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Hi Nathan,
Thanks for your further comments. It’s now clearer to me what your concerns are. And yes, I think you’ve summarised the situation correctly. In particular, for an ensemble, the distribution of final states in my model is simply assumed to satisfy the Born rule. I see this as a separate issue to be solved for most, if not all models including mine. And yes, you’re also correct that feeding in a “wrong” choice for the initial (hidden) position distribution in my model won’t necessarily lead to “wrong” statistics at a subsequent measurement if the distribution of final states is still the “right” one as given by the Born rule.
Concerning this rule, if you have a way of deriving it I’d be interested to see your method. In particular, I haven’t seen either the toy model or the comparison table which you’ve mentioned, so please let me know where to look.
Also, just in case you’re interested, I should mention that I proposed a way of deriving the Born rule some years ago in a paper published in Foundations of Physics Letters 13, 379 (2000). Any such derivation requires the introduction of extra structure though.
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