I just read it. It does not answer the question.
Mixtures are quite natural for quantum statistical mechanics.
The problem I have with John's version is that it gives the impression that, in a game of roulette, the players influence the outcome i.e. they should not peek when the ball rolls. The solution is minimize all human interference and to automate this game. However I doubt if that is so much of a problem. IMO this is impossible. A general problem which each measurement is that always during the measurement, what you want to measure is disturbed.