This is the first piece in a series introducing the Parametric Process Assumption (PPA), a new model of anthropics which allows us to resolve very nearly all anthropic paradoxes I am aware of. With the right prior, the PPA rejects both the Doomsday Argument and the Presumptuous Philosopher and can operate seamlessly over both finite and infinite universes.

The motivating idea behind the PPA is that there are really two different ways to interpret a statement like "the probability of X":

The Frequentist approach, where probabilities represent the convergence of random trials. Flip many coins and about half will come up heads.
The Bayesian approach, where probabilities are beliefs. We don't know if the googolth digit of pi is even or odd, so we might as well say there's a 50% chance it's even.

The first interpretation makes more sense for some types of questions, while the second approach makes more sense for others. But it turns out that if you take the standard framing for anthropic problems - where a universe is first produced and then you are assigned an observer identity within it - you will get different answers depending on whether you model the [...]