Can Self-Locating Probability Select the Physical World?
1. Start from Bostrom's own mature position
It is misleading to identify Bostrom's mature view with a simple SSA that directly yields the Doomsday Argument. In the later part of Anthropic Bias, SSA is treated as provisional and reformulated through the Strong Self-Sampling Assumption (SSSA), observer-moments, observer-moment-relative reference classes, and the Observation Equation.
At the same time, Bostrom does not adopt SIA as the way to cancel the Doomsday Argument. He rejects SIA while also treating the simple Doomsday Argument as inconclusive and dependent on further applicability conditions.
The issue here is therefore not that Bostrom overlooked the reference-class problem. It is the further question that remains after that problem has already been recognized: what epistemically licenses a nontrivial reference class?
2. An observer-moment is not the epistemic minimum
A Bostromian observer-moment is a short temporal segment of an observer. This already presupposes that observers exist, that they can be divided temporally, that multiple possible observer-moments exist across possible worlds, and that these moments can be compared and classified.
This differs from this site's epistemic minimum. At the minimal layer, “observer,” “temporal segment,” and “other possible observer-moments” are not treated as primitives. The thinnest candidate is only that something is presently appearing.
Temporal shortness is therefore not the same as epistemic thinness. Observer-moments may be momentary, but they still belong to an inferential layer.
3. Bostrom's R⁰ is not this project's minimal foundation
Bostrom considers a minimal reference class R⁰ consisting of possible observer-moments that are subjectively indistinguishable from the present observer-moment. R⁰ need not be a singleton, and it already presupposes possible worlds, observer-moments, and a relation of subjective indistinguishability.
Bostrom then rejects R⁰ because it is too weak to support ordinary scientific discrimination in Big World cases involving normal and freak observers. He therefore moves toward broader classes of “relevantly similar” observer-moments.
So the phenomenon that an overly narrow reference class weakens scientific inference is not novel to this project. Bostrom already recognizes it.
4. The additional question is one step further
The remaining question is what justifies moving from R⁰ to a broader reference class.
Categories such as “human,” “same kind of cognitive subject,” “similar information-processing capacity,” or “relevantly similar observer-moments” depend on substantive assumptions about physics, cognition, subjecthood, causal structure, evolutionary history, or simulation.
Thus, the more scientifically useful the reference class becomes, the more it inherits structure from an already inferred world model.
This is not automatically viciously circular. One can include the reference class and observer measure explicitly inside a Bayesian model. But then SSSA is not a foundational principle that independently selects the physical world; it is an observation-selection layer connecting a world model to evidence.
5. At the epistemic minimum, the self-location problem is not yet defined
An earlier version of this page said that reducing the reference class to the minimum yields singleton sampling and therefore no information. The more precise claim stops one step earlier.
At the epistemic minimum, there is not yet an observer population in which one can ask “which observer am I?” The self-location problem becomes well-defined only after an inferential layer containing other subjects, time, observer identity, and possible worlds has been constructed.
So this project does not reject anthropic reasoning. It places it one epistemic level above the foundation.
6. Self-locating evidence can update non-indexical hypotheses
This page does not deny that indexical evidence can bear on non-indexical world hypotheses. A central aim of Bostrom's framework is precisely to explain how such updates can occur.
The issue is instead which self-location likelihood should be used. That likelihood depends on a set of observer-moments, a reference class, and a measure. It may therefore be more transparent to think not merely in terms of P(H | E), but of P(H,M | E), where M contains the observer measure and reference-class rule.
7. The absence of a physical lottery is not a refutation
SSA and SSSA do not claim that the universe literally ran a randomizer and selected “you.” Epistemic probabilities over self-location can in principle be meaningful without a physical lottery.
The stronger and more accurate point is that ordinary causal dynamics may not uniquely determine a self-location likelihood. Even after a physical hypothesis specifies which world is generated, an additional rule may still be needed for how observer-moments inside that world are weighted as candidate self-locations.
Where a selection mechanism is physically or institutionally explicit—survey sampling, telescope detection limits, medical selection bias—ordinary statistical modeling applies without any special anthropic mystery.
8. In simulation hypotheses, “who gets generated” becomes part of M
Simulation hypotheses make this point concrete. A hypothesis in which an entire world is simulated through physical dynamics and a hypothesis in which one or a few viewpoint subjects are selected and only the environment needed for those subjects is generated may both be called “simulation,” but they contain different observation-selection structures.
In a world simulation, individual observers arise within a history unfolded from initial conditions and physical laws. No further step that selects “this person” as the viewpoint subject is required. In a viewpoint-centered simulation, by contrast, we need a distribution such as Q(i | purpose) describing which persons the simulator chooses to instantiate as targets.
This difference enters the self-location likelihood directly. If future simulators replay historically important people, unusually informative subjects, or participants in particular events at much higher rates than ordinary people, then Q(i) is not uniform over humanity. In that case, the evidence that “I exist as this person” could update not only the probability of being simulated, but also the probability that a person like me receives high weight under the simulator's selection function.
That does not by itself justify the conclusion “I must be important.” The crucial question is how independently constrained the selection function Q is. If Q is nearly unconstrained, one can always invent a convenient reason after observing the subject, and the model loses predictive force.
This illustrates that the selection model M is not merely a technical correction. The further computational economizing pushes a hypothesis from full physical simulation toward observer-centered simulation, the more the Simulation Argument shifts from an observer-counting argument toward an observer-selection-model argument. At that point, counting observers alone no longer determines a self-location probability; M must specify who is generated, how often, and for what purpose.
9. SIA is an alternative, but not Bostrom's solution
SIA rewards hypotheses containing more observers, roughly in the direction PSIA(H) ∝ N · P(H). In simple finite models, this can cancel the 1/N-style effect associated with SSA and thereby cancel a Doomsday update.
But Bostrom does not adopt this solution. Bostrom and Ćirković reject SIA while also denying that the Doomsday Argument is thereby vindicated.
So the more accurate summary is: Bostrom reconstructs the theory around SSSA and observer-relative reference classes, rejects SIA, and rejects the universal force of the simple Doomsday Argument.
10. How to place the Doomsday Argument
The Doomsday Argument is a useful stress test because its conclusion changes sharply with the self-location likelihood. Treating birth rank as strong evidence about humanity's total population requires an additional account of what observer population and measure one is sampled from.
Unless that structure is independently well justified, this project does not treat birth rank alone as strong new physical evidence about humanity's extinction time or final population.
This does not make the argument meaningless. It makes it a vivid demonstration of reference-class and measure sensitivity.
11. FNC as one route around reference classes
Radford Neal's Full Non-indexical Conditioning conditions on one's full available evidence, including concrete memories, rather than beginning with a selected reference class and the bare fact of being an observer. This is relatively close to the present project's preference for ordinary world inference from total evidence.
Still, FNC is not assumed to be final. The causal provenance of memory and self-models remains inferential, and infinite-world duplication and measure problems may persist.
12. Provisional epistemic hierarchy
- Epistemic minimum: something is presently appearing.
- Ordinary world inference: infer an external world, time, other minds, persisting subjects, and causal structure.
- Observer model: define what counts as an observer and how observer-moments are individuated.
- Observation-selection layer: specify a reference class, observer measure, and self-location likelihood.
- Anthropic update: use self-locating evidence to update non-indexical world hypotheses.
This ordering preserves anthropic reasoning while making its additional assumptions visible.
13. Implication for the Core
The main point is no longer merely that a minimal reference class becomes uninformative. Bostrom already recognizes much of that problem in his rejection of R⁰.
The deeper question is: once R⁰ is rejected, what licenses the move to a scientifically useful class of “relevantly similar” observer-moments?
From the standpoint of epistemic minimalism, the answer is not found at the foundation. Reference classes are constructed on top of inferred claims about the physical world, subjects, time, and causation. SSSA may therefore be a powerful auxiliary theory, but it is not an independent route from the epistemic minimum to the physical structure of the world.
Before using self-locating probabilities, make explicit what is being counted as a candidate self-location and where that ontology comes from.
Sources / notes
Nick Bostrom, Anthropic Bias, Chapter 10: the provisional status of SSA, SSSA, observer-relative reference classes, R⁰, and the Observation Equation. Nick Bostrom & Milan M. Ćirković, “The Doomsday Argument and the Self-Indication Assumption: Reply to Olum”: rejection of SIA without endorsing the Doomsday Argument. Bostrom, “Existential Risk Prevention as Global Priority”: distinction between the theoretical argument and its applicability to humanity. Radford M. Neal, “Puzzles of Anthropic Reasoning Resolved Using Full Non-indexical Conditioning”. The epistemic hierarchy, the further question about the justification of broader reference classes, and the simulation selection-model stress test are additions from this project's epistemic minimalism.