I was an IMO coordinator in 2013 and 2014, and this is what we usually do:

• As soon as we are assigned the problems, we try to collect as many alternative solutions as possible. I had problem 4, which was G1 (easy geometry), on both years, and we had about 10 solutions each year.
• We try to group the solutions into classes by similarity, in order to evaluate how the marks could be equivalent.
• We come up with a marking scheme, which are the rules for awarding points. A good marking scheme is based on facts (we award points for proving stuff; we also write down examples of statements that are not worth any points and, in the case that there is not a consensus on what needs a proof or not, we clarify that as well). We try to make it as broad as possible to try to consider all possible solutions.
• We test the marking scheme on possible partial solutions based on the alternative solutions; we should be able to grade any solution that is based on any of these solutions. If we had done a good job on finding these solutions, the work is vastly improved later, because we cover most of the cases.
• In case the student tries more than one approach we give the maximum of the points. Sometimes a mixed approach is also valid and we might award the sum.
• The marking scheme is presented to the jury (which is essentially the set of the team leaders). The jury can make questions and requests, and the marking scheme is then revised.
• Notice that all the preceding procedures are carried out before the test.
• Of course, exceptions might occur, and a new solution might appear as we grade the papers after the test. The most important thing to do is to immediately report to the problem captain so we come up with a grading scheme for this new solution, to ensure consistency. Again, if we do well our job of finding alternative solutions, there are few cases. By the way, we have about 15 hours to grade all 600+ papers, in more than 20 languages. It's pretty tough!
• If everything is well done, then the coordinations (which are the negotiations between leaders and coordinators) run smoothly. The disagreements are few and far between, and when they happen we ask the leaders to come back later so we can reevaluate (we might have missed something, something might have been lost in translation, sometimes we need a full translation; it also applies to the leaders - they might have overlooked a missing link, they are too overzealous etc). If even later there is not an agreement, we invoke the problem captain, and he's in charge of negotiating; if the deal is not closed it goes to the chief coordinator; finally if nothing can be done the case goes to the jury: the captain and the leader defend their case, and the jury votes. The coordinators usually win, so it's not a good idea to go to the jury.

So, as you can see, grading the IMO is a complex, delicate procedure, with a lot of thought out steps.