Urban Primacy Index

A primate city is the leading city of a country that is disproportionately large and dominant relative to the others — not merely the biggest, but several times larger than the second city and pre-eminent in economic, political, and cultural life. Jefferson's original criterion was qualitative dominance; the two-city index operationalizes it, with values well above one (often cited around two or more) indicating primacy. Classic examples include Paris in France, London in the United Kingdom, and Bangkok in Thailand.

Both describe city-size distributions but from different angles. The rank-size rule fits the whole distribution with a power-law exponent, while the primacy index isolates how dominant the single largest city is. A perfectly rank-size (Zipf) system would have a two-city index of about two, because the second city is half the first, yet still be called balanced rather than primate; primacy is flagged when the top city exceeds even that, so the two tools are best used together to characterize both the head and the body of the hierarchy.

Because they weight the rivals differently. The two-city index can look high simply because the second city happens to be small, even if the third and fourth cities are large, overstating primacy. The four-city index pools the second through fourth cities, so it is less sensitive to any single rival and gives a steadier reading of whether the leading city dominates a group. When they diverge, it usually signals an unusual gap between the second city and those just below it, and reporting both is good practice.