All “sufficient” statistics are only “sufficient” for some particular set of policy or epistemic implications. You could always care about the number of 1 bits, if you’re allowed to care about anything.
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?)
All “sufficient” statistics are only “sufficient” for some particular set of policy or epistemic implications. You could always care about the number of 1 bits, if you’re allowed to care about anything.
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?)