Vanessa Kosoy's Shortform

Vanessa Kosoy

This is a special post for quick takes by Vanessa Kosoy. Only they can create top-level comments. Comments here also appear on the Quick Takes page and All Posts page.

Master post for ideas about infra-Bayesianism.

The anti-Newcomb problem is a puzzle proposed by LessWrong user @drnickbone as a challenge to UDT. I rediscovered it in 2015 and gave it a name. Recently, Richard Ngo mentioned a reminiscent but actually pretty different puzzle called "Newcomb's revenge". All of those are cases in which CDT apparently outperforms FDT.

Of course, one can always construct a decision problem that diagonalizes against any given decision theory. The interesting question is defining a natural class of "fair" problems for which a given decision theory is optimal. One can then argu... (read more)

2Vanessa Kosoy7mo

Above, I compare different decision theories to FDT. At the same time, I claim that in a deeper sense, FDT is ill-defined. One may doubt whether that is a coherent line of reasoning. Therefore, instead of a comparison to FDT, I propose to frame these observations as being about stability to precommitments. Details follow. Definition: A precommitment game is a decision problem in which 1. We are given some (the precommitment policies). We will denote . 2. We are given : for each precommitment , it says to which policy this is precomitting. 3. For any , if then : if a precommitting decision is made, then it is the only decision. 4. Denote , . (Notice that .) We are given a relation s.t. (i) implies and (ii) and implies . This tells us which precommitted outcomes correspond to which unprecomitted outcomes. The restriction of to is called the underlying decision problem of . Definition: An EDT precommitment game is a precommitment game which is also an EDT problem (i.e. extensive form and equipped with ) s.t. the following property holds. Denote (the "external" i.e unprecomittable policies) and . We require that there is some and s.t. 1. is a convex combination of and .[1] 2. is in the convex hull of where ranges over . The underlying decision problem is then an EDT decision problem with the belief . as above with is called formally causal when for any and (Is there a natural generalization without the assumption ? I don't know.) Proposition: EDT is precommitment-stable in formally causal precommitment games. That is, in any such game there is which is EDT-optimal. For example, XOR blackmail can be formalized as an EDT precommitment game which is not formally causal and EDT is not precommitment-stable there (the only optimal policy is precommitting to reject). Definition: [EDIT: The treatment of CDT here is problematic, see child post.] A CDT precommitment game is a precommitment game which is also a CDT problem (in the sense that we are given and formally ca

2Vanessa Kosoy7mo

The above treatment of "CDT precommitment games" is problematic: the concept made sense in the context of "FDT to CDT translation" but it's not clear what it's doing here (i.e. what is the first argument?) Here is a better treatment. Definition: A CDT decision problem is the following data. We have a set of variables and for each we have its range , its set of parents and its kernel The parent relation must induce an acyclic directed graph. We also have a selected subset of decision variables and a selected subset of outcome variables s.t. . For each there is a special element (denoting that the decision wasn't made) and we denote . We are a given a loss function ---------------------------------------- This is connected to our overall formalism by setting and . We also define The CDT counterfactuals and decision-rule are defined via a do-operator that forces to take the value unless the value was in which case it remains . Definition: A CDT precommitment game is a CDT decision problem in which there is some special (the precommitment decision) s.t. , denoting , 1. 2. For some we have (where denotes the decision to not precommit). 3. For every it holds that and is s.t. if has any value other than then takes the value . 4. For every , there is a special s.t. (i) (ii) (iii) is the only variable with parent (iv) is defined s.t. if has value or then has the same value as , whereas if has value then has the value . This is connected to our abstract notion of precommitment game by setting , and for . We define to hold whenever (i) for some (ii) (iii) for every , . The underlying decision problem of the precommitment game is constructed by deleting and identifying and in the obvious way. The game is said to be trivial when all variables with parent are of the form or . Proposition: CDT is precommitment-stable in trivial precommitment games. Definition: Given a CDT precommitment game with , its DDT-translation is defined by setting and Proposition: If is

Vanessa Kosoy's Shortform

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Vanessa Kosoy's Shortform

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