When the criteria are measurable, there is no room for complaints.
Hahahahahahaha!
I teach mostly engineering classes. I have rubrics for some problems like "Used the ideal gas law on a liquid, 0 points". I still get complaints out the wazoo because "That's only a minor mistake and that's way too much of a deduction for a minor mistake".
I actually get the same number of complaints for my somewhat-fuzzy grading based on essays as I get on the iron-clad "this is math. It's right or wrong" grading. The only difference is the student population. Some of my students will fight anything that isn't full credit and some students will reflect, look at the examples/answer key, and accept that their work wasn't as good as the example.