You're missing the poll and you have already stated in the topic "no choice". Why ask us if we do not have a choice? If we do have a choice, I would have to say no, I will not resort to cannibalism and instead try to find food on or around the island. Even though you have stated it is deserted, it is still an island and therefore you can still try to catch fish.
If the other person I am with is skinnier than me, then I don't think I would have much to worry about because I am not fat, can run fast, and likely take him out. No I will not eat him, yes I will defend myself if he attacks me.
Lastly, if there is help coming, I would assume it wouldn't take them a month to get to me, so I'll be fine in case I wasn't able to get food. I've gone 7 days without any food so it's not like its impossible even if it took them a week to rescue me.