Rank Size Rule

To understand the urban hierarchy of a country—how cities are distributed in size and number—we need more than just the idea of a single dominant city (like in the Primate City concept). That’s where the Rank-Size Rule (RSR) comes in.

The Rank-Size Rule, proposed by G.K. Zipf in 1949, is a mathematical model that explains how all cities in a country or region are related in terms of population.

While Primate City Theory focuses on just the biggest city, the Rank-Size Rule studies the entire urban system—from largest to smallest towns.

The Core Idea: Ranking Cities by Size

Imagine listing all the cities in a region in order of population:

The largest city is ranked 1
The second-largest is ranked 2
The third-largest is ranked 3, and so on…

Now, according to Zipf:

The population of the nth city = Population of the largest city ÷ n
This can be expressed as:

Where:

= Population of the nth city
= Population of the largest city
n = Rank of the city

So, if the largest city has 10 million people:

2nd city = 10 million ÷ 2 = 5 million
3rd city = 10 million ÷ 3 ≈ 3.33 million
4th city = 10 million ÷ 4 = 2.5 million
…and so on.

In short: the second city is half, the third is a third, the fourth is a quarter of the largest.

This creates a predictable and balanced urban pattern, quite unlike the skewed structure seen in countries with primate cities.

Why Does This Pattern Emerge? – Zipf’s Explanation

Zipf didn’t give a strict mechanism, but he suggested two important processes:

1. Agglomeration

Villages and small towns are often self-contained—they produce, consume, and survive on their own.
So, they don’t compete much with nearby towns.
Hence, many small settlements can co-exist peacefully.

2. Diversification

Larger cities are not self-contained.
They depend on a hinterland (rural support zone) for raw materials, labor, and markets.
Therefore, two large cities can’t survive close together—they would compete and drain each other’s resources.
Hence, large cities tend to space themselves out, creating a balanced urban structure.

Rank-Size Rule in India

Let’s apply this to India and see what happens.

Nationally, the Rank-Size Rule does not apply well.
- Why? Because Mumbai, Delhi, and Kolkata have very similar population sizes, unlike the clear 1:2:3 ratio that Zipf predicts.
In many states, there is urban primacy:
- In 15 out of 28 states, one city dominates.
- In 8 states, the largest city is just slightly bigger than the second.
RSR works only in a few cases, like:
- Jammu & Kashmir
- Rajasthan

So, for India: Rank-Size Rule is an exception, not the norm.

Criticism of the Rank-Size Rule

Just like every model, the RSR has its limitations.

1. Too Rigid

It expects an ideal mathematical sequence, which rarely fits reality.
Actual population data is messy, shaped by history, politics, colonialism, economy, etc.

2. Overemphasis on Population Size

Cities are not just about how many people live there.
Functional roles, economic influence, spatial extent—none of these are considered.

3. Definition Problem

There’s no universal definition of what counts as a “city”.
Does a city include its metropolitan area? Just the urban core? Census zones?
This makes comparing populations inconsistent.

Comparative with Primate City Concept:

Aspect	Primate City Concept	Rank-Size Rule (RSR)
Proposed by	Mark Jefferson (1939)	G.K. Zipf (1949)
Focus	Only on the largest city	On entire urban hierarchy
Definition	A city twice as large and significant as the second largest city	population declines in a predictable ratio
Urban Pattern	Highly unbalanced; one dominant city	Balanced distribution of city sizes
Relation between cities	Other cities are insignificant in comparison to the primate city	Each city has defined proportionate relation with the largest
Economic Structure	Economy is centralized; primate city controls major functions	Economy is decentralized; functions spread across cities
Examples	Bangkok (Thailand), Paris (France), London (UK), Nairobi (Kenya)	USA, Germany, Canada (where city sizes follow predictable patterns)
India’s Case	No national primate city, but regional primacy exists in many states	Does not fit well nationally, fits only in few states like Rajasthan
Criticism	Leads to overconcentration and regional imbalance	Too mathematical, rarely fits real data, ignores functional importance
Usefulness	Explains urban dominance and resource centralization	Helpful in assessing urban balance and development levels

Example:

Rank	Primate City Concept (Disproportionate dominance)	Rank-Size Rule (Balanced urban hierarchy)
City 1	10 million	10 million
City 2	3 million	5 million
City 3	1.5 million	3.33 million
City 4	1 million	2.5 million
City 5	0.5 million	2 million

Conclusion

The Rank-Size Rule offers an elegant theoretical model for urban distribution:

It’s like a mathematical balance of cities based on size and rank.
It helps geographers identify balanced vs unbalanced urban growth.

But in practice, it’s:

Rarely a perfect fit
Often disturbed by colonial histories, political centralization, or economic forces

India, with its regional diversity, colonial legacy, and uneven development, often violates this rule—showing instead a mixed pattern of primacy and fragmented hierarchies