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Gurkenglas comments on Anatomy of Multiversal Utility Functions: Tegmark Level IV - Less Wrong Discussion
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In the first formula of "A Simple Example", the constant beta is exponentiated by t, Did you mean to use a binary sequence in betas place, instead indexing the beta symbol with t? What does the beta mean anyway? Does it encode the instants of time about which G cares, so as not to get an unbounded U (meaning you probably want to add that beta is only 1 in finitely many places)? That doesn't seem like the right solution, I wouldn't want our FAI to stop caring after Busybeaver(2^100) steps because we couldn't give it a later bound on which instants to care about. Probably more questions later, I just don't want to fall prey to Harry bias.
Thx for commenting!
The beta^t factor is exponential time discount. G cares about all instants of time, but it cares about future instants less. Indeed, without this factor the sum over time would diverge. Thus, changing beta amounts to shifting the trade-off between short-term and long-term optimization (although in the multiverse setup the effect is not very strong - see "time discount" section).