The population that was estimated twice

Two respected estimates of a city's population in 1650 differ by a factor of three. Both are defensible, and the difference is almost entirely in one assumption.

Neither figure comes from a count. The evidence is a list of houses compiled for a tax, and converting houses into people requires a household size. One historian used five, drawn from parish registers in a nearby rural district. The other used nine, drawn from a later survey of the same city that recorded multiple families per dwelling. Everything else in the two calculations is identical, and the whole disagreement is carried by a number nobody observed.

This is the normal condition of pre-statistical demography, and the professional response is not to choose. Papers in the field now present a range with the assumption stated as a parameter, so that a reader can see which conclusions depend on it. The useful question becomes conditional: at a household size of five, the city was smaller than its rival; at nine, larger. Conclusions that hold across the whole range are the ones that can be asserted, and in this case there were two: the city grew faster than the region, and its growth stopped abruptly in the 1660s.

The method has a wider application. Where a figure rests on an unobserved parameter, the honest presentation is the range and the dependency rather than the best guess, and the discipline of writing it that way reveals something useful: most arguments turn out not to depend on the contested number at all. The ones that do are the arguments worth spending the next decade of research on.

That is the function of making an assumption visible. It sorts the questions by whether the missing evidence would settle them.