That's enlightening and encouraging. A formula-based/matrix approach might make it more acceptable because it isn't personal. One thing I haven't seen is how to handle COLA. I'm sure that can also be added as an additional factor, though.
(Late to the reply, sorry.) COLA is addressed on a per office basis. Our headquarters is in a relatively inexpensive large city, and so other offices in pricier places like SF or DC get a blanket COLA adjustment, with the percentage bump based on some particular survey's index or something.