Branch weight ($w_i=\Vert {\Psi }_i{\Vert }^2$)

For an orthogonal decomposition $\Psi ={\sum }_i{\Psi }_i$, the squared norms add to the total norm. Refining one component into orthogonal subcomponents preserves its total weight by the Pythagorean theorem. In an Everettian account these weights are candidates for governing probabilities, rational credences or decisions; the algebra alone does not select which interpretive role is justified. Counting arbitrarily refined components is not the same measure.^[ref]