Entanglement Symmetry, Amplitudes, and Probabilities: Inverting Born's   Rule
  Symmetry of entangled states under a swap of outcomes ("envariance") implies their equiprobability, and leads to Born's rule. Here I show that the amplitude of a state given by a superposition of sequences of events that share same total count (e.g., n detections of 0 and m of 1 in a spin 1/2 measurement) is proportional to the square root of the fraction - square root of the relative frequency - of all the equiprobable sequences of 0's and 1's with that n and m. 
Wojciech H. Zurek
quant-ph cond-mat.stat-mech math-ph math.MP