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Is there available a mapping between US voting precincts and census-recognized geographical units, like census block groups, or even to ZIP codes?

There are nice data sets now of US election results at the very granular level of the voting precinct (about 168k in the nation), e.g., at Harvard's "dataverse". I would like to merge this with census data. The difficulty is that "voting precinct" is not one of the census geographical units. Usually a precinct is made of "census blocks", and is something closer (but usually not equal to) a "block group" or maybe "census tract", I gather.

There is a 2017 journal article discussing methods of merging election and census data, with a summary here. It sounds a little involved, and a lot of choices need to be made. I was hoping that someone has done this for 2016 or other more recent precincts.

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