*"The two that bothered me most (and still do) are stroke and death. There are other serious things that can go wrong, but if their effects are temporary, then for me that puts them in a different league from a stroke, which could end my productive life, and death, which would end my life altogether.*

*The risk of death is put at one in a thousand, and this is where things get interesting. How worried should I be about a 0.1% risk? How do I even think about that question? Perhaps if my life expectancy from now on is around 30 years, I should think of this as an expected loss of 30/1000 years, or about 10 days. That doesn’t sound too bad — about as bad as having a particularly nasty attack of flu. But is it right to think about it in terms of expectations? I feel that the distribution is important: I would rather have a guaranteed loss of ten days than a 1/1000 chance of losing 30 years."*

- So how would you reason about this? How would you decide?Nov 5, 2012
- For starters, even if your goal is to maximize expected utility, there's no reason to equate utility with 'lifespan' - unless, of course, your only goal is to live as long as possible.

If your utility is some*nonlinear*function of your lifespan and other variables, the expected value of your utility for a given probability distribution of lifespans is not equal to the utility evaluated at the expected value of your lifespan.

For example, you may value your early years more than your older years, because you can do more things when you're young. In this case, the loss of expected utility caused by a 1% chance of losing 30 years of life will exceed the loss of expected utility caused by a 10% chance of losing 3 years of life... even though the expected loss of lifetime is equal in both cases.

Of course, in reality you also have to 'pay' to take actions that tend to extend your lifespan, so the cost of this should be included.

I haven't read the blog post, so these are just my instant thoughts.Nov 5, 2012 - By the way, this is a perfect example of the kind of scenarios that I would love to see being dissolved by lesswrong.com. I'd love to learn how to rationally handle such real world situations. I wonder how +gwern branwen would reason about this situation.Nov 5, 2012
- +John Baez Not sure how much that matters, but the post was written by Timothy Gowers. There should be some math prowess involved.

It also matters to me because I am personally interested to see such great minds staying alive and healthy for as long as possible.Nov 5, 2012 - Okay, now I read the article. I'm sure the points I made would be obvious to Gowers, and he's made his decision already, so now I'll just wait and hope for him to post another blog article!Nov 5, 2012
- The distribution of utility over your lifetime is an interesting question, but IMO minor compared to the more general question: how should you weigh mortal risks, the grown-up version of 'gambler's ruin'? That's a harder problem since regular exponential discounting and expected utility seem to give strange answers which ought to be easily outperformed like Eliezer's 'lifespan dilemma'.

One approach I've thought about a little is to model dying as 'all possible returns go to zero'. Exponential discounting doesn't handle variations in returns very well, and there's one paper which claims that if you model returns as a random walk and then ask what the optimal discounting strategy is, you get**hyperbolic**discounting instead of exponential! http://www.gwern.net/Sunk%20cost#fn6

So my suggestion is: if on death all available investments go to zero (the dead suffer neither gains nor losses in their portfolio - 'call no man (net) happy until he be dead'), then this is definitely a variation in available returns. With this taken into account, do we get some non-exponential discount rate which combined with estimates of future utility tell us which mortal risks we want to run?Nov 5, 2012