Then every “sufficient-for-policy-implications” statistic can become a “sufficient-for-implications-for-beliefs-about-the-future” statistic, under a coarsening of the sample space by some future-action-preserving and conditional-ratios-of-expected-payoff-differences-preserving equivalence relation?
(Would we expect deliberative thinking and memory to physically approximate such coarsenings, as linear controllers do?)
Then every “sufficient-for-policy-implications” statistic can become a “sufficient-for-implications-for-beliefs-about-the-future” statistic, under a coarsening of the sample space by some future-action-preserving and conditional-ratios-of-expected-payoff-differences-preserving equivalence relation?
(Would we expect deliberative thinking and memory to physically approximate such coarsenings, as linear controllers do?)