Tiny Probabilities of Vast Utilities: A Problem for Longtermism?

I wrote this sequence all in one go several years ago, funded by CEA. I still stand by it and think it's an important contribution to the literature, especially for readers who are new to it. (In particular, I think that framing the problem as the problem of how to deal with funnel-shaped action profiles immediately cuts through 85% of the proposed solutions to the problem one typically encounters, and makes it obvious what the costs and benefits of a remaining 10% are.)