Silly poll. Not a feasible situation. If there was enough food to feed 10 people until the famine was over, there would be more than double the amount required to feed a family of four. Thus, at the very least, your family and half the other family would be sufficiently provided for. As both families have been accessing the granary up to this point, there is presumably no reason why they still cannot both access the remaining rations. Therefore, even if the other family only got what was left after your own family had eaten (60% of the remaining grain), they could go onto have rations and still have food left over. If, as you've later suggested as an apologetic for the unfeasability of this poll, the bigger family has such ridiculously disproportionate metabolisms, then they are obviously mutant freaks and deserve death.
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Seriosly, what you are really asking, in simpler terms, is would we value our own family over the lives of others, or would we sacrifice a minority, regardless of their personal significance, for the sake of the many?
Such questions are, of course, ridiculous to hypothesise about on a theoretical level, as no one knows what they will do until such a moment arises, and the scenario you have painted is so unlikely that it will never come to pass.
May as well ask 'if you were forced to drop a nuke on one of two locations, and one place was an island with just your family, and the other was New York city, which one would you choose?' Of course it would be something of a dilemma, but there would be no chance of such a scenario taking place. Thus=pointless conjecture=waste of time=go back to school