I have experience in grading math Olympiad papers; one principle we adopted there is to always grade in pairs, with one pair grading a single problem, or more pairs sharing a long or tricky exercise. I recommend this strategy especially for grading more important papers such as final exams, where good accuracy is important.
It may seem that this is a waste of resources; however there are several benefits:
- Accuracy increases much. A subtle error has to slip through two people instead of one.
- You do not waste so much time as it seems at first sight. Grading often follows an 80-20 law: 80% of the papers takes you 20% of the time, while grading the remaining 20% consumes the remaining 80% of it. This may be due to particularly non-standard solutions, bad handwriting, or edge cases that evade your marking scheme (as suggested by Dan C, always have a marking scheme, especially if there are multiple pairs on the same problem, and discuss together the more complicated cases). So, while you waste some time by having two sets of eyeballs looking at the easier papers, it is often invaluable to have a ready help in the more complicated cases. Your colleague may be faster than you in spotting a definition that you missed, a hidden line of reasoning, or deciphering a strangely-looking hieroglyph. This saves a lot of time on the more complicated cases.
- You will feel a lot less tired and find that you can go on with a steady rhythm for hours. You can chat together every now and then, share comments on good solutions, or make fun of particularly bad ones; this helps relieving tiredness.
Often we see one person trying to explain the solution to the other, or the pair spontaneously evolving a good cop-bad cop behaviour (one looks for weak points in the solution, the other defends the student). This method also doubles as training for beginner graders, that can learn from working with a more experienced partner.