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.

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?

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?

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.

Probably, not, as he has a lot of information about the subject. DA is helpful in case if you don't have any other information about the subject. Also DA is statistical argument thereby it could not be disproved by counterexample. It is always possible to construct a situation where it will not work. Like some molecules in the air are not moving, despite the fact that median velocity is very high.

It may be used in such problems as bus waiting problem (variant of Laplace sunrise problem). If last bus was 5 minutes ago, want is the probability that it will come in next 1 millisecond, next 5 minutes? next 1 year?

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.

DA should be applied to the situation where we know our position in the set, but do not know any other evidence. Of course if we have another source of information about the set size it could overweight DA-logic. If in this experiment the substrate is designed to support bacterial growth, it have is very strong posteriory evidence for future exponential growth.

But if you put random bacteria on random substrate it most likely will not grow. In this case DA works. DA here says that 1 bacteria most likely will have only several off springs, and it is true for most random bacteria on random substrates.

So, will DA works here or not depends of details of the experiment with you did not provide.

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?

(I did not downvote you)

Look, we could replace "self sampling" with "random". Random bacteria (from all existing bacteria on Earth) will not start exponential growth. Infinitely small subset of all bacteria will start it. There is no difference between prediction of statistic and biologist in this case. DA is statistical argument. It just say that most of random bacteria will not start exponential growth. The same may be true for young civilizations: most of them will not start exponential growth in the universe. But some may be.

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?

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.

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.

Weird, I will talk to Salon people about this.

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.

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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 peopleyou 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

notbe the one provided by the DA.So the examples he should be looking at are

exactlyones 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?*0 points [-]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.