The flaws in both of these dilemmas seems rather obvious to me, but maybe I'm overlooking something.

The Repugnant Conclusion

First of all, I balk at the idea that adding something barely tolerable to a collection of much more wonderful examples is a net gain. If you had a bowl of cherries (and life has been said to be a bowl of cherries, so this seems appropriate) that were absolutely the most wonderful, fresh cherries you had ever tasted, and someone offered to add a recently-thawed frozen non-organic cherry which had been sitting in the back of the fridge for a week but nonetheless looked edible, would you take it?

"But how can you equate HYOOMAN LIIIIIVES with mere INANIMATE CHERRIES, you heartless rationalist you?" I hear someone cry (probably not one of us, but they're out there, and the argument needs to be answered).

Look, we're not talking about whether someone's life should be saved; we're talking about whether to create an additional life, starting from scratch. To suppose anything else is to make an assumption about facts not mentioned in the scenario. Why would anyone, under these circumstances, add even one life that was barely worth living, if everyone else is much better off?

I think what happens in most people's minds, when presented with conundrums like this, is that they subconsciously impose a context to give the question more meaning. In this case, the fact that we know (somehow) the quality-of-life of this one additional person implies that they already exist, somewhere -- and therefore that we are perhaps rescuing them. Who could turn that down? Indeed, who could turn down a billion refugees, rather than let them die, if we knew that we could then sustain everyone at a just-barely-positive level? Surely we would soon be able to put them to work and improve everyone's lot soon enough.

I could go on with the inquiries, but the point is this: the devil is in the details, and scenarios such as these leave us without the necessary context to make a rational decision.

I propose that this is a type of fallacy -- call it Reasoning Without Context.

Which brings me to today's main dish...

The Lifespan Dilemma

The essential fallacy here is the same: we lack sufficient context to make a rational decision. We have absolutely no experience with human lifespans exceeding even 1000 years, so how can we possibly guage the value of extending life by an almost incomprehensible multiple of that, and what are the side-effects and consequences of the technique being used?

Some further context which I would want to know before making this decision:

1. How do I know that you can extend my life by this much? How do you know it? (Just when did you test your technique? How reliable is it? How do I know you're not a Brooklyn Bridge salesman, or a Republican?)
2. If you can extend it, why can't I do it without your help?
3. How do I know there isn't someone else who can do it better, i.e. without the 20% chance of dying today?
4. What are you getting out of this deal, that you are essentially giving away immortality for whatever it is you are doing that gives me an approximately 20% chance of dying today? Perhaps whatever that thing is, I should be selling it to you for quite a high price.
5. How many others have already accepted this offer? Can I talk with them (the ones who haven't died yet) before deciding? Can you prove that your fatality rate really is only 20%?

Math and logic deal in absolute certainties and facts; real life, which is the realm of rational decisionmaking, depends on context. You can't logically or mathematically analyze a problem with no real-world context and expect the answer to make rational sense.