Sure, so everyone’s utility function puts a value 1 (ETA: or a value x > 0 that varies unboundedly as a function of some feature of the universe) on all possible universe-histories where they take the actions they actually take, and 0 on all other possible universe-histories. I don’t think that’s an answer.
Sure, so everyone’s utility function puts a value 1 on all possible universe-histories where they take the actions they actually take, and 0 on all other possible universe-histories.
Only a reductio ad absurdum. The Texas Sharpshooter Utility Function is completely useless, and is not a utility function.
It is useless, because it makes no predictions. It does not constrain your expectations in any way.
It is not a utility function in the sense of the Utility Theorem, because utility functions in that sense are defined not over outcomes but over lotteries of outcomes. Extending a TSUF to lotteries by linear interpolation does not work, since lotteries can themselves be conducted in the real world, and all real occurrences of such lotteries are given a value of 0 or 1 by the TSUF.
Utility theory therefore does not apply to the TSUF. Calling it a utility function does not make it one.
It is like defining a universal theory of physics by assigning “true” to whatever happens and “false” to whatever does not.
and what attitude were you expressing to steven0461′s negative judgement about the TSUF when you said this:
Acknowledgement that yes, technically, one of the infinite number of utility functions which can result in a given behavior over time for a given input happens to be the one he mentions.
Sure, so everyone’s utility function puts a value 1 (ETA: or a value x > 0 that varies unboundedly as a function of some feature of the universe) on all possible universe-histories where they take the actions they actually take, and 0 on all other possible universe-histories. I don’t think that’s an answer.
That’s one way to make the reducio, yes.
Only a reductio ad absurdum. The Texas Sharpshooter Utility Function is completely useless, and is not a utility function.
It is useless, because it makes no predictions. It does not constrain your expectations in any way.
It is not a utility function in the sense of the Utility Theorem, because utility functions in that sense are defined not over outcomes but over lotteries of outcomes. Extending a TSUF to lotteries by linear interpolation does not work, since lotteries can themselves be conducted in the real world, and all real occurrences of such lotteries are given a value of 0 or 1 by the TSUF.
Utility theory therefore does not apply to the TSUF. Calling it a utility function does not make it one.
It is like defining a universal theory of physics by assigning “true” to whatever happens and “false” to whatever does not.
It wasn’t an example I gave. I care almost nothing about Straw Texas Sharpshooters.
What were you referring to when you claimed:
and what attitude were you expressing to steven0461′s negative judgement about the TSUF when you said this:
Acknowledgement that yes, technically, one of the infinite number of utility functions which can result in a given behavior over time for a given input happens to be the one he mentions.
Did you mean to claim that some other utility function also results in the given behavior, but isn’t useless like the TSUF is?
Someone seems to have voted down the entire subthread; I wonder why.
An infinite number of of utility functions, some of them simpler and more useful than others.