Rank-Size Rule

Definition:

• Relatively developed societies produce a pattern in the size of their cities according to a mathematical formula.

“Ideal” line

How Well does the USA fit?1. New York City, NY 8.4 m2. Los Angeles, CA 3.8 m3. Chicago, IL 2.7 m4. Houston, TX 2.1 m5. Philadelphia, PA 1.5 m6. Phoenix , AZ 1.4 m7. San Antonio, TX 1.2 m8. San Diego, CA 1.3 m9. Dallas, TX 1.1 m10.San Jose, CA 945,000

U.S. Line - 2007

How does the U.S. Compare?

PRIMATE CITIES

• In less developed countries/regions the largest city is overly large. The pattern of settlements is such that the largest settlement has more than twice as many people as the second largest settlement.

Rank-Size Distribution: Mexico

01,000,0002,000,0003,000,0004,000,0005,000,0006,000,0007,000,0008,000,0009,000,000

Mex

ico C

ity

Guada

lajar

a

Ecate

pec

Puebla

Cuidad

Juar

ez

Tijuan

aLe

on

Zapopa

n

Mon

terre

y

Country Primate City Population Next largest city

Population

Mexico México City

8.6 m Guadalajara 1.6 m

France Paris 9.6 m Marseille 1.3 m

United Kingdom London 7 m Birmingham 1 m

Thailand Bangkok 7.5 m Nanthabury 481,000

Denmark Copenhagen 1 m Århus 200,000

Romania Bucharest 1.9 m Iasi 315,000

Rank-Size Distribution: Argentina

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

BuenosAires

Cordoba LaMatanza

Rosario La Plata Lomas deZamora

Mar delPlata

Rank-Size Distribution: China

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

14,000,000

16,000,000

Shang

hai

Beijing

Guang

zhou

Tianjin

Wuha

n

Shenz

hen

Chongq

uing

Sheny

ang

Chengd

u

Fosha

n

Rank-Size Distribution: Chile

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

4,500,000

5,000,000

Santiago Puente Alto Vina del Mar Antofagasta Valparaiso

Rank Size Distribution: Iran

0

1,000,0002,000,000

3,000,0004,000,000

5,000,0006,000,000

7,000,0008,000,000

9,000,000

Tehra

n

Mas

hhad

Esfaha

n

Tabriz

Karaj

Shiraz

Ahvaz

Qom

Kerm

ansh

ah

Rank-Size Distribution: Haiti

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

1,000,000

Port-au-Prince

Carrefour Delmas Petionville Cite Soleil Gonaives

Rank-Size Distribution: South Korea

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

Seoul

Busan

Inch

eon

Daegu

Daejeon

Gwangju

Ulsan

Suwon

Changw

on

Seong

nam

Rank-Size Distribution: India

0

2,000,000

4,000,000

6,000,000

8,000,00010,000,000

12,000,000

14,000,000

16,000,000

18,000,000

Mum

bai

Kolkata

Dehli

Chenna

i

Hyder

abad

Benga

luru

Ahmad

abad

Pune

Surat

Kanpu

r

Rank-Size Distribution: Canada

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

Toron

to

Mon

treal

Vanco

uver

Ottawa

Calgary

Edmon

ton

Quebe

c

Winn

ipeg

Hamilton

Rank-Size Distribution: Japan

01,000,0002,000,0003,000,0004,000,0005,000,0006,000,0007,000,0008,000,0009,000,000

10,000,000

Tokyo

Yokoha

ma

Osaka

Nagoya

Sappo

roKob

e

Kyoto

Fukuo

ka

Kawasa

ki

Saitam

a

Hirosh

ima

Why do we care?- Interesting math!

- Countries that have good rank-size distribution improve the quality of life of their citizens. A regular hierarchy (USA) indicates that a society is wealthy enough to provide services for its people.

- Absence of rank-size means people may struggle to access large urban settlements, thus high level services like hospitals.