The infinite return argument isn't that great in general. It is especially not great when you are talking to someone who has already decided that they care about the actual probability.
The infinite return rate runs into a lot of problems:
First, someone's utility function may be bounded. There's some decent argument that human utility may be bounded. Note that this is not the same as having only a finite set of preferences. Thus for example, I could for any n, assuming n+1 people exist prefer "n people tortured" to "n+1 people tortured", and still have bounded utility.
Second, even if utility can be unbounded, it isn't clear that you can talk about infinite (rather than arbitrarily large) utilities. In particular, a lot of the standard theorems about utility curves start breaking down. To see the essential problem consider trying to distinguish "I live forever in paradise but first stub my toe" v. "I live forever in paradise." You would need a mathematical framework that distinguishes them and yet you can still do most of your arithmetic. There are such frameworks, such as the surreal numbers, but it isn't at all clear that you can use them to talk about utility in a useful way.
Third, my expected lifespan assuming cryonics works is not infinite. Say there's always a finite fixed probability k greater than zero that I will die on any given day. Then the expected lifespan I will have is finite (working it out is a nice little exercise). And it isn't like there aren't lots of obvious things that could cut off a civilization even if it had the tech level to do nanotech revival or direct uploads. Even with those technologies, a nearby gamma ray burst could still fry everything. And aside from all the possible disaster scenarios, and wars and the like, pretty much nothing you do can deal with the (in my opinion very small) chance that we are in a simulation and the simulators decide to pull the plug.
I've seen reasonable estimates for expected lifespan given cryonics from a few hundred years to the tens of thousand. I don't think we have any really good knowledge base for what the technology will be like to do anything more than an extremely rough guess at this point. But claiming it is infinite seems wrong and claiming that the expected utility is infinite seems to be more wrong.
I agree with your first two points, particularly the first, but the third seems wrong.
...Third, my expected lifespan assuming cryonics works is not infinite. Say there's always a finite fixed probability k greater than zero that I will die on any given day. Then the expected lifespan I will have is finite (working it out is a nice little exercise). And it isn't like there aren't lots of obvious things that could cut off a civilization even if it had the tech level to do nanotech revival or direct uploads. Even with those technologies, a nearby gamma ray bur
If an American signs up for cryonics and pays their ~$300/year, what are their odds of being revived? Talking to people at LessWrong meetups I've heard estimates of 1 in 2. My friend George Dahl, whose opinion I respect a lot, guesses "less than 1 in 10^6". Niether has given me reasons, those numbers are opaque. My estimate of these odds pretty much determines whether I should sign up. I could afford $300/year, and I would if I thought the odds were 1:2, but not if they were 1:10^6. [1]
In order to see how likely this is to work, we should look at the process. I would sign up with a cryonics company and for life insurance. I'd go on living, enjoying my life and the people around me, paying my annual fees, until some point when I died. After death they would drain my blood, replace it with something that doesn't rupture cell walls when it freezes, freeze me in liquid nitrogen, and leave me there for a long time. At some point, probably after the development of nanotechnology, people would revive me, probably as a computer program.
There's a lot of steps there, and it's easy to see ways they could go wrong. [3] Let's consider some cases and try to get probabilities [4]:
Update: the probabilities below are out of date, and only useful for understanding the comments. I've made a spreadsheet listing both my updated probabilities and those for as many other people as I can find: https://docs.google.com/spreadsheet/...
Combined Probability Of Failure: 99.82%
Odds of success: 1 in 567.
If you can think of other ways cryonics might fail, moving probability mass from "other" to something more quantifiable, that would be helpful. If you think my numbers are off for something, please let me know what a better number would be and why. This is not final.
Am I going about this right? Do people here who think it's rational to sign up for cryonics take a "the payoff is really high, so the small probability doesn't matter" view? Am I overly pessimistic about its chances of success?
Note: I originally posted this on my blog, and the version there has a silly javascript calculator for playing with the probabilities.
[1] To figure out what odds I would accept, I think the right approach is to treat this as if I were considering signing up for something certain and see how much I would pay, then see what odds bring this below $300/year. Even at 1:2 odds this is less effective than Village Reach at averting death [2], so this needs to come out of my 'money spent on me' budget. I think $10,000/year is about the most I'd be willing to spend. It's a lot, but not dying would be pretty nice. This means I'd need odds of 1:33 to sign up.
[2] Counter argument: you should care about quality adjusted life years and not deaths averted. Someone revived maybe should expect to have millenia of life at very high quality. This seems less likely to me than just the claim "will be revived". A lot less likely.
[3] In order to deal with independence issues, all my probability guesses are conditional on everything above them not happening. Each of these things must go right, so this works. For example, society collapsing and my cryonics organization going out of business are very much not independent. So the probability assigned to the latter is the chance that society won't collapse, but my organization goes out of business anyway. This means I can just multiply up the subelements to get probabilities for sections, and then multiply up sections to get an overall probability.
[4] This has a lot in common with the Warren formula, which was inspired by the Drake equation. Robin Hanson also has a breakdown. I also found a breakdown on LessWrong that seems really optimistic.
EDIT 2011-09-26: jsalvatier suggested an online spreadsheet, which is very sensible. Created
EDIT 2011-09-27: I've updated my probabilities some, and made the updates on the spreadsheet.