The closer something is to me, the more I value it. This applies to people and animals too. Therefore, if I could save you or my pet dog, you would be out of luck. Unless you were a friend or at least an acquaintance, that is.
If the question was "Save a family member/friend or 100 kids you don't know in a country far away", then there would be 100 dead kids. Hell, I'd probably even save my dog over the 100 kids, although there would be at least half a second of seriously debating before choosing dear old Patches.
That being said, if I was responsible for putting both you and my pet in the life-or-death situation in the first place, I would have to save you.
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I see this as a modified trolley problem. The only difference is that instead of trying to determine if a person sees multiple lives as more valuable than a single one, this is designed to see if a different type of life is more valuable than a standard human life.
I approach this problem the same way as I approach the typical trolley problem- I walk up to the track and see the situation at hand, realize someone is going to die either way, and don't do anything about it. If people die because I didn't pull a lever, then it's not my fault. They would have died anyway. However, if I do pull that lever and a different person is killed instead, I participated in it. Even if the train hits one person instead of 4, I still partially caused that one person's death.
The only reason I would interfere with the situation at all is if one of the parties involved is important to me. In this case, it's the pet. In this case, I pull the lever to save a loved one over a stranger.
(Oh, and I value rights, and hate human rights abuses. I would never kill another person to save my dog, or even another person really. But in a situation of "They're both in a random life-or-death situation that is completely not my fault, I can only intervene to save one, and they'll both die if I don't step in," I pick my personal attachment.)