Is there a compiled dataset of all administrative units (ADM-1) of the world with population data?
I know that https://www.geonames.org/ has the raw data, I am looking for a pre-compiled dataset
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I don't know of a pre-compiled dataset; there are a multitude of factors that would need to be considered in assembling something like that.
Another option for creating your own would be IPUMS Terra, the Integrated Population and Environmental Data project that's part of the IPUMS series at the Minnesota Population Center, Univ of Minnesota. The data has been gathered from census and statistical agencies of individual countries, or in some cases from estimates generated by the project:
Choose the "Create Your Custom Dataset" option, then on the next screen on the right choose "Start Extract Area Level Output". On the Extract Builder (see pic below) choose variables on the left, like Demographic and Total Population. Then under Datasets on the right you can choose countries and filter by year. Once you move on to the next screen, you can choose to harmonize the output or choose specific years. This is also where you get the chance to choose your administrative level: national, ADM-1, or smallest available.
You do have to create an account to use it, but it's free and is an academic / non-commercial organization.