That aside, I do have an object-level comment. Nick states (in section 6.3.1) that Period Independence is incompatible with bounded utility function, but I think that's wrong. Consider a total utilitarian who exponentially discounts each person-stage according to their distance from some chosen space-time event. Then the utility function is both bounded (assuming the undiscounted utility for each person-stage is bounded) and satisfies Period Independence.
I agree with this. I think I was implicitly assuming some additional premises, particularly Temporal Impartiality. I believe that bounded utility + Temporal Impartiality is inconsistent with bounded utility. (Even saying this implicitly assumes other stuff, like transitive rankings, etc., though I agree that Temporal Impartiality is much more substantive.)
Another idea for a bounded utility function satisfying Period Independence, which I previously suggested on LW and was originally motivated by multiverse-related considerations, is to discount or bound the utility assigned to each person-stage by their algorithmic probability.
I am having a hard time parsing this. Could you explain where the following argument breaks down?
Let A(n,X) be a world in which there are n periods of quality X.
The value of what happens during a period is a function of what happens during that period, and not a function of what happens in other periods.
If the above premise is true, then there exists a positive period quality X such that, for any n, A(n,X) is a possible world.
Assuming Period Independence and Temporal Impartiality, as n approaches infinity, the value of A(n,X) approaches infinity.
Therefore, Period Independence and Temporal Impartiality imply an unbounded utility function.
The first premise here is something I articulate in Section 3.2, but may not be totally clear given the informal statement of Period Independence that I run with.
Let me note that one thing about your proposal confuses me, and could potentially be related to why I don't see which step of the above argument you deny. I primarily think of probability as a property of possible worlds, rather than individuals. Perhaps you are thinking of probability as a property of centered possible worlds? Is your proposal that the goodness of a world A with is of the form:
g(A) = well-being of person 1 prior centered world probability of person 1 in world A + well-being of person 2 prior centered world probability of person 2 in A + ...
? If it is, this is a proposal I have not thought about and would be interested in hearing more about its merits and why it is bounded.
Could you explain where the following argument breaks down?
My proposal violates Temporal Impartiality.
I primarily think of probability as a property of possible worlds, rather than individuals. Perhaps you are thinking of probability as a property of centered possible worlds?
Yes, sort of. When I said "algorithmic probability" I was referring to the technical concept divorced from standard connotations of "probability", but my idea is also somewhat related to the idea of probability as a property of centered possible worlds.
I gues...
Nick Beckstead: On the Overwhelming Importance of Shaping the Far Future
ABSTRACT: In slogan form, the thesis of this dissertation is that shaping the far future is overwhelmingly important. More precisely, I argue that:
Main Thesis: From a global perspective, what matters most (in expectation) is that we do what is best (in expectation) for the general trajectory along which our descendants develop over the coming millions of years or longer.
The first chapter introduces some key concepts, clarifies the main thesis, and outlines what follows in later chapters. Some of the key concepts include: existential risk, the world's development trajectory, proximate benefits and ripple effects, speeding up development, trajectory changes, and the distinction between broad and targeted attempts to shape the far future. The second chapter is a defense of some methodological assumptions for developing normative theories which makes my thesis more plausible. In the third chapter, I introduce and begin to defend some key empirical and normative assumptions which, if true, strongly support my main thesis. In the fourth and fifth chapters, I argue against two of the strongest objections to my arguments. These objections come from population ethics, and are based on Person-Affecting Views and views according to which additional lives have diminishing marginal value. I argue that these views face extreme difficulties and cannot plausibly be used to rebut my arguments. In the sixth and seventh chapters, I discuss a decision-theoretic paradox which is relevant to my arguments. The simplest plausible theoretical assumptions which support my main thesis imply a view I call fanaticism, according to which any non-zero probability of an infinitely good outcome, no matter how small, is better than any probability of a finitely good outcome. I argue that denying fanaticism is inconsistent with other normative principles that seem very obvious, so that we are faced with a paradox. I have no solution to the paradox; I instead argue that we should continue to use our inconsistent principles, but we should use them tastefully. We should do this because, currently, we know of no consistent set of principles which does better.
[If there's already been a discussion post about this, my apologies, I couldn't find it.]