The value of a QALY n years from now is equal to the value of a QALY now, multiplied by a discount function. An exponential discount function would be of the form (1-r)^n, with 0 < r < 1. This is the same concept as interest rate discounting in economics. There, a payment of $1 per year from now to eternity would be assigned a finite value of $1/r, where r is the interest rate. For example, if the interest is 5%, then $1 per year has the same value as $20 now.
You can apply the same discounting to QALYs, and there are some good reasons both to do so, and to do so with a specifically exponential discounting function. If you fail to do so, then anything that even trivially reduces your odds of living forever is unboundedly bad, which seems odd. Once you have attained probable immortality, you could no longer rationally take any risk whatsoever, even if the payoff is significant. For example, you couldn’t engage in manned interstellar exploration beyond easy reach of the absolute best available medical facilities, even if you were fairly confident of survival and could take a merely excellent hospital with you.
Failing to use an exponential discounting function means that your decision involving risk of death will be subject to akrasia, which hardly seems desirable.
In conclusion, the only question remaining is what discounting rate to use. 5% seems a bit nearsighted. We might compare to life expectancy without counting natural causes, which is something like 400 years. So a discount rate in the range of 0.01% to 0.5% seems plausible.
In order for a 1:3000 risk of true death by someone signed up for a cryonics program with 100% odds of success to make sense, in return for a 10 QALY (certain) life extension of a non-cryonics program person, the discount rate would have to be less than 0.3%. I’m actually rather surprised by this result; when I started writing this post, I expected to conclude that RomeoStevens was being selfish, arrogant, and overly disparaging of the value of people who haven’t signed up for cryonics.
That said, if we take the odds of success of cryonics as less than 100%, the equation changes. It now depends on both RomeoStevens current non-cryonics life expectancy and the odds of success of the cryonics program. If, for example, the cryonics program has odds of success of merely 10%, then at a 0.1% discount rate, the indefinite lifespan is comparable to 100 QALYs at present. That means a risk as high as 10% in exchange for a certain 10 QALYs would be reasonable.
I think I can safely conclude that either RomeoStevens thinks cryonics has a higher chance of working than I do, or that he is using a very small discount rate for long lifespans.
(EDIT: fixed r vs 1-r confusion. A discount rate of 1% implies that a QALY (or $) n years in the future is valued at 0.99^n times its present value. IOW, discount rate r → discount function (1-r)^n. I believe the post now uses all such terms in an internally consistent fashion.)
good stuff, but I was in fact being selfish and arrogant. I should have been more specific and said I’d risk my life to save an AI researcher, upload researcher, or radical life extension researcher whom I feel significantly increases my odds of continuing to exist longer more so than the risk of dying immediately. I would do this even if they weren’t signed up for cryonics, but this seems somewhat unlikely for anyone sufficiently awesome enough to meet my criteria.
Well, one would start with discounting a cryonicsers’s life to infinity to the net present value, and then see how many mayfly lives that translates to...
If you exponentially discount, can’t it make sense?
I’m not sure how to calculate that.
The value of a QALY n years from now is equal to the value of a QALY now, multiplied by a discount function. An exponential discount function would be of the form (1-r)^n, with 0 < r < 1. This is the same concept as interest rate discounting in economics. There, a payment of $1 per year from now to eternity would be assigned a finite value of $1/r, where r is the interest rate. For example, if the interest is 5%, then $1 per year has the same value as $20 now.
You can apply the same discounting to QALYs, and there are some good reasons both to do so, and to do so with a specifically exponential discounting function. If you fail to do so, then anything that even trivially reduces your odds of living forever is unboundedly bad, which seems odd. Once you have attained probable immortality, you could no longer rationally take any risk whatsoever, even if the payoff is significant. For example, you couldn’t engage in manned interstellar exploration beyond easy reach of the absolute best available medical facilities, even if you were fairly confident of survival and could take a merely excellent hospital with you.
Failing to use an exponential discounting function means that your decision involving risk of death will be subject to akrasia, which hardly seems desirable.
In conclusion, the only question remaining is what discounting rate to use. 5% seems a bit nearsighted. We might compare to life expectancy without counting natural causes, which is something like 400 years. So a discount rate in the range of 0.01% to 0.5% seems plausible.
In order for a 1:3000 risk of true death by someone signed up for a cryonics program with 100% odds of success to make sense, in return for a 10 QALY (certain) life extension of a non-cryonics program person, the discount rate would have to be less than 0.3%. I’m actually rather surprised by this result; when I started writing this post, I expected to conclude that RomeoStevens was being selfish, arrogant, and overly disparaging of the value of people who haven’t signed up for cryonics.
That said, if we take the odds of success of cryonics as less than 100%, the equation changes. It now depends on both RomeoStevens current non-cryonics life expectancy and the odds of success of the cryonics program. If, for example, the cryonics program has odds of success of merely 10%, then at a 0.1% discount rate, the indefinite lifespan is comparable to 100 QALYs at present. That means a risk as high as 10% in exchange for a certain 10 QALYs would be reasonable.
I think I can safely conclude that either RomeoStevens thinks cryonics has a higher chance of working than I do, or that he is using a very small discount rate for long lifespans.
(EDIT: fixed r vs 1-r confusion. A discount rate of 1% implies that a QALY (or $) n years in the future is valued at 0.99^n times its present value. IOW, discount rate r → discount function (1-r)^n. I believe the post now uses all such terms in an internally consistent fashion.)
Excellent analysis!
good stuff, but I was in fact being selfish and arrogant. I should have been more specific and said I’d risk my life to save an AI researcher, upload researcher, or radical life extension researcher whom I feel significantly increases my odds of continuing to exist longer more so than the risk of dying immediately. I would do this even if they weren’t signed up for cryonics, but this seems somewhat unlikely for anyone sufficiently awesome enough to meet my criteria.
Well, one would start with discounting a cryonicsers’s life to infinity to the net present value, and then see how many mayfly lives that translates to...