Also, it's not clear to me that strict Period Independence is a good thing. It seems reasonable to not value a time period as much if you knew it was an exact repetition of a previous time period. I wrote a post that's related to this.
I agree that Period Independence may break in the kind of case you describe, though I'm not sure. I don't think that the kind of case you are describing here is a strong consideration against using Period Independence in cases that don't involve exact repetition. I think your main example in the post is excellent.
I don't think that the kind of case you are describing here is a strong consideration against using Period Independence in cases that don't involve exact repetition.
What if we assume Period Independence except for exact repetitions, where the value of extra repetitions eventually go to zero? Perhaps this could be a way to be "timid" while making the downsides of "timidity" seem not so bad or even reasonable? For example in section 6.3.2, such a person would only choose deal 1 over deal 2 if the years of happy lives offered in deal 1 ...
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.]