Decision-determined was used in the manuscript to mean completely determined (up to a probability distribution) by “decision-type,” and ditto action-determined was used to mean completely determined up to a probability distribution by actions in a causal way. So it’s simple to show that something isn’t decision-determined, in the sense used; you only need one exception, one case where it depends on the algorithm and not just the decision.
Decision-determined was used in the manuscript to mean completely determined (up to a probability distribution) by “decision-type,” and ditto action-determined was used to mean completely determined up to a probability distribution by actions in a causal way. So it’s simple to show that something isn’t decision-determined, in the sense used; you only need one exception, one case where it depends on the algorithm and not just the decision.