The Desert Island Exercise is a mental test used to evaluate the quality of corporate securities. When applying the test to a potential investment, you would ask yourself if you would feel comfortable owning the stock or bond, knowing that you would be stuck on a desert island for a longer period.
Being unable to act in any way, the only way the investment would pass the test would be if its long-term competitive position would be relatively secure. Therefore this you are effectively performing a test of the investments qualitative factors as opposed to its quantitative factors.