Ruby v1.9.0Sep 12th 2020 (+17/-16) Import fix-up, fix lack of indentation with quote boxes. Add in some links to counterfactual tag and Scott's user page. 2

The **5-and-10 problem** addresses the question of how to construct a theory of logical ~~counterfactuals.~~counterfactuals.

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Created by Jake Miller at 4y

- Two Major Obstacles for Logical Inductor Decision Theory by Scott Garrabrant

The algorithm A~~ that~~ reasons something like:

Let there be a decision problem which involves the choice between $5 and $10, a utility function that values the $10 more than the $5, and algorithm A optimizing for this utility function.

Another version, sometimes known as the heavy ghost problem, ~~is~~raises a ~~problem in~~difficulty with certain types of UDT-like decision theories, when the fact that a counterfactual is known to be false makes the algorithm implement it.

~~Specifically, let there be a decision problem which involves the choice between $5 and $10, a utility function that values the $10 more than the $5, and an~~The algorithm A that reasons something like:

The 5-and-10 problem addresses the question of how to construct a theory of logical counterfactuals.

Another version, sometimes known as the heavy ghost problem, is a problem in certain types of UDT-like decision theories, when the fact that a counterfactual is known to be false makes the algorithm implement it.

~~Another version,~~version, sometimes known as the heavy ghost problem, is a problem in certain types of UDT-like decision theories, when the fact that a counterfactual is known to be false makes the algorithm implement it.

~~The five-~~One version of the 5-and-~~ten~~10 problem~~ (sometimes~~ is "I have to decide between $5 and $10. Suppose I decide to choose $5. I know that I'm a money-optimizer, so if I do this, $5 must be more money than $10, so this alternative is better. Therefore, I should choose $5."

Another version, sometimes known as the heavy ghost ~~problem)~~problem, is a problem in certain types of UDT-like decision theories, when the fact that a counterfactual is known to be false makes the algorithm implement it.

Jake Miller v1.0.0Oct 19th 2012 (+1194) Created page with "The five-and-ten problem (sometimes known as the heavy ghost problem) is a problem in certain types of UDT-like decision theories, when the fact that a counterfactual is known to..." 1

The five-and-ten problem (sometimes known as the heavy ghost problem) is a problem in certain types of UDT-like decision theories, when the fact that a counterfactual is known to be false makes the algorithm implement it.

Specifically, let there be a decision problem which involves the choice between $5 and $10, a utility function that values the $10 more than the $5, and an algorithm A that reasons something like:

`"Look at all proposition of the type '(A decides to do X) implies (Utility=y)', and find the X that maximises y, then do X."`

When faced with the above problem, certain types of algorithm can reason:

`"The utility of $10 is greater than the utility of $5. Therefore I will never decide to choose $5. Therefore (A decides to do 'choose $5') is a false statement. `

`Since a false statement implies anything, (A decides to do 'choose $5') implies (Utility=y) for any, arbitrarily high, value of y. `

`Therefore this is the utility maximising decision, and I should choose $5."`

That is the informal, natural language statement of the problem. Whether the algorithm is actually vulnerable to the 5-and-10 problem depends on the details of what the algorithm is allowed to deduce about itself.

See also: Logical Uncertainty, Logical InductionLet there be a decision problem which involves the choice between $5 and $10, a utility function that values the $10 more than the $5, and algorithm

Aoptimizing for this utility function.