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Manfred comments on Utilitarianism and Relativity Realism - Less Wrong
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Caring about times within some time limit in a single reference frame is sufficient.
The problem with a time limit is that it encourages you to not care what happens afterwards.
Hm, I think any integrable time-discounting function would also work. And the trouble with an AI that doesn't time-discount is that it gets Pascal's mugged by literally any chance of eternity.