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AnthonyC comments on The Meaning of Right - Less Wrong
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"Even if you try to have a chain of should stretching into the infinite future - a trick I've yet to see anyone try to pull, by the way, though I may be only ignorant of the breadths of human folly"
I thought this was a part of the principle of utility. Happiness today is no more inherently valuable than happiness tomorrow. The consequences of an action, and the utility associated with those consequences, ripple forever throughout time and space, far beyond the ability of my finite mind to predict and account for.
At least, that thought is what led me to decide that "I can accept this principle as true, but it isn't often going to be useful for making decisions."
He means a chain of justifications, where each value is only instrumental to the next thing it causes to happen. Not "X is good because I have terminal values XYZ" but "A is good because it will cause B which is good because it will cause C..." which is clearly a silly idea (and completely indeterminate as a description of terminal values).
This is different to what you're saying. Yes, every action has more or less infinite consequences into the far future, so to calculate the expected utility of that action you have to sum the (expected) utility function over all time from now to infinity. Doing this you might find "action A has lots of utility, it's good, because I predict (via this chain of causality) good consequences of X utility at Y probability at time T, and also utility X' probability Y' at time T', and also..." where the utilities are determined by the utility function which encodes your terminal values.
Or, returning to the language of should-ness chains, every action has a more or less infinite chain of consequences, but that doesn't make should-ness an infinite chain. You get the should-ness of an action by adding up (a lot of) finite chains of the form "Action A causes B which causes C which causes D which is good, so A is good." Every chain has a finite length, but there's no limit on how long they can be.