 This postulate (named the Born-Vaidman rule by Tappenden 2011) is a counterpart of the collapse postulate of the standard quantum mechanics according to which, after a measurement, the quantum state collapses to a particular branch with probability proportional to its squared amplitude. (See the section on the measurement problem in the entry on  philosophical issues in quantum theory.)  However, it differs in two aspects. First, it parallels only the second part of the collapse postulate, the Born Rule, and second, it is related only to part (ii) of the MWI, the connection to our experience, and not to the mathematical part of the theory (i).