OK, firstly, having never been in such a situation, i can only provide a hypothetical answer based on knowledge, not an answer based on wisdom, experience, or understanding.
secondly, i do not believe such a situation would ever happen in reality to me or any other living human being. given that we are on an island, numerous food sources would be found (provided you had the ability to locate and capture them), such as crabs, fish, birds, &c. &c.
thirdly, i think that if such a situation happened, it would only happen out of the love of God for us, and therefore whatever we do it must also be done out of love towards God and our neighbour.
fourthly, not enough information is given to really understand this situation. presumably this tree & its fruit is also the only water source for these people? how long would it take to grow another tree that would be edible from the seeds of these plants? how long could both families survive with both eating this fruit? i know you said both would starve if they tried to eat the fruit, but in reality this would not be the case. in addition, how long could one family survive with only them eating this fruit? presumably it contains all the necessary nutritional value as well as a substantial enough quantity of fruit to keep them all alive for a substantial period of time? if not, what would be the point of removing any competition for the food? how did we get on this island? what means of communication are available with the outside world?
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to the point however, hypothetically speaking, if i were in a situation where 1. eating the food and having it for my family would cause the other family to starve to death, 2. allowing the other family to eat it would starve my family to death, 3. none of us eating it and all of us starving to death, or 4. fighting to the death for the tree... would all result in one and the same result: the death of innocent people,
(i am going to make 2 assumptions here: the food supply will stretch to feed a single family, no matter how large that family becomes; and 2. the island has no established government.)
i believe the solution is quite simple.
we would first hold a
democratic election and elect the head of the opposite household as president of the island, with emergency powers over the legislature, executive, military, and judiciary functions of that nation.
secondly, i would
give up all my children for adoption by the other family (given that the food supply stretches, they are guaranteed to have enough food).
thirdly, i would have the now-president & sole magistrate of this nation agree to a
divorce between me & my wife (i consider this the lesser of 2 evils in this case), making us both now legally single
finally, i'd have the other family
adopt me & my wife as their children as well.
dilemma solved.