This is indeed what happens to the best-known decision theories (CDT and EDT): they want to commit to paying, but if they don’t, by the time they get to the Heads world they don’t pay. We call this dynamic instability, because different (temporal) versions of the agent seem to be working against each other.
Unless you are using “dynamic stability” to mean something other than “dynamic consistency”, I don’t think this is quite right. The standard philosophical theory of dynamic choice, sophisticated choice (see e.g. the SEP entry on decision theory), would not pay but is still dynamically consistent.
Let me check if I understand what you’re saying (what these standard academic terms mean). “Dynamic inconsistency” is when you make a plan, initially acts according to that plan, but then later fail to follow the plan. (You failed to take into account what you’d later decide to do when making the plan. This is what the “naive” approach does, according to SEP.) “Dynamic consistency” is when you never do this. (The “sophisticated” approach is to take into account what you’d decide to do later when making the initial plan, so dynamic inconsistency never happens. Also called “backwards reasoning” which I think is the same as “backwards induction” which is a term I’m familiar with.[1]) Rest of this comment assumes this is all correct.
I think this is different from what the OP means by “dynamic stability” but perhaps their definition is too vague. (What does “want to commit” mean exactly? Arguably sophisticated choice wants to commit to paying, but also arguably it doesn’t because it knows such commitment is futile.) Here’s a related idea that is maybe clearer: Suppose an agent has the ability to self-modify to use any decision theory, would they decide to stick with their current decision theory? (I’m actually not sure what term has been explicitly defined to mean this, so I’ll just call it “self-endorsement” for now.)
(Partly this is about AI, trying to figure out what decision theory future AIs will or should have, but humans also have some ability to choose what decision theory to use, so it seems interesting from that perspective as well.)
Sophisticated choice seemingly lacks “self-endorsement” because before it’s told how the counterfactual mugger’s coin landed, it would self-modify (if it could) into an agent that would pay the counterfactual mugger in the Heads world. (Lots more can be said about this, but I’ll stop here and give you a chance to clarify, respond, or ask questions.)
Here’s a related idea that is maybe clearer: Suppose an agent has the ability to self-modify to use any decision theory, would they decide to stick with their current decision theory? (I’m actually not sure what term has been explicitly defined to mean this, so I’ll just call it “self-endorsement” for now.)
This sounds similar to what’s called “self-recommendation”—see e.g. Skyrms (1982, pp. 707-709), Meacham (2010, §3.3) and Pettigrew (2023). In the abstract Pettigrew writes: “A decision theory is self-recommending if, when you ask it which decision theory you should use, it considers itself to be among the permissible options.”.
I have actually been thinking about ways of extending Pettigrew’s work to theories of dynamic choice. That is: is sophistication/resoluteness self-recommending? I don’t think it is immediately clear what the answers are, and it might depend on the interpretations of sophistication and resoluteness one adopts, but yeah, I do agree that it seems like sophistication might be self-undermining.
Thank you Sylvester for the academic reference, and Wei for your thoughts!
I do understand from the SEP, like Wei, that sophisticated means “backwards planning”, and resolute means “being able to commit to a policy” (correct me if I’m wrong).
My usage of “dynamic instability” (which might be contrary to academic usage) was indeed what Wei mentions: “not needing commitments”. Or equivalently, I say a decision theory is dynamically stable if itself and its resolute version always act the same.
There are some ways to formalize exactly what I mean by “not needing commitments”, for example see here, page 3, Desiderata 2 (Tiling result), although that definition is pretty in the weeds.
I do understand from the SEP, like Wei, that sophisticated means “backwards planning”, and resolute means “being able to commit to a policy” (correct me if I’m wrong).
That seems roughly correct, but note that there are different interpretations of resolute choice floating around[1], and I think McClennen’s (1990) presentation is somewhat unclear at times. Sometimes resoluteness seems to be about the ability to make internal commitments, and other times it seems to be about being sensitive to the dynamic context in a particular way, and I think these can come apart. You might be interested in these notes I took while reading McClennen’s book.
My usage of “dynamic instability” (which might be contrary to academic usage) was indeed what Wei mentions: “not needing commitments”. Or equivalently, I say a decision theory is dynamically stable if itself and its resolute version always act the same.
Then that sounds a bit question-begging. Do you think dynamic instability is a problem (normatively speaking)?
Unless you are using “dynamic stability” to mean something other than “dynamic consistency”, I don’t think this is quite right. The standard philosophical theory of dynamic choice, sophisticated choice (see e.g. the SEP entry on decision theory), would not pay but is still dynamically consistent.
Let me check if I understand what you’re saying (what these standard academic terms mean). “Dynamic inconsistency” is when you make a plan, initially acts according to that plan, but then later fail to follow the plan. (You failed to take into account what you’d later decide to do when making the plan. This is what the “naive” approach does, according to SEP.) “Dynamic consistency” is when you never do this. (The “sophisticated” approach is to take into account what you’d decide to do later when making the initial plan, so dynamic inconsistency never happens. Also called “backwards reasoning” which I think is the same as “backwards induction” which is a term I’m familiar with.[1]) Rest of this comment assumes this is all correct.
I think this is different from what the OP means by “dynamic stability” but perhaps their definition is too vague. (What does “want to commit” mean exactly? Arguably sophisticated choice wants to commit to paying, but also arguably it doesn’t because it knows such commitment is futile.) Here’s a related idea that is maybe clearer: Suppose an agent has the ability to self-modify to use any decision theory, would they decide to stick with their current decision theory? (I’m actually not sure what term has been explicitly defined to mean this, so I’ll just call it “self-endorsement” for now.)
(Partly this is about AI, trying to figure out what decision theory future AIs will or should have, but humans also have some ability to choose what decision theory to use, so it seems interesting from that perspective as well.)
Sophisticated choice seemingly lacks “self-endorsement” because before it’s told how the counterfactual mugger’s coin landed, it would self-modify (if it could) into an agent that would pay the counterfactual mugger in the Heads world. (Lots more can be said about this, but I’ll stop here and give you a chance to clarify, respond, or ask questions.)
I still remember the first moment that I started to question backwards induction. Things were so much simpler before that!
This sounds similar to what’s called “self-recommendation”—see e.g. Skyrms (1982, pp. 707-709), Meacham (2010, §3.3) and Pettigrew (2023). In the abstract Pettigrew writes: “A decision theory is self-recommending if, when you ask it which decision theory you should use, it considers itself to be among the permissible options.”.
I have actually been thinking about ways of extending Pettigrew’s work to theories of dynamic choice. That is: is sophistication/resoluteness self-recommending? I don’t think it is immediately clear what the answers are, and it might depend on the interpretations of sophistication and resoluteness one adopts, but yeah, I do agree that it seems like sophistication might be self-undermining.
Thank you Sylvester for the academic reference, and Wei for your thoughts!
I do understand from the SEP, like Wei, that sophisticated means “backwards planning”, and resolute means “being able to commit to a policy” (correct me if I’m wrong).
My usage of “dynamic instability” (which might be contrary to academic usage) was indeed what Wei mentions: “not needing commitments”. Or equivalently, I say a decision theory is dynamically stable if itself and its resolute version always act the same.
There are some ways to formalize exactly what I mean by “not needing commitments”, for example see here, page 3, Desiderata 2 (Tiling result), although that definition is pretty in the weeds.
Thanks for the clarification!
That seems roughly correct, but note that there are different interpretations of resolute choice floating around[1], and I think McClennen’s (1990) presentation is somewhat unclear at times. Sometimes resoluteness seems to be about the ability to make internal commitments, and other times it seems to be about being sensitive to the dynamic context in a particular way, and I think these can come apart. You might be interested in these notes I took while reading McClennen’s book.
Then that sounds a bit question-begging. Do you think dynamic instability is a problem (normatively speaking)?
See e.g. Gauthier (1997) and Buchak (2013, §6).