 Solution

Born rule probabilities can be given a coherent role in an Everettian interpretation, but that role cannot simply be the chance that one branch alone will be created. In the many-worlds interpretation, unitary measurement produces all of the decohering outcome components. The question is why their squared amplitudes should govern rational expectation, typical recorded frequencies or concern for future observers.

For a state ${\sum }_i{c}_i|s_i⟩$ and a measuring apparatus, the resulting correlated state has components $c_i|s_i⟩|A_i⟩$. The squared norms $w_i=|c_i{|}^2$ supply additive branch weights. They are preserved by unitary refinements of an outcome into orthogonal subcomponents: if a branch splits internally, its descendants' weights sum to its original weight. Everett's original paper introduces the relative-state description and a measure associated with the statistical analysis; this should not be confused with an independent stochastic collapse law.^[ref]

A simple example shows why counting branches is not an alternative rule without further structure. Begin withIf an irrelevant environment interaction refines B into two orthogonal components of equal amplitude, there are now three displayed components, each of amplitude $1/\sqrt{3}$. The total weight of B is still $2/3$. Counting displayed components instead changes A's assigned share from $1/2$ to $1/3$, merely because the description has resolved additional environmental detail. Real decoherent branching is approximate and has no unique fundamental branch count. Squared norm, in contrast, respects such refinements.

There are at least two ways to understand the remaining epistemic issue. An observer may have self-locating uncertainty in Everettian quantum mechanics, especially after branching but before accessing a record: the uncertainty concerns which centred observer situation is theirs, not ignorance of the global wave function. Alternatively, a decision-theoretic account can ask how a present observer should value all future successors without assuming that exactly one successor is uniquely them. These are distinct proposals, and the second does not become incoherent simply because the first is disputed.

David Wallace's decision-theoretic programme argues that suitable rationality and measurement-equivalence assumptions lead to expected-utility weights equal to squared amplitudes. The assumptions, including the appropriate neutrality of the measurement implementation, do real work.^[ref] A critic can question whether the constraints already privilege the desired measure or whether a preference theorem establishes the empirical role of chance. The defender must answer those objections; unitarity and normalization alone do not automatically turn a deterministic global theory into ordinary single-outcome randomness.

Repeated experiments add a consistency check. With Born weights, the total weight of frequency records is binomial and concentrates near the Born frequency as the number of trials increases. Yet calling the high-weight records typical already uses a measure, so this is not by itself a noncircular derivation of the weighting rule. The balanced conclusion is that Born probabilities are not meaningless in Everettian quantum mechanics: they can organize credence, decisions and typical records. Their status requires an argued connection between branch weights and those roles, rather than a bare appeal either to all outcomes happening or to the algebraic identity ${\sum }_i|c_i{|}^2=1$.