The above calculation seems to be considering only current people, and not much valuing additional years of happy life for current people or better lives relative to current Western standards. Nick Bostrom's Astronomical Waste paper discusses those issues. Time-discounting isn't enough to wipe out the effect either, since populations may expand very quickly (e.g. brain emulations/artificial wombs and AI teachers).
Gaverick Matheny's paper "Reducing the Risk of Human Extinction" is also relevant, although it arbitrarily caps various things (like the rate of population growth) to limit the dominance of the future.
If you care about bringing future people into being, then the expected future population if we avoid existential risk is many, many orders of magnitude greater than the current population of the world and looms very large.
If you don't care about future people then you have to grapple with the Nonidentity Problem:
Suppose that agents as a community have chosen to deplete rather than conserve certain resources. The consequences of that choice for the persons who exist now and who will come into existence over the next two centuries will be “slightly higher” than under a conservation alternative (Parfit 1987, 362). Thereafter, however, for many centuries the quality of life would be much lower. “The great lowering of the quality of life must provide some moral reason not to choose Depletion” (p. 363). Surely we ought to have chosen conservation in some form or another instead. But at the same time depletion seems to harm no one: while distant future persons, by hypothesis, will suffer the adverse effects of choice of depletion, it is also true that a conservation choice very probably would have changed the timing and manner of the conceptions. Future persons, in other words, owe their suffering but also their very existence to the depletion choice. Provided that that existence is worth having, we seem forced to conclude that depletion does not harm, or make things worse for, and is not otherwise “bad for,” anyone at all (p. 363).
Separately, there seems to be a typo in this paragraph of your post:
Off the top of my head, I think the global population estimate for 2050 is around 8 billion, assuming the current trend in reducing the number of people in extreme poverty continues (reducing extreme poverty reduces pop. growth). That means you have to arrive at a probability greater than 8,000,000:1 to get a cost-per-life estimate of under $1,000.
If you mean "what reduction in the probability of (immediate) extinction is equivalent in expected-lives--of-currently-living-people to saving one life today" then that will be near 1 in 8 billion, not 1 in 8 million. That figure is also a slight underestimate if you only care about curent people because medium-term catastrophes would kill future people who don't yet exist and many current people may have died by then.
Also, if you're looking for easier-to-evaluate charities, or bigger higher-status ones endorsed by folk such as Warren Buffett, foreign policy elites, etc, I suggest the Nuclear Threat Initiative as an existence proof of the possibility of spending on x-risk reduction. I wouldn't recommend giving to it in particular, but it does point to the feasibility of meaningful action. Also see Martin Hellman's on reducing nuclear risk.
Are nukes really an x-risk?
Update: I should've said "non-existential risk charity", rather than specifically exclude SIAI. I'm having trouble articulating why I don't want to give to an existential risk charity, so I'm going to think more deeply about it. This post is close to my source of discomfort, which is about the many highly uncertain assumptions necessary to motivate existential risk reduction. However, I couldn't articulate this argument properly before, so it might not be the true source of my discomfort. I'll keep thinking.
I received my first pay-cheque from my first job after getting my degree, so it's time to start tithing. So I've been evalating which charity to donate to. I'd like to support the SIAI but I'm not currently convinced it's the best-value charity in a dollars-per-life sense, once time-value of money discounting is applied. I'd like to discuss the best non-SIAI charity available.
By far the best source of information I've found is www.givewell.org. It was started by two hedge fund managers who were struck by the absence of rational charity evaluations, so decided that this was the most pressing problem they could work on.
Perhaps the clearest, deepest finding from the studies they pull together and discuss is that charity is hard. Spending money doesn't automatically translate to doing good. It's not even enough to have smart people who care and know a lot about the problem think of ideas, and then spend money doing them. There's still a good chance the idea won't work. So we need to be evaluating programs rigorously before we scale them up, and keep evaluating as we scale.
The bad news is that this isn't how charity is usually done. Very few charities make convincing evaluations of their activities public, if they carry them out at all. The good news is that some of the programs that have been evaluated are very, very effective. So choosing a charity rationally is absolutely critical.
Let's say you're interested specifically in HIV/AIDS relief.[1] You could fund a program that mainly distributes Anti-Retroviral Therapy to HIV/AIDS patients, which has been estimated conservatively to cost $1494 per disability adjusted life-year (DALY). Alternatively, you could fund a condom distribution program, which has been estimated conservatively to cost $112 per DALY. Or, you could fund a program to prevent mother-to-child transmission, which has been estimated conservatively to cost $12 per DALY. So even within HIV/AIDS, funding the right program can make your donation two orders of magnitude more effective. By tithing 10% of my income every year for the next thirty years, I could have a bigger impact than a $25 million donation, if the person who placed that donation only did an okay job of choosing a charity.
GiveWell currently gives its top recommendation to VillageReach, a charity that seeks to improve logistics for vaccine delivery to remote communities. The evidence is less cut-and-dried than you'd ideally want, but it's still compelling. They took vaccine rates up to 95%, and had very low stock-out rates for vaccines during the 4 year pilot project in Mozambique. They're estimated to have spent about $200usd per life saved. Even if future projects are two or three times less efficient, you're still saving a life for $600. Think about how little money that is. If you tithe, you can probably expect to save 10 lives a year. That's massive.
Instead of donating directly to VillageReach, I'm going to just donate to GiveWell. They pool the funds they get and distribute them to their top charities, and I trust their analytic, evidence-based, largely utilitarian approach. Mostly, however, I think the work they're doing gathering and distributing information about charities is critically important. If more charities actually competed on evidence of efficacy, the whole endeavour might be a lot different. Does anyone have any better suggestions?
[1] I don't understand why people would want to help sufferers of one disease or condition specifically, instead of picking the lowest-hanging fruit, but apparently they do.