New answers tagged statistics
I'd be afraid of multi-collinearity if your results are spatially autocorrelated. I am not 100 percent certain, but that is my best guess.
One way to solve this would be to use a sql clause in a arcpy.da.SearchCursor to sort your values in descending order. Then you would store the third value of the sorted column. The trick is that you only want to get the third highest so you can utilize a counter variable. Without testing the code something like this could get the job done: searchFields = ...
Its not going to be a eloquent solution, but using "Summary Statistics" tool, you could get the MAX value of an attribute. Then do a join using that MAX value to select from your FC that record, remove that record from your original FC and put it aside (Switch Selection). Repeat three times and merge the outputs.
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