QGIS: Allocation data by Voronois to admin units according to area

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In QGIS, I need to assign values from Voronoi cells into admin 2 units (e.g., counties) with a weighted average according to the amount of territory of each county covered by the cell. So, for example, if some county contains parts of various Voronoi cells--V1 taking up proportion p1 of the territory, V2 taking up p2, and so forth--then I want to create a weighted average of some attribute for each relevant cell that's weighted according to p1, p2, etc.

Page 4 of this paper by Frias-Martinez and Virsesa gives an idea what I'm trying to do with QGIS.

(Eventually I'd like to weight according to population, but that requires finding a population distribution, so let's start by weighting on land area.)



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