Is the 'you' on mars the same as 'you' on Earth?
There's one of you on earth, and one on mars. They start out (by assumption) the same, but will presumably increasingly diverge due to different input from the environment. What else is there to know? What does the word 'same' mean for you?
And what exactly does that mean if the 'you' on earth doesn't get to experience the other one's sensations first hand? Why should I care chat happens to him/me?
That's between your world model and your values. If this happened to me, I'd care because the other instance of myself happens to have similar values to the instance making the judgement, and will therefore try to steer the future into states which we will both prefer.
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I don't know, and unless you're trying to market it, I don't think it matters. People make silly judgements on many subjects, blindly copying the majority in this society isn't particularly good advice.
Any reaction of this kind is either irrational, based on divergence which has already taken place, or based on value systems very different from my own. In real life, you'd probably get a mix of the first two, and possibly also the last, from most people.
For me, this would be a quantitative judgement: it depends on how much both instances have changed since the split. If the time lived before the split is significantly longer than that after, I would consider the other instance a near-backup, and judge the relevance of its destruction accordingly. Aside from the aspect of valuing the other person as a human like any other that also happens to share most of your values, it's effectively like losing the only (and somewhat out-of-date) backup of a very important file: No terrible loss if you can keep the original intact until you can make a new backup, but an increased danger in the meantime.
Maybe, maybe not, depends on the exact strategy I'd mapped out beforehand for what each of the copies will do after the split. If I didn't have enough foresight to do that beforehand, all of my instances would have to agree on the strategy (including allocation of initial resources) over IRC or wiki or something, which could get messy with a hundred of them - so please, if you ever do this, give me a week of advance warning. Splitting it up evenly might be ok in the case of two copies (assuming they both have comparable expected financial load and income in the near term), but would fail horribly for a hundred; there just wouldn't be enough money left for any of them to matter at all (I'm a poor university student, currently; I don't really have "life savings" in transferrable format).