(Thanks for your response! I’m pessimistic that this conversational subtree will lead to great insights for either of us, but am jotting down my scattered thoughts in case they’re of interest.)
It seems to me that you can represent a sequential setting as a one-shot Situation whose Action type is a function from “observations so far” (in your +50%/-40% example, List<"win"|"lose">) to “action I take in that sub-situation” (in your example, the fraction of my bankroll I bet on the next flip.
(...maybe you can’t do this transform if you violate dynamic consistency? But violating dynamic consistency seems Actually Crazy in a way that merely violating consequentialism isn’t. Something is deeply broken if you simultaneously think “I’m going to do X if Y happens” and “I know that after Y happens I won’t do X.”)
In your “fair coin, +50%/-40%” example: if I have the opportunity to play this game for 10 rounds, and my life savings are $100k, then I agree “always bet everything” seems like a bad plan, and optimizing for my median net worth at the end seems pretty reasonable.
...but if $100k is just the contents of my wallet, and I have $X in illiquid assets that can’t participate in this game… and $X is much larger than ($100k)x(1.5^10)… then optimizing for my median net worth at the end no longer seems reasonable.
My best guess at your resolution to this is something like “in the second case, 10 rounds isn’t necessarily sequential enough, you need a number of iterations that depends on X”; but me having an extra $100T at home doesn’t affect my preference ordering of outcomes, and it seems to me that a median-utility-based decision theory should be insensitive to the magnitude of [my illiquid savings] vs [my bankroll].
(Thanks for your response! I’m pessimistic that this conversational subtree will lead to great insights for either of us, but am jotting down my scattered thoughts in case they’re of interest.)
It seems to me that you can represent a sequential setting as a one-shot
SituationwhoseActiontype is a function from “observations so far” (in your +50%/-40% example,List<"win"|"lose">) to “action I take in that sub-situation” (in your example, the fraction of my bankroll I bet on the next flip.(...maybe you can’t do this transform if you violate dynamic consistency? But violating dynamic consistency seems Actually Crazy in a way that merely violating consequentialism isn’t. Something is deeply broken if you simultaneously think “I’m going to do X if Y happens” and “I know that after Y happens I won’t do X.”)
In your “fair coin, +50%/-40%” example: if I have the opportunity to play this game for 10 rounds, and my life savings are $100k, then I agree “always bet everything” seems like a bad plan, and optimizing for my median net worth at the end seems pretty reasonable.
...but if $100k is just the contents of my wallet, and I have $X in illiquid assets that can’t participate in this game… and $X is much larger than ($100k)x(1.5^10)… then optimizing for my median net worth at the end no longer seems reasonable.
My best guess at your resolution to this is something like “in the second case, 10 rounds isn’t necessarily sequential enough, you need a number of iterations that depends on X”; but me having an extra $100T at home doesn’t affect my preference ordering of outcomes, and it seems to me that a median-utility-based decision theory should be insensitive to the magnitude of [my illiquid savings] vs [my bankroll].
No response required!