Non competitive grading system
As a graduate student I had to grade exams for the courses my supervisor taught. We had a very intricate system of establishing what would be a passing grade:


Prepare a set of questions.
Let all the Teaching Assistants (TAs) solve the problems, keeping track of how long they took for each question.
Distribute an arbitrary number of points over the questions relative to how much time, on average, was spent on each question by the TAs.
Let the students take the exam.


Let me be very explicit that until this point, no grading scale has been established!


Mark the exams. This just consisted of going through the questions and assigning points for correct solutions, partially correct solutions, etc... Every question was marked by a different TA and this TA was free to distribute points as he/she saw best. Usually we would go through a pile of 10-20 exams, see how the problems were solved, e.g. what pitfalls were encountered or how far most people got, and then establish a scheme we would use for the rest of the exams.
Every TA hands in an exact description of how they marked their question, i.e. how points were assigned.
With this list, go through the questions one by one and decide what constituted the minimum requirement in each question. This decision was signed-off by my supervisor.
Using the marking schemes written by the TAs, calculate how many points the minimum requirements would have given if they had been handed in as an exam.
The number of points for the minimum requirements constitute a passing grade. Anything below that fails, anything above that passes.


In my university, grades were on a scale from 1 (fail), over 4 (pass), to 6 (perfect) in steps of 0.25 grade points. This gives us three grades to map zero, the minimum requirement, and the maximum number of points to respectively. This can be fitted to a function $G(p) = ap^2 + bp + c$ which maps points $p$ to a grade $G(p)$.

The advantage of this approach is that it is, in principle, independent of the TAs specific style of marking, as the marking is taken into account when computing the minimum requirement points. It is also completely non-competitive in that it's independent of the students' actual performance during the exam. To make sure our decisions were sound, my supervisor and I would go through the 10 exams just below and just above the passing grade and see if they were all clear pass/fails. They usually all were. When not, it was usually just a matter of tweaking the rounding.

There is an open question regarding the amount of time given to the students, e.g. is it possible for them to solve all the questions, and thus is the mapping of maximum points to maximum grade justified? Here we played it safe by choosing only a few questions to make sure nobody would run out of time. The point is that if you do or don't know how to solve a problem, time won't be an issue. We also had two-hour exams, which gave the students ample time to show what they could, and what they couldn't do.

This system also works if you're the only person marking all the exams.

I would be very interested if anybody could suggest improvements or detect amendable flaws in this scheme, as it is what I plan to use myself, now that I'm a lecturer.