disclaimer.... I will quote liberally from the wikipedia article "The Doomsday argument (DA)
is a probabilistic argument that says that supposing the 'humans' alive today are in a random place in the whole 'human' history timeline, chances are we are about halfway thought it."
Now this methodology appears to work ok for a number of variables (like the length of time a Broadway show will run). So it has some validity at its face. It takes the form of
"we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born."
One big question is what variable should we use in place of 'human' - if there is not a clear variable to use there the argument looses its force.
the main options seem to be
this changes depending on if life exists elsewhere in the universe - and if it is reasonable to think that it does it gives a very far off doomsday date vastly greater than 8 million.
2) Sentient beings (this is the set of beings able to contemplate the question)
This gives a closer dooms day date than the above but still potentially very distant depending on the probability of aliens. Given the logic we are using it would be reasonable at least to assume every galaxy had at least one sentient being!
this is relevant since we already know we are human and appear to be debating HUMAN extinction. It gives about 95% chance humans become extinct in next 5000 years. However - this depends on the definition of human also if immortality becomes common, and the birth rate drops to zero, dooms day could be pushed to infinity. However what is ‘human extinction? do we include instances of humans becoming Cyborgs?
4) Instants of human existence
This is probably even better than the above since you are 'a human considering this problem at this instant. This may be the best because this is the most clearly defined and well known fact you have. It gives about 95% chance humans die in next 4560 years.
5) Humans who have considered the doomsday argument
this presumably gives a shorter doomsday <4560 yrs
It also creates an interesting debate over if carter (who proposed the idea) should have rejected it by his own logic!
6) Instances of consideration of the doomsday argument
7) Intensity of consciousness (mine)
i.e. you are more likely to be a more conscious person. This implies there are limits on how far we might progress and in a sense is a compliment to our own intelligence (i.e. it is greater odds that we are ‘smart’, or at least more conscious than the mean.
I think this is what the original carter theory used lengthens the date of reckoning by ignoring the increase in population. It gives about 95% chance humans die in next 7.8 million years. However I cant see why a unit of time is a valid unit of measure
9) Probability of atomic destruction
this limits the set to post invention of the bomb populations - this is considerably more arbitrary than time.
We can however also question whether ‘we are missing relevant data. For example
if we apply similar logic to extinctions of a dominant species we can say that this happens less often than once in a million years. Therefore, it is argued that Human extinction is unlikely within the next ten millennia.
This uses time (which seems a little less fundamental than ‘humans’) and adds extra knowledge apparently selectively (e.g. the extinction timeframe) which exposes it to being seen as biased.
One valid counter is that in Doomsday Argument is that the expected total human population is actually infinite. We can combine this with a multi universe model and a touch of the anthropological principle and say that we would probably inhabit the world where there is an infinite number of people as long as there is a finite possibility of there being a infinite number of people.
“One objection is that the possibility of you existing at all depends on how many humans will ever exist (N). If this is a high number, then the possibility of you existing is higher than if only a few humans will ever exist.”
Counter to that is to say ‘well obviously the distribution is not entirely flat – it is just a reasonable assumption over normal numbers’. Which is a nice out.
Some argue "if each finite value of total population size is realized in a different future, then learning of our present position from the beginning of the human race does not change our prior belief about which particular total population size we will find ourselves experiencing in one of humanity's many futures (assuming that versions of us live long enough to see versions of Doomsday)."
But surely it does... because in the many worlds argument all options are not equally probable.
Finally there is the argument “this makes an unwarranted assumption: that humanity's extinction is inevitable.”
But I would be inclined to reject that too on entropy grounds.
Basically there are two extremes on a continum - one is to say "i assume only the most basic information - eg that we exist at a certain time and that we have no reasonh to think we are special" and hte other is to take on as much information as posible. the former results in you ignoring a lot of relevant information but the latter exposes ou to a huge amount of bias. the above uses the former logic.