Abstract: Four main forms of Doomsday Argument (DA) exist—Gott’s DA, Carter’s DA, Grace’s DA and Universal DA. All four forms use different probabilistic logic to predict that the end of the human civilization will happen unexpectedly soon based on our early location in human history. There are hundreds of publications about the validity of the Doomsday argument. Most of the attempts to disprove the Doomsday Argument have some weak points. As a result, we are uncertain about the validity of DA proofs and rebuttals. In this article, a meta-DA is introduced, which uses the idea of logical uncertainty over the DA’s validity estimated based on a virtual prediction market of the opinions of different scientists. The result is around 0.4 for the validity of some form of DA, and even smaller for “Strong DA”, which predicts the end of the world in the near term. We discuss many examples of the validity of the DA in real life as an instrument to prove it “experimentally”. We also show that DA becomes strongest if it is based on the idea of the “natural reference class” of observers, that is, the observers who know about the DA (i.e. a Self-Referenced DA). Such a DA predicts that there is a high probability of a global catastrophe with human extinction in the 21st century, which aligns with what we already know based on analysis of different technological risks.
Highlights:
· There are four main types of DA: future population prediction (Gott’s DA), Bayesian update of risks (Carter’s DA), the more probable Late Filter (Grace’s DA) and the Universal DA.
· Meta-DA treats logical uncertainty about the predictive power of the DA as a probability that DA will work.
· We used a virtual prediction market of scientists to assess the logical uncertainty of the DA, which produced estimation of around 0.4 of its validity.
· The strongest, and thus most important form of DA is the Self-Referenced DA, and for this class “the end” may be as early as middle of the 21th century, though this is not necessarily human extinction.
· Knowledge about the DA could be used to update our global risks prevention strategies by paying more attention to universal risks or by using random prevention strategies.
I am one of those who feel like the DA is utter BS. To test it further, I’d run a bunch of simulations and see how predictive the past history is of future developments. I don’t know if the simulations or their mathematical equivalents have been done, but here is what I would do:
Take a fixed-length fixed-population-size version, calculate the accuracy of the predictions based on the time of the prediction (it would be the best for those exactly midway-through the run). The rest of the observers would be biased in one of the two directions.
Take a fixed length exponentially growing population that ends abruptly, estimate the remaining future time based on the number of observers and on the growth rate. The unbiased prediction happens at the time of A-ln(2), which is basically at the very end of a run of any duration.
Repeat with: exponential total duration distribution with a given rate, with a variety of linear, exponential and other growth rates, Gaussian distribution with the same, logistic growth rates with all of the above total duration distributions, and anything else that makes sense to try.
My guess would be that the result of these calculations would show that there is absolutely no correlation in general between predictions and actual outcomes, and that the accuracy would vary wildly based on the assumptions, and there is little or no a priori reason to pick one specific distribution over another, except the impetus to speculate based on the lack of information, a natural human trait.
Anyway, the main idea of the article above is not to “prove” DA, but the assumption that DA has probability to be true around 0.5, that is, there is some logical uncertainty about it. As Nancy Leibowitz commented once: Sleeping Beauty should be 5⁄12, if we assume the uncertainty about the correct version.
Similar experiments was done by R.Gott. He had chosen a process of unknown duration which he had observed in a random moment of time, that is, the duration of the Broadway shows. Based on the past duration of a show, he was able to predict future duration.
In your case, let’s assume that there is a population in some planet X, which exists for 100 years and doesn’t know it. Each year they use Gott’s DA to predict their future existence with 90 per cent confidence (equal to the order of magnitude). In that case:
First year predicts extinction in 10 years (false, but already “decades” order of magnitude, which is true)
5 years − 50 years (false)
10 − 100 (true)
50 −500 (true)
90- 900. (true, but too vague)
In other words, Gott’s DA is gives correct predictions about the future age for 90 per cent of inhabitants of the planet X, which is a good result.
However, for the first few days of the planet X existence, the DA prediction will be very wrong, around 10 days (I have a suspicion that it will be so wrong that it will compensate the predictive power of DA if we sum up all predictions multiplied on their expected utility or something like this). But it is very unlikely to appear in such unlikely position.