The reason per capita reverses many rankings

A league table of totals is largely a league table of how big the participants are. Divide each total by its population and the order rearranges, sometimes completely, because the quantity being compared has changed from how much happens to how much happens per person, and only the second is comparable across different sizes.

What everyone sees

Totals and per-capita figures are treated as two views of one fact, with the choice between them a matter of presentation. They are different quantities that answer different questions. A total measures aggregate magnitude, which is dominated by scale; a rate measures intensity, which is what a comparison across unequal units requires.

What is actually happening

Pearson identified the general problem in 1897: when two quantities are each divided by a common third, the resulting indices can be correlated even if the original quantities are independent, so ratio comparisons carry artefacts of the divisor. Kronmal revisited the ratio standard and showed that dividing by a size variable does not simply remove size but imposes a specific and often unjustified model of how the quantity scales with it. The practical consequence is not that per-capita figures are wrong. It is that both totals and rates encode assumptions about scaling, and the ranking obtained depends on which assumption was adopted rather than only on the data.

Why it stays hidden

The dependence hides because each version looks like a plain fact. A table of totals cites no model and a table of rates cites no model, and neither presentation reveals that a choice about scaling was made. Readers compare the numbers in front of them, and the numbers in front of them already contain the answer to a question nobody asked aloud.