The broad categories of causal/evidential/logical are definitely right in terms of what people generally talk about, but it is important to keep in mind that these are clusters rather than fully formalized options. There are many different formalizations of causal counterfactuals, which may have significantly different consequences. Though, around here, people think of Pearlian causality almost exclusively.
“Evidential” means basically one thing, but we can differentiate between what happens in different theories of uncertainty. Obviously, Bayesianism is popular in these parts, but we also might be talking about evidential reasoning in a logically uncertain framework, like logical induction.
Logical counterfactuals are wide open, since there’s no accepted account of what exactly they are. Though, modal DT is a concrete proposal which is often discussed.
Again, the causal/evidential/logical split seems good for capturing how people mostly talk about things here, but internally I think of it more as two dimensions: causal/evidential and logical/not. Logical counterfactuals are more or less the “causal and logical” option, conveying intuitions of there being some kind of “logical causality” which tells you how to take counterfactuals.
Also, getting into nitpicks: some might say “evidential” is the non-counterfactual option. A broader term which could be used is “conditional”, with counterfactual conditionals (aka subjunctive conditionals) being a subtype. I think evidential conditionals would fall under “indicative conditional” as opposed to “counterfactual conditional”. Academic philosophers might also nitpick that logical counterfactuals are not counterfactuals. “Counterfactual” in academic philosophy usually does not include the possibility of counterfacting on logical impossibilities; “counterlogical” is used when logical impossibilities are being considered. Posts on this forum usually ignore all the nitpics in this paragraph, and I’m not sure I’m even capturing the language of academic decision theorists accurately—just attempting to mention some distinctions I’ve encountered.
Other Dimensions:
You’re right that reflective consistency is something which is supposed to emerge (or not emerge) from the specification of the decision theory. If there were a ‘reflective consistency’ option, we would want to just set it to ‘yes’; but unfortunately, things are not so easy.
Another source of variation, related to your ‘graphical models’ point, could broadly be called choice of formalism. A decision problem could be given as an extensive-form game, a causal Bayes net, a program (probabilistic or deterministic), a logical theory (with some choices about how actions, utilities, etc get represented, whether causality needs to be specified, and so on), or many other possibilities.
This is critical; new formalisms such as reflective oracles may allow us to accomplish new things, illuminate problems which were previously murky, make distinctions between things which were previously being conflated, and so on. However, the high-level clusters like CDT, EDT, FDT, and UDT do not specify formalism—they are more general ideas, which can be formalized in multiple ways.
Various comments, written while reading:
The broad categories of causal/evidential/logical are definitely right in terms of what people generally talk about, but it is important to keep in mind that these are clusters rather than fully formalized options. There are many different formalizations of causal counterfactuals, which may have significantly different consequences. Though, around here, people think of Pearlian causality almost exclusively.
“Evidential” means basically one thing, but we can differentiate between what happens in different theories of uncertainty. Obviously, Bayesianism is popular in these parts, but we also might be talking about evidential reasoning in a logically uncertain framework, like logical induction.
Logical counterfactuals are wide open, since there’s no accepted account of what exactly they are. Though, modal DT is a concrete proposal which is often discussed.
Again, the causal/evidential/logical split seems good for capturing how people mostly talk about things here, but internally I think of it more as two dimensions: causal/evidential and logical/not. Logical counterfactuals are more or less the “causal and logical” option, conveying intuitions of there being some kind of “logical causality” which tells you how to take counterfactuals.
Also, getting into nitpicks: some might say “evidential” is the non-counterfactual option. A broader term which could be used is “conditional”, with counterfactual conditionals (aka subjunctive conditionals) being a subtype. I think evidential conditionals would fall under “indicative conditional” as opposed to “counterfactual conditional”. Academic philosophers might also nitpick that logical counterfactuals are not counterfactuals. “Counterfactual” in academic philosophy usually does not include the possibility of counterfacting on logical impossibilities; “counterlogical” is used when logical impossibilities are being considered. Posts on this forum usually ignore all the nitpics in this paragraph, and I’m not sure I’m even capturing the language of academic decision theorists accurately—just attempting to mention some distinctions I’ve encountered.
Other Dimensions:
You’re right that reflective consistency is something which is supposed to emerge (or not emerge) from the specification of the decision theory. If there were a ‘reflective consistency’ option, we would want to just set it to ‘yes’; but unfortunately, things are not so easy.
Another source of variation, related to your ‘graphical models’ point, could broadly be called choice of formalism. A decision problem could be given as an extensive-form game, a causal Bayes net, a program (probabilistic or deterministic), a logical theory (with some choices about how actions, utilities, etc get represented, whether causality needs to be specified, and so on), or many other possibilities.
This is critical; new formalisms such as reflective oracles may allow us to accomplish new things, illuminate problems which were previously murky, make distinctions between things which were previously being conflated, and so on. However, the high-level clusters like CDT, EDT, FDT, and UDT do not specify formalism—they are more general ideas, which can be formalized in multiple ways.