I have a census block shapefile with a land cover TIFF underneath it. The Raster layer has three different cell values. I am trying to select the census blocks that have a minimum of 50% of cells withing its area with a value of 3. I have access to all extension within ArcGIS Desktop 10.7.
I would reclassify your land cover tiff to remove the cell values you are not interested in so leaving you with a raster where the you only have pixels with your desired value (3), the rest are nodata. You could then use the Tabulate Area tool to compute the area of pixels within each polygon. Run the Join Field tool to join the pixel area to your polygon data and then you will be able to select the polygons where there is more than 50% coverage.