I think the simplest way to answer this is to introduce a new scenario. Let’s call it Scenario 0. Scenario 0 is similar to Scenario 1, but in this case your body is not disintegrated. The result seems pretty clear: you are unaffected and continue living life on earth. Other yous may be living their own lives in space but it isn’t as if there is some kind of metaphysical consciousness link that connects you to them.
And so, in scenarios 1 and 2, where the earth-you is disintegrated, well, you’re dead. But not to worry! The normal downsides of death (pain, inability to experience new things, sadness of those left behind) do not apply! As far as the physical universe is concerned (i.e. as far as reality and logic are concerned) there are now two living beings that both perceive themselves as having once been you. Their connection to the original you is no less significant than the connection between the you that goes to sleep and the you that wakes up in the morning.
EDIT: I realize this does not actually answer Questions 3 and 4. I don’t have time to respond to those right now but I will in a future edit.
EDIT 2: The approach I’d take with Q3 and Q4 would be to maximize total wealth of all clones that don’t get disintegrated.
Let X be how much money is in my wallet and L is the ticket price. In scenario 1, the total wealth is 2X without the lottery or 2(X-L)+100 with the lottery. We buy the lottery ticket if 2(X-L)+100 > 2X, the inequality can be simplified to −2L + 100 > 0, which is further simplified to L < 50. The ticket is only worth buying if it costs less than $50.
For Q4 we should have a similar formula but we have three clones in the end rather than two, so I would only buy the ticket if it cost less than $33.34.
I think the simplest way to answer this is to introduce a new scenario. Let’s call it Scenario 0. Scenario 0 is similar to Scenario 1, but in this case your body is not disintegrated. The result seems pretty clear: you are unaffected and continue living life on earth. Other yous may be living their own lives in space but it isn’t as if there is some kind of metaphysical consciousness link that connects you to them.
And so, in scenarios 1 and 2, where the earth-you is disintegrated, well, you’re dead. But not to worry! The normal downsides of death (pain, inability to experience new things, sadness of those left behind) do not apply! As far as the physical universe is concerned (i.e. as far as reality and logic are concerned) there are now two living beings that both perceive themselves as having once been you. Their connection to the original you is no less significant than the connection between the you that goes to sleep and the you that wakes up in the morning.
EDIT: I realize this does not actually answer Questions 3 and 4. I don’t have time to respond to those right now but I will in a future edit.
EDIT 2: The approach I’d take with Q3 and Q4 would be to maximize total wealth of all clones that don’t get disintegrated.
Let X be how much money is in my wallet and L is the ticket price. In scenario 1, the total wealth is 2X without the lottery or 2(X-L)+100 with the lottery. We buy the lottery ticket if 2(X-L)+100 > 2X, the inequality can be simplified to −2L + 100 > 0, which is further simplified to L < 50. The ticket is only worth buying if it costs less than $50.
For Q4 we should have a similar formula but we have three clones in the end rather than two, so I would only buy the ticket if it cost less than $33.34.