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That's a very good summary of Caves' argument, thanks for providing it.
EDIT: I upvoted you, but now I see someone else has downvoted you. As with me, no reason was given.
I am new here at LW. I thought it would be a place for rational discussion. Apparently, however, this is not a universally held belief here.
Why is that case "non random"? A randomly selected person could well turn out to be a 1 month old child. If you know in advance that this is not typical, then you already know something about median life expectancy, and that is what you are using to make your estimate, not the age of the selected person.
Do you have a criticism of Caves' detailed mathematical analysis? It seems definitive to me.
And: to the person who keeps downvoting me. Are you treating my "arguments as soldiers", or do you have a rational argument of your own to offer?
For a general analysis along the same lines of life expectancies of various phenomena, see Carl Caves, "Predicting future duration from present age: Revisiting a critical assessment of Gott's rule", http://arxiv.org/abs/0806.3538 . Caves shows (like Dieks) that the original priors are the correct ones. In my example of the biologist and the the bacterium, the biologist is correct.
I've been doing some more reading on DA, and I now believe that the definitive argument against it was given by Dennis Dieks in his 2007 paper "Reasoning about the future: Doom and Beauty". See sections 3 and 4. The paper is available at http://www.jstor.org/stable/27653528 or, in preprint form, at http://www.cl.cam.ac.uk/~rf10/doomrev.pdf Dieks shows that a consistent application of DA, in which you use the argument that you are equally likely to be any human who will ever live, requires you to first adjust the prior for doom that you would have used (knowing that you live now). Then, inserting the adjusted prior into the usual DA formula simply gives back your original prior! Brilliant, and (to me) utterly convincing.
At least some DA proponents claim that there should always be a change in the probability estimate, so I am pleased to see that you agree that there are situations where DA conveys no new information.
OK, let me rephrase the question.
The biologist has never heard of DA. He sets up the initial conditions in such a way that his expectation (based on all his prior knowledge of biology) is that the probability of exponential growth is 50%.
Now the biologist is informed of DA. Should his probability estimate change?
So do you agree with me that, in the experiment I described (a biologist sets up a petri dish with a specific set of initial conditions, and wants to find out if a small bacteria colony will grow exponentially under those conditions), DA logic cannot be applied (by either the biologist or the bacterium) to judge the probable outcome?
I claim that self-sampling plays no essential role in DA logic.
If you think that self-sampling is essential, then you still must allow one of the bacteria in the petri dish to use DA logic about its own future. If you do not allow the biologist to use DA logic, then the bacterium and the biologist will make different predictions about the likely future. One of them must be more accurate than the other (as revealed by future events). If it is the bacterium that is more accurate, what prevents the biologist from adopting the bacterium's reasoning? I argue that nothing prevents it. And since, in the real world, biologists (and scientists of all fields) do not adopt DA logic, I claim that the most compelling reason for this is the invalidity of DA logic from the get-go.
I think it is an excellent idea to try DA logic in other domains.
Example: A a biologist prepares a petri dish with some nutrients, and implants a small colony of bacteria. The question is: will this colony grow exponentially under these conditions? According to DA logic (with a reference class of all bacteria that will ever live in that petri dish), the biologist does not need to bother doing the experiment, since it is very unlikely that the colony will grow exponentially, because then the current bacteria would be atypical.
To the best of my knowledge, this sort of DA logic is never used by scientists to analyze experiments of this sort (or to decide which experiments to perform). I believe this casts severe doubt on the validity of DA.
You must have written the article off-campus while logged into the OSU proxy server. All links are the ones provided by the OSU proxy. This allows you to read subscription-only journals while off campus, but if you copy them, they won't work for anyone else. Salon won't be able to help you.
It does indicate that Salon doesn't proofread or copyedit, which is good to know.