The point about "adding more information" making the reference class more complex (and hence less plausible) is spot on. However, the interesting thing here is that counting person-years of observations actually uses strictly less information than counting births of observers.

To count person-years of observations, we just have to integrate population through time, and this simply requires information about population sizes at various stages of history. Whereas to count births, we also have to guess at the birth-rate per 1000 people as well as the population size, and integrate the product of population and birth-rate over time. See Carl Haub's article on this.

This is why, for instance, there is variation in the literature on the birth rank assumed for us right now; in Leslie's and Bostrom's papers, a birth rank of about 60 billion is assumed, whereas more recent estimates give a birth rank of about 100 billion. Even earlier estimates were for a birth rank of about 20-30 billion. We really don't know our own birth rank very well.

Correct - we can't predict that we are exactly in the middle of human observational history, only roughly in the middle. This is why the prediction from the random observation model is ~200 years, with the ~ representing a range of variation around the central estimate.

Giving formal confidence intervals (like Gott does) seems a bit of a stretch in my view, since the bounds of these then become acutely sensitive to the prior distribution. Under the "vague" prior over total person-years of observations, and with a 90% confidence interval, we could predict between 100 billion and 40 trillion of person-years to come.

The very simplest population model is an exponential growth pattern, which flattens out at a maximum when the population overshoots its planet's resources, and then drops vertically downward. That fits our current observations, since almost all observations will be made at or near the maximum. (Notice that human population is no longer growing exponentially, since percentage birth rates are falling dramatically almost everywhere. Recently, our growth is quite linear, with roughly equal periods going from 4-5 then 5-6 and 6-7 billion, and by a number of measures we are now in overshoot).

To make this model generic, assume that a generic planet supporting observers has a mixture of renewable and non-renewable resources. At some stage, the observers work out how to exploit the non-renewable resources and their population explodes. Use of the non-renewables allows the death-rate to fall and the population to grow far beyond a point where it can be sustained by the renewables alone; then as the non-renewable resources become exhausted, population plummets down again.

These dynamics arise out of a really simple population model, such as the Lotka-Volterra equation (a predator-prey model); the application to non-renewable resources is to treat them as the "prey" but then set the growth rate of the prey to zero. There are also plenty of real-life examples, such as yeast growing in a vat of sugar, where the population crashes as a result both of exhausting the non-renewable sugar in the vat, and the yeast polluting themselves with the waste product, alcohol. (This seems disturbingly like human behaviour to be honest: compare fossil fuels = sugar; co2 emissions = alcohol.)

Now I agree that other population models would fit as well. A demographic transition model whereby birth-rate falls below death-rate everywhere will lead to exponential behaviour on either side of the peak (exponential up, peak, exponential down) and a concentration of observations at the peak. One thing that's suspicious about this model though is understanding why it would apply generically across civilisations of observers, or even generically to all parts of human civilisation. If only a few sub-populations don't transition, but keep growing, then they quickly arrest the exponential decline, and push numbers up again. So I don't see this model as being very plausible to be honest.

It's also worth noting that a number of population models really don't fit under the reference class of all observations, assuming our current observations are random with respecr to that class. Here are a few which don't fit:

1. Populations of civilisations keep growing exponentially beyond planetary limits, as a result of really advanced technology (ultimately space travel). Population goes up into the trillions, and ultimately trillions of trillions. Our current observations are then very atypical.

2. Most civilisations follow a growth -> peak -> collapse model, but a small minority escape their planetary bounds and keep growing. The difficulty here is that almost all observations will be in the "big" civilisations which manage to expand hugely beyond their planet, whereas ours are not, so they are still atypical observations. Ken Olum made this point first (I think).

3. Long peak/plateau. Civilisations generally stabilise after the exponential growth phase, and maintain a "high" population for multiple generations. For instance ~10 billion for more than ~1000 years. Here the problem is that most observations will be made on the long plateau, well after the growth phase has ended, which makes our own observations atypical.

4. Decline arrested; long plateau. Here we imagine population dropping down somewhat, and then stabilising say at ~1 billion for more than ~10000 years. Again the difficulty is that with a long plateau, most observations are made on the plateau, rather than near the peak. Finally, it's a bit difficult to see how population could stabilise for so long; you'd have to somehow rule-out the civilisation ever creating space settlements while it's on the plateau (since these could then expand in numbers again). Perhaps it is just impossible to get the first settlements going at that stage in a civilisation's history (can't do it after the non-renewable resources have all gone).

Another issue... Yes restricting the reference class to people who are discussing the DA is possible, which would imply that humans will stop discussing the DA soon... not necessarily that we will die out soon. This is one of the ways of escaping from a doomish conclusion.

Except when you then think "Hmm, but then why does the DA class disappear soon?" If the human race survives for even a medium-long period, then people will return to it from time to time over the next centuries/millennia (e.g. it could be part of a background course on how not to apply Bayes's theorem) in which case we look like atypically early members of the DA class right now.. Or even if humanity struggles on a few more decades, then collapses this century, we look like atypically early members of the DA class right now (I'd expect a lot of attention to the DA when it becomes clear to the world that we're about to collapse).

Finally, the DA reference class is more complicated than the wider reference class of all observations, since there is more built into its definition. Since, it is more complex and has less predictive power (it doesn't predict we'd be this early in the class) it looks like the incorrect reference class for us to use right now.

Maybe we should use not adult observers but observers who know and could understand probability theory.

You can't just set the observer class to whatever you want. You get different answers. You have to use the class of every possible observer. I can explain this mathematically if you wish, but I don't have time right now.

Actually, I think it is more like the charge of subjectivism in Bayesian theory, and for similar reasons.

If we take a Bayesian model, then we have to consider a wide range of hypotheses for what our reference class could be (all observers, all observations, all human observers, all human observations, all observations by observers aware of Bayes's theorem, all observers aware of the DA). We should then apply a prior probability to each reference class (on general grounds of simplicity, economy, overall reasonableness or whatever) as well a a prior probability to each hypothesis about population models (how observer numbers change over time; total number of observers or total integrated observer experiences over time). Then we churn through Bayes' theorem using our actual observations, and see what drops out.

My point in the post is that a pretty simple reference class (all observations) combined with a pretty simple population model (exponential growth -> short peak -> collapse) seems to do the job. It predicts what we observe now very well.