Self-sampling vs self-indication

Anthropic probabilities become strange because the evidence includes ‘I exist, and I am this observer.’ Two rules try to say what that evidence means. The Self-Sampling Assumption, SSA, tells you to reason as if you were a random sample from a suitable class of actual observers. The Self-Indication Assumption, SIA, adds that discovering you exist favors hypotheses containing more observers, because there were more chances for someone like you to exist.

The difference is invisible when every hypothesis contains the same number of observers. It becomes decisive when one future has a thousand people and another has a trillion. SSA asks where your rank lies inside each future. SIA first gives the populous future extra prior weight for containing more possible observation slots. In the simplest Doomsday calculation, those two factors cancel exactly.

The two-urn universe

Imagine a fair coin chooses between a small world with ten observers and a large world with a million. You wake without seeing the coin. SSA begins with equal prior odds for the worlds, then notes that your early rank is likelier in the small world. SIA begins by saying your existence was one hundred thousand times likelier if the large world was created, then conditions on your rank. The large world's population advantage cancels the unlikeliness of being early.

Why SSA produces Doomsday

Suppose two human histories were otherwise equally plausible: extinction after 200 billion births, or survival through 200 trillion. Your rank near 117 billion occupies an ordinary position in the short history and an extraordinarily early one in the long. Under SSA, the observation shifts probability toward the shorter history. That is the core of the Doomsday Argument, before confidence intervals and birth rates decorate it.

The conclusion depends on the reference class. Are you sampled from all Homo sapiens, all biological observers, all intelligent minds, or all observer-moments? Future digital populations can dominate some classes. Extraterrestrials can dominate others. SSA does not choose the class; it only tells you how to reason once one has been chosen.

Why SIA cancels it

SIA treats the fact that you exist as evidence for hypotheses that create more observers. A civilization lasting long enough to produce trillions offered more opportunities for your observation than one that ended early. When the hypotheses differ only in population size, this prior boost cancels SSA's penalty for your low rank. Ken Olum used this to argue that the classic Doomsday update disappears.

But SIA has its own notorious cost: the Presumptuous Philosopher. If two cosmological theories fit every observation equally well but one predicts a universe with vastly more observers, SIA can favor it by an enormous factor before any telescope looks. A philosopher in an armchair appears able to decide between physical theories merely by counting predicted people. Supporters call that legitimate Bayesian evidence; critics call it a reductio.

No neutral default

SSA can produce counterintuitive observer-relative probabilities and Doomsday updates. SIA can swamp ordinary physical evidence with population counts, and those counts are usually deeply uncertain. Both also inherit the reference-class problem. Moving from observers to observer-moments changes how long lives and repeated experiences are weighted; including simulated minds changes the population again.

Modern treatments often replace both slogans with fuller Bayesian models: state the hypotheses, the process generating observers, the information available to each observer, and the sampling procedure. That does not make the philosophical choice vanish, but it prevents one line of English from hiding five assumptions. It also reveals cases where SSA is a good approximation and cases where it is not.

What the toy assumes

The Doomsday calculator on this site implements the SSA-style birth-rank likelihood. It does not apply an SIA population bonus, choose among reference classes, or assign priors to future histories. The number it returns is therefore conditional: if you treat your human birth rank as an ordinary draw and hold the other assumptions fixed, here is the bound. The real debate lives in the italicized ‘if.’