How macroscopic properties dictate microscopic probabilities

Given that quantum theory is probabilistic, is there a fundamental physical principle that dictates the form of the quantum probability law? We will argue that, indeed, the assigned probabilities for a given test performed on a large sample of identical systems are dictated by the classical-like properties of macroscopic systems. Consider a sample of N identically prepared nonentangled spins in the state uc&. The state of the sample is then