Also the correct footnote statement of the conditions for the LLN result you use with decreasing correlations has pretty strong conditions and your informal statement of it in the main text has trivial counterexamples, e.g. with just one outcome independent from the rest, and the rest all identical as random variables.
For any positive epsilon, you need all but finitely many of the covariances to be less than epsilon in absolute value. This means that it canโt be the case that infinitely many of the outcomes have non-negligible (bounded below in absolute value by epsilon) covariance with any other ourcome. But if we expect non-negligible correlations at all between causally separated outcomes in an infinite universe, I think we should expect non-negligible correlations between infinitely many pairs of them.
Also the correct footnote statement of the conditions for the LLN result you use with decreasing correlations has pretty strong conditions and your informal statement of it in the main text has trivial counterexamples, e.g. with just one outcome independent from the rest, and the rest all identical as random variables.
For any positive epsilon, you need all but finitely many of the covariances to be less than epsilon in absolute value. This means that it canโt be the case that infinitely many of the outcomes have non-negligible (bounded below in absolute value by epsilon) covariance with any other ourcome. But if we expect non-negligible correlations at all between causally separated outcomes in an infinite universe, I think we should expect non-negligible correlations between infinitely many pairs of them.