The result of calculation of the state of observer is linear evolution: the state of observer splits and entangles with the observed state and each part observes the respective outcome. Ironically Copenhagen gave the same result for Schrodinger's cat experiment: even before measurement it's known what states are in superposition and those states are "dead" and "alive", and it's still known without measurement too.

>that the number of observers that observe one outcome is proportional to the wave function amplitude of that outcome

If you mean the number, the norm of each state of observer that observes the respective outcome can be calculated. The statistics over the outcomes can be calculated too.