Probabilities without uncertainty in the Everett interpretation of quantum mechanics

Following the work of D. Deutsch, D. Wallace has proposed a derivation of the Born rule in the context of the Everett interpretation. However, it seems to require a genuine uncertainty of the observers, which is difficult to justify in this deterministic framework. H. Greaves proposed another point of view, which does not imply any uncertainty of the observers, but renders the Deutsch-Wallace derivation pointless. I will propose a slightly different framework (without any uncertainty of the observers), which consists in interpreting directly the squared modulus of the amplitudes as proportions of worlds (without supposing that any counting of discrete worlds can be defined); it requires to examine the principles of rationality associated with the notion of proportion of observers in thought experiments involving non-quantum fission of the observers. I will then analyse the role of the Deutsch-Wallace derivation in this framework, which consists in an ordering of the rationality principles in the quantum splitting case (distinguishing the primitive principles from the derived ones).