C.28:4.10 - Causal action policy class
Use CausalActionPolicyClass only when the action-selection regime changes the causal question. Identify the decision variables, horizon and natural mechanism; say whether the question compares one specified rule or an admissible family. Keep that rule or family with the question. When both behavior and evaluation policies occur, identify which one the field summarizes.
The mechanism distinctions follow Maiti and Bareinboim, Sequential Causal Games, Definitions 2.3, 2.5, 2.7–2.8. Let X° be the natural action and Z the allowed pre-action information. Order actions causally; Z excludes descendants of the current or later action variables.
| Value | Operative distinction |
|---|---|
naturalBehaviorPolicy | Leave the natural action mechanism in place. |
interventionalPolicy | Replace it by a rule X = g(Z), including a fixed action or declared randomized rule. The current natural proposal is not an additional input. |
counterfactualPolicy | Permit a replacement X = g(Z, X°) after observing the natural proposal. This family includes the identity and natural-proposal-independent special cases. |
mixedPolicy | Use a declared combination of natural and interventional choices, corresponding to the available-class union in Definition 2.8. State the component choices and their selection rule or distribution. |
For this interface, when a concrete rule is represented in the wider counterfactual family, record its simpler natural or interventional case when that reduction holds throughout the stated scope. Keep mixedPolicy when the specified combination matters. If selection itself requires the current natural proposal, expose that counterfactual dependence. For a family comparison, retain the declared available family and any restrictions. Thus the scalar is an informative summary of the supplied rule or family, not a disjoint ontology of policies.
Authored three-rule replay. For binary X°, compare:
| Rule | Outputs for X° = 0, 1 | Concrete classification |
|---|---|---|
| Follow the natural action | 0, 1 | naturalBehaviorPolicy |
| Replace it by zero | 0, 0 | interventionalPolicy |
Replace it by 1 - X° | 1, 0 | counterfactualPolicy |
The last evaluation needs the natural proposal and its relation to outcomes; a fixed-action evaluation does not answer it. A mixed example chooses with equal probability, using an independent coin, between following the natural mechanism and replacing its action by zero. Retain both component choices and their probabilities.
unknown records unresolved classification, not another member. Omit the field when it changes no support, comparison or receiving decision.