway

Norway's list has 60 cities. Ranked by the population figure we had resolved for each, the top ten came out:

Sandvika is the sixth-largest city in Norway. It is not. Sandvika is a tettsted — a built-up area — and the administrative centre of Bærum, a kommune in the Oslo suburbs. The 115,543 is a kommune-scale figure: it is Bærum's order of magnitude, not Sandvika's. The unit attached to the row is not the unit the name refers to.

This is a much more dangerous shape of error than the Taiwanese one. Taiwan's list overflowed the country and announced itself. Norway's list sums to something entirely believable; the only symptom is that a commuter suburb outranks Drammen. You catch it by knowing Norway, or you do not catch it. Norway therefore ships without population weights — 60 cities, three columns, uniform selection — because a weighted list we cannot validate is worse than an unweighted list we have documented.

The general problem

"The population of a city" is not one quantity. It is a family of quantities that differ by factors of up to 26, and the choice between them is administrative, not factual.

Tokyo is the case that shows the question is not merely ambiguous but sometimes unanswerable as posed. There is no legal city of Tokyo. The City of Tokyo was abolished in 1943 and has no single-municipality successor. What exists is 23 special wards, each a municipality in its own right, sitting inside a prefecture. Any figure for "Tokyo" is a choice among entities, and we ship 9,733,276 — the 23 wards — because it is closest to what people mean.

Chongqing is worth a second look because our own shipped file does not use either figure in the table. It carries 16,343,989, which is neither the ~9M urban core nor the 32M municipality. It is a third unit again. That is defensible — it is a consistent choice within the Chinese locale — but it illustrates how easily a fourth definition appears the moment you look at a real file rather than an encyclopaedia.

The rule that matters is not which definition you pick. It is that the definition must be consistent within a locale, because the weights are relative. Take a metropolitan figure for one city and a municipal figure for the city next to it, and you have silently tripled the first city's probability of being drawn. Nothing in the output looks wrong. Every address is real.

The same substitution occurs inside single national sources. Argentine tables mix municipio and localidad in one column — San Carlos de Bariloche is 112,887 or 109,305, Trelew is 99,430 or 97,915 — and neither figure is labelled. Armenia distinguishes քաղաք (city) from համայնք (consolidated community), and Ճամբարակ is 5,468 or 12,416 accordingly, a 2.3× trap. Georgia nests three deep: Kaspi is 41,841 as a municipality, 13,729 as an administrative unit, 12,911 as a city.

Greece produced the largest single-country haul, because automatic resolution kept landing on the δήμος or the whole island instead of the town:

And two large countries where the seductive number is the wrong one: São Paulo is the municipio at 11,451,999, not the ~21M metropolitan region; Montréal is the subdivision at 1,762,949, not the 4,291,732 census metropolitan area; Brasília's municipio code covers the entire Federal District.

The locale we left alone

Saudi Arabia's list has exactly 39 cities, and it ships unweighted.

GASTAT, the Saudi statistics authority, publishes population by governorate. For 25 of our 39 cities a defensible urban figure can be assembled. For the remaining 14 it cannot — the city-level number does not exist in the published statistics. The available options were: weight 25 cities and give 14 an arbitrary default; substitute governorate populations, which would wildly overstate small cities inside large governorates; or ship uniform.

We shipped uniform. A uniformly-drawn Saudi address is a documented approximation that anyone can reason about. A list where two thirds of the rows carry one kind of unit and one third carry another is a defect invisible to everyone, including us. Where the source does not support the metric, not computing it is the correct answer.

That is the current state across the whole set: of 64 locality files, 44 carry population weights and 20 remain uniform. The 20 are not a backlog of laziness. Each is a country whose statistics office either does not publish city-level figures, or publishes them in a unit we could not make consistent.

Why the "sum against the whole" check is the one to run first

It is the cheapest test in the set and among the most productive, because it needs no knowledge of the country. Add up the parts, compare against the whole, look at the ratio.

But run it with the right threshold. Taiwan at 106.9% was caught because it broke a physical limit. Australia's list came in at 84.7% and would have passed a 100% test — yet 60 cities holding 84.7% of Australians is implausible on its face, and the cause was the same class of error (agglomerations standing in for local government areas). Sydney's staging file carried 5,219,674, the Greater Sydney figure. Australia ships unweighted too.

So the threshold is not 100%. It is a plausible urban share for that specific country, which you have to think about for a moment per locale. And note the limits honestly: the check cannot see a defect where one city is overstated and another understated by the same amount, and it does nothing at all for the 25 files that carry no weights to sum.

The checklist

1. Sum the parts and divide by the whole. One line. It caught Taiwan at 106.9% immediately.
2. Use a plausible urban share as the threshold, not 100%. Australia at 84.7% is as broken as Taiwan at 106.9% and passes the naive test.
3. Check for nesting before summing. Is any row administratively inside any other row? Taiwan's 23 districts sat inside its own six municipalities.
4. Sort by population and look at the top twenty. Sandvika at rank 6 is the entire diagnosis for Norway, and it is visible in five seconds.
5. Ask what unit the source publishes, and whether it publishes one at all. Fourteen of 39 Saudi cities have no city-level figure in existence.
6. Enforce one unit per locale, not one unit globally. Consistency inside the list is what the weights actually require.
7. Ship unweighted rather than ship a mixture. A known approximation beats an invisible defect.

The question "how many people live in Kaohsiung" has no answer. The question "how many people live in Kaohsiung, counted as a 直轄市, in the 2020 census, in the same unit as every other row in this file" has exactly one. Most geographic datasets are built as though the first question were the one being asked, and the arithmetic is what tells you it was not.

For what happens downstream when these weights are missing entirely — why a generator picks Kamianets-Podilskyi as often as Kyiv — see Why Address Generators Produce Implausible Cities. For defects where the source rows themselves are corrupt rather than merely mislabelled, see Four Surnames That Do Not Exist and Authority Is Not a Property of Rows.

Data as of 2026-07-18

All sums were recomputed on 18 July 2026 directly from the shipped and staging locality files. Where working notes disagreed with the files, the files win.

Sources and notes:

• Locality files — 64 locales. Re-counted 22 July 2026: 44 carry a 4th column of population weights; 20 are 3-column and uniform, including ar_SA, en_GB, en_IE, ko_KR and nl_NL. zh_TW, en_AU and no_NO were uniform when this article was written and have been weighted since.
• Taiwan — staging file of 60 rows summing to 25,005,363 against a national population of ~23.4M = 106.9%. The six 直轄市 sum to 16,278,931 (臺北市 2,439,507 · 新北市 4,044,831 · 桃園市 2,355,106 · 臺中市 2,868,465 · 臺南市 1,852,477 · 高雄市 2,718,545); 23 further rows carry one of those six as their region and sum to 5,221,850. Removing them gives 19,783,513 = 84.5%. zh_TW ships 3-column. <stat.gov.tw/&gt;
• Norway — 60 cities, ships 3-column. The staging population set gives Sandvika 115,543 (2021), ranking it 6th. Sandvika is a tettsted and the centre of Bærum kommune; the 115,543 is a kommune-scale value. The specific tettsted population is not re-derived from a file here — what is verified on disk is the 115,543 attached to the name, its resulting rank of 6, and that no_NO ships without weights. <ssb.no/&gt;
• Japan — Statistics Bureau. Tokyo represented by the 23 special wards, 9,733,276; the City of Tokyo was abolished in 1943. <stat.go.jp/english/&gt;
• Germany — Destatis / Länder offices. Gemeinde populations; Frankfurt am Main 760,656 as shipped. <destatis.de/&gt;
• China — 重庆 ships at 16,343,989, a figure between the urban-core and full-municipality definitions; consistent within zh_CN, and stated here because it is neither of the two figures usually quoted.
• Saudi Arabia — GASTAT. Publishes by governorate; city-level urban figures unavailable for 14 of our 39 listed cities, so ar_SA remains uniform. <stats.gov.sa/&gt;
• Australia — ABS. Staging file carried Sydney at 5,219,674 (Greater Sydney GCCSA) against a City of Sydney LGA of roughly 200,000; en_AU ships unweighted. <abs.gov.au/&gt;
• Greece, Georgia, Armenia, Brazil, Canada, Argentina — unit-substitution cases as recorded in our source documentation, corrected where correction was possible via a manual patch registry.

On the 106.9% and 84.7% figures. Both originated as session measurements rather than as logged output; the Taiwanese figure was re-derived exactly from the staging file on 18 July 2026 (25,005,363 / 23.4M = 106.9%). The Australian 84.7% was not re-derived — what is confirmed on disk is its consequence, that en_AU ships without weights. Treat 84.7% as a recollection and 106.9% as a measurement.

On the Argentine figures. The municipio / localidad pairs come from our working notes and were not re-derived from a primary Argentine file. The mechanism is well documented; treat the individual numbers as indicative.