Jamma, your comment about the energy of the jump being the same put me on the right track. It turns out to be a very simple relationship: increase in vertical jump is directly proportional to decrease in mass/weight. Weigh half as much, jump twice as high!
So to answer my original question...
It is certainly possible to lose weight without losing a significant amount of strength. So the loss of strength can be safely neglected for my purposes. But you're right, it would make for a more interesting/more difficult problem. Training methods would be a large factor, e.g. is strength...
Imagine an athelete that weighs 180 pounds (81.6 kg) is able to jump 20" (0.51 meters) vertically. How high could he jump if he were able to decrease his weight to 170 pounds (77.1 kg)?
I think the basic idea here is to find out, given the mass, what force is required to reach the specified...