Have you looked into the Detect Graphic Conflict Tool in the toolbox under Graphic Conflict?
You could use that tool to find the graphically (make sure outlines are 0 width) overlapping areas. The newly created shapefile's attribute table is populated with the FID from both overlapping polygons. You could join your data using the FID field then create a new field and calculate the rankings. You can only use this tool with two shapefiles at once, so you will need to repeat the process. Once finished, you could merge all the original shapefiles together and merge all the overlapping areas shapefiles together, then erase the merged overlapping areas (Advanced License Level - If you don't have an advanced license then try Xtools for free) from the merged original shapefile. Then merge everything back together again.
Example: I have two shapefiles (Federal Forest and State Forest). I want to symbolize them three ways Federal, State, or Federal and State (overlapping) and I don't want to have to mess around with transparences or drawing order.
Toolbox > Graphic Conflict > Detect Graphic Conflict
Join Federal Forests and State Forests using FID fields to the Detect Graphic Conflict Output. Created two new fields (State Forest Name and Federal Forest Name) and used Field calculator to populate the new fields with the Forest Name.
- Merge State and Federal Forests shapefiles
- Erase Overlapping Areas (Analysis Tools > Overlay > Erase)
Input: Merged State and Federal Forests Output
Erase Features: Detect Graphic Conflict Output
- Merge the Erase Output with the State and Federal Merge Output. Make sure to clean up the attribute table and make sure all the fields are calculated in the final output.