Anyway, since this question keep coming back into my mind, I now think I know what types of people I would not enjoy be left alone with on any empty island.
I would definitely hate to be dependent on one of those guys who maybe are a little bit stupid, but who believe they are really smart (and therefor don't think any input from anybody else, in that case me, is needed). At a first thought, it would feel safe to be in the company of a physically strong person, but I believe some brains and a bit of imagination would be more valuable in most situations.
I would appreciate to explore the place, and not find the best tree and then just sit under it all the time. Talking would I prefer before endless silence. Some new jokes would be nice, or at least a person who would enjoy my silly ones. But the most important and valuable gifts are probably kindness and helpfulness when there is some kind of trouble.
What I myself would be like on a deserted island? What do you think, probably hungry and thirsty... let's hope I never end up there in the first place.