I don't see how this is cheating. Cave's central claim is this (paraphrased rather than quoted): "If you wish to predict how long something will last on the basis of how long it has existed so far, and you have any further information about relevant time scales, then the DA will give bad predictions because it implicitly uses a prior that's invariant under temporal scaling."

He agrees that if you take a thousand random people and proclaim that half of them are in the first halves of their lives, you will probably be about right. But he disagrees with any version of the DA that says that for each of those people you should assign a 0.5 probability that they're in the first half of their life -- because you have some further information about human lifespans that you should be taking into account.

Cases in which the DA is applied usually have vaguer information about relevant timescales; e.g., if you want to predict how long the US will continue to exist as a nation, there are all kinds of relevant facts but none of them quite takes the form "we have a huge sample of nations similar to the US, and here's how their lifetimes were distributed". But usually there are some grounds for thinking some lifetimes more credible than others in advance of discovering how long the thing has lasted so far (e.g., even if you had no idea when the US came into existence you would be pretty surprised to find it lasting less than a week or more than a million years). And, says Caves, in that situation your posterior distribution for the total lifespan (after discovering how long the thing has existed so far) should not be the one provided by the DA.

So the examples he should be looking at are exactly ones where you have some prior information about lifespan; and the divergence between the "correct" posterior and the DA posterior, if Caves is right, should be greatest for examples whose current age is quite different from half the typical lifespan. So how's it cheating to look at such examples?

I know the paper, read it and found a mistake. The mistake is that while illustrating his disproval of DA, he creates special non random case, something like 1 month child for estimation of median life expectancy. It means that he don't understand the main idea of DA logic, that is we should use one random sample to estimate total set size.

Thanks for the link. Does it work on toy models of DA in other domains?

For example, if I ask your age and you will say "30 years old" (guessing), I can conclude from it that medium human life expectancy is around several decades years with 50 per cent confidence, and that it is less than 1000 years with 95 per cent confidence.

Which priors I am using here?

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.

Solution are not only about research if DA is wrong, but about how we should live if it is true.

Personally I think that it is true and the doom is almost inevitable.

We should make some research to prove or disprove DA. The main line of such research would be to try similar to DA logic in other domains, starting from most mundane, like human age, and up to most complex and civilizational level ones.

For example, it is possible to measure size of the Earth using only Copernican mediocracy principle. All we need to know is distance from my birth place to equator, and assumption that human birth places are distributed on randomly distances from equator. I was born 6000 km from equator, and it may be used to conclusion that Earth's radius is around 7000 km which is almost true (real radius is near 6300) Exact calculations here should be more complex, as it must take in account spherical distribution of the observers and will result in bigger (edited) radius.

Weird, I will talk to Salon people about this.