SIA doomsday

It's a tough job, but someone has to do it :P

Imagine these cosmic civilizations of different sizes exist in parallel universes. Then you are more likely to exist in the universe with many humans than with few. This exactly compensates for the effect you describe.

More pictorially: there are two parallel universes (think of them as different planets). In one, Mitchell Porter lives and nobody else. In the other, Mitchell Porter lives along with a billion other people.

But from your perspective, these other people are irrelevant: what you care about is that there are two Mitchell Porters, one in each universe/planet. So you should feel that it's equally likely that you are in either universe.

The situation may be a priori unlikely, but I don't think it's at all presumptuous to argue that the amount of evidence available to us is enough to shift the likelihood upwards dramatically.

The Doomsday Argument applies to any population of any species, ever. I think it's pretty reasonable to say that humans are in a pretty exceptional position out of the set of all known species.

Here's an idea, based on Quantum Mechanics, by someone who hardly knows any Quantum Mechanics at all -- therefore it's probably complete nonsense. (If it's not nonsense, feel free to name said solution after me. :-)

Doesn't the amplitude of a configuration need to be squared in order to figure out the probability of its observation? And also don't configurations tend to split more than merge? So doesn't that mean that if an amplitude-10 configuration splits to two amplitude-5 configurations, the relative probability of the first configuration is 10^2=100 compared to 5^2 + 5^2=50?

So, to put it differently, don't earlier instances have a greater probability of observation than later instances?

So long as we have imprecise measurements and only a finite amount of matter and energy then time is not an issue because we eventually run out of unique (or distinguishable by any of our measurements) humans that can exist and we can just ask the nearly equivalent question: "what is the probability that I am in the last 95% of unique humans to ever exist?" At some point every possible human has been created and out of that huge finite number each one of us is an index. The question is whether the heat death stops the creation of humans in this universe before 20 times the current number of humans has been created (for the 95% argument).

However, the statement of the problem completely ignores prior probabilities. For instance it's possible that we now have more than 5% of the total human population alive right now (that would be true if only 100 billion have ever lived). That would mean that the oldest people alive right now have a 0 probability of being in the last 95%. Additionally, we have a very good idea of whether we are in the last 99.9999999% of humans who have ever lived; the last 7 babies baby born on Earth have a slightly positive probability, everyone else has a 0 probability. What is the probability that 7 more babies will be born, replacing the current 7 who have the possibility of being the last? 1 for all practical purposes. 100 babies? Same. In fact it probably already happened while I was writing this comment. A billion? Probably still very, very close to 1. The calculation can be extended into the future based on our knowledge of our environment and society and the probability of existential risk. Unless we have a good reason for predicting the destruction of all humans we shouldn't predict that we are in the last 95% of unique humans. Humans are built to reproduce, they have an environment that will probably last thousands if not hundreds of thousands of years, and they are learning to build their own environments anywhere they want. These facts are far more important than which particular brain is randomly selected to think of the doomsday argument.

EDIT: The part about the last 95% of humans is wrong if there are more than 5% still alive; it would have to be some of the first 5% still alive for the argument to be wrong for them today.

SSA Doomsday: You are the hundred billionth human who ever lived (or something like that). If there are two hundred billion humans total, this is not very unusual. But if there are to be a quadrillion humans, you would be in a very unlikely situation, in the first 0.0...% or something.

Analogous argument: you're told that you're the smartest person in your extended family. This makes it more likely your extended family is small, rather than large. Replace "smartest" with any property that distinguishes you from the rest of humanity, and the argument follows.