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Anja comments on Universal agents and utility functions - Less Wrong
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AIXI actually has a configurable horizon function. It's described on page 30 of AIXIgentle.
There is also a more detailed paper by Lattimore and Hutter (2011) on discounting and time consistency that is interesting in that context.
This is a very interesting paper. Reminds me of HIGHLANDER for some reason... those guys lived for thousands of years and weren't even rich? They hadn't usurped control of vast econo-political empires? No hundred-generations-long family of bodyguards?
If a human line of descent can't do that, why should an immortal be able to do that?
Consistency? And, in fairness, human lines of descent have become monarchies, which worked out pretty well for a while.
I think people would get pretty antsy when it became clear that the guy running their town was an immortal. If I were a 13th century peasant with a hankering for revolt and a touch of the plague, I would do terrible, terrible things to someone who was both immortal and rich. Probably best not to get too showy.