Who should have control over the border dispute between China and India?
The best thing to do would be to have some sort of body that could mediate and arbitrate the dispute. It would be good if some sort of arbiter could meet with the two sides and mediate their dispute. It could try to work out a compromise position between the two. Then, if need be, it could act as an arbitrator to impose a settlement on the two sides if they could not agree.
Sadly, this is not possible unless the two countries were somehow to agree to it. The countries do not seem to be willing to compromise and so they would not be very likely to agree to arbitration that could be binding on them.
Ideally, then, there would be an arbiter who could have control over the resolution of this dispute. Since there is not, things will continue as they are until one side (or both) has an incentive to make a deal. Until then, no one will actually have control.