Interesting idea, but it’s an infinite money hack in sort of the same way that “find a rich person who hates money” is an infinite money hack.
It's true that Alice needs to be rich for it to work, but I wouldn't say she needs to "hate money". If she seriously believes in this continuity of personhood, she is sending the money because she wants more money in the end. She truly believes she's getting something out of this exchange.
BTW, you also need to be already rich and generally have a nice life, otherwise Alice's cost of switching may be higher than the money she has. Conversely, if in the eyes of Alice you already have a much better life than hers, her cost of switching will be lower, so such a swap may be feasible. Then, this could actually snowball, because after each swap your life becomes a bit more desirable to others like Alice.
But maybe you mean that people like Alice would be quite rare? Could be so.
Yeah, that's also what I expect. Actually I'd say my main hope for this thought experiment is that people who claim to believe in such continuity of personhood, when faced with this scenario may question it to some extent.
I'm not sure what this thought experiment shows us other than the fact that these views of what constitutes identify are in fact different?
To be honest I just shared it because I thought that it's a funny dynamic + what I said in the comment above.
BTW, if such swaps were ever to become practical (maybe in some simpler form or between some future much simpler beings than humans), minds like Alice would quickly get exploited out of existence. So you could say that in such environments belief in "continuity of personhood" is non-adaptive.
Imagine a scenario where you can switch bodies with someone: both of you are anesthetized, then undergo plastic surgery to match each other’s appearance. You both have your brains rewired to essentially switch brains, and finally, you swap houses, names, bank accounts and all social and legal identities.
Let's say Alice (like many people) believes in continuity of personhood and in this situation she'd say she's still "bound to the same atoms", only her mind and name etc. has been changed. (And I'll assume you identify more with your mind etc.)
You can then ask her how much she'd need to be paid to agree to undergo this procedure - let’s assume she says 10 million dollars . But, since she believes she’ll end up in your body and with your bank account, Alice actually needs to pay you. And then you switch.
So then she (according to her) ends up as you with 10 million dollars. And you also end up as you with 10 million dollars. (Unfortunately someone also ends up as Alice in debt but it's "neither of you" shrug)
Repeat this, until you have more money than you know how to use ;)
(Edit: maybe I should clarify that I don't expect many people to agree to such a swap from Alice's side, and even if they do, they'd be exploited out of existence. This thought experiment is rather aimed at people who claim to believe in continuity of personhood, to test how "committed" they are to this idea, and hopefully seed some doubt in them.)