Under Zipf's law, how does the size of the second-largest city compare to the largest?

Under Zipf's law, how does the size of the second-largest city compare to the largest?

• A. About the same size as the largest.
• B. About twice the size of the largest.
• C. About half the size of the largest.
• D. Independent of the largest.

Answer: (C)

Zipf's law states that city sizes follow a rank-size rule: the population of a city is inversely proportional to its rank. This means the largest city sets the scale, and each step down in rank roughly halves the size. Specifically, the second-largest city is about half the size of the largest, the third about a third, and so on. In other words, P2 ≈ P1/2. Real-world data show deviations, but the general pattern is that the second city is roughly half as large as the largest.

Zipf's law states that city sizes follow a rank-size rule: the population of a city is inversely proportional to its rank. This means the largest city sets the scale, and each step down in rank roughly halves the size. Specifically, the second-largest city is about half the size of the largest, the third about a third, and so on. In other words, P2 ≈ P1/2. Real-world data show deviations, but the general pattern is that the second city is roughly half as large as the largest.