As a general rule if you have a domain like this that extends indefinitely in one direction, the correct prior is one that diminishes as you move further away in that direction, rather than picking a somewhat arbitrary end point and using a uniform prior on that.
Just a quick thought on this issue: Using Laplace’s rule of succession (or any other similar prior) also requires picking a somewhat arbitrary start point. You suggest 200000BC as a start point, but one could of course pick earlier or later years and get out different numbers. So the uniform prior’s sensitivity to decisions about how to truncate the relevant time interval isn’t a special weakness; it doesn’t seem to provide grounds for prefering the Laplacian prior.
I think that for some notion of an “arbitrary superlative,” a uniform prior also makes a lot more intuitive sense than a Laplacian prior. The Laplacian prior would give very strange results, for example, if you tried to use it to estimate the hottest day on Earth, the year with the highest portion of Americans named Zach, or the year with the most supernovas.
Moreover in your case in particular, there are also good reasons to suspect that the chance of a century being the most influential should diminish over time.
I agree with this intuition, but I suppose see it as a reason to shift away from a uniform prior rather than to begin from something as lopsided as a Laplacian. I think that this intuition is also partially (but far from entirely) counterbalanced by the countervailing intuitions Will lists for expecting influence to increase over time.
I’m a bit concerned that this post is blurring the distinction between two different questions: “Do we have obligations to others?” and “What way of ‘framing’ effective altruism to yourself is most productive or sits best emotionally?”
For example, it may be the case that “guilt and shame are poor motivators,” but this would have no bearing on the question of whether or not we have moral obligations. People who say that we “ought to” help others don’t normally say it because they think that obligation is an instrumentally useful framing—they say it because they believe that what they’re saying is true.
Internalising this principle might make many people happier—and might even lead many altruistically-inclined people to do more good in the long run.
But I also think the principle is probably false. It implies, for example, that sadists and abusers should just do what they want to do as well. If there are actually any “oughtthorities to ordain what is right and what is wrong,” then it seems unlikely these oughtthorities would endorse harming others in such cases. On the other hand, if the post is right about there not being any oughtthorities (i.e. normative facts), then the principle is still at minimum no more correct than the principle that people should “just do what helps others the most.”