If you have a utility function, I can predict your preferences from it. If I want to know what you’d pick when given the choice between an apple or a banana, I don’t have to ask you. I can just consult your utility function and see which ranks higher.
If you’re looking for a utility function that reproduces human behavior in all contexts, I’d say the empirical evidence is overwhelming that humans don’t have utility functions, bounded or otherwise.
If you’re looking for a utility function that merely reproduces human behavior approximately, how good does the approximation have to be in what circumstances? Does the utility function that someone “has” reproduce his behavior when the behavior is mediated by conscious philosophizing, or when it’s mediated by his gut? If conscious philosophizing, how much and what kind of conscious philosophizing? If gut, what framing of a given decision problem causes someone’s gut to make those decisions that are reproduced by the utility function that he “has”? (For example, if someone is more keen on paying some price to save 20 out of 100 lives than on paying the same price to allow 80 out of 100 people to die, does the utility function that he “has” say do it, or not?)
If you’re looking for a utility function that reproduces human behavior in all contexts, I’d say the empirical evidence is overwhelming that humans don’t have utility functions, bounded or otherwise.
Practically, I agree, but I would maintain that people do have utility functions—it’s just that they are so complex that they are impossible to write down as a neat mathematical expression, just like it’s practically impossible to construct a function to accurately predict next week’s weather.
But if we define the utility function as the relation between (many!) input variables and the ultimate behavior chosen, certainly it exists. Just like that illusive function for predicting the weather.
Might I suggest tabooing “utility function”? The phrase is used in this community at various levels of abstraction, and useful responses to your question depend on which level of abstraction you intend.
No, a utility function is a perfectly well-defined mathematical object. The question is what it means for a human to “have” such an object; so “have” is the word we should be tabooing.
Does Abraham Lincoln have a six-dimensional vector space? Does Spain have an abelian group? The question “do humans have a bounded utility function” is kind of like that.
Does Abraham Lincoln have a six-dimensional vector space? Does Spain have an abelian group? The question “do humans have a bounded utility function” is kind of like that.
“Does Abraham Lincoln have a personality?” would be somewhat analogous. (By somewhat I mean ‘more’.)
If you’re looking for a utility function that reproduces human behavior in all contexts, I’d say the empirical evidence is overwhelming that humans don’t have utility functions, bounded or otherwise.
A utility function can reproduce any combination of behavior.
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.
What do you mean by “have”?
If you have a utility function, I can predict your preferences from it. If I want to know what you’d pick when given the choice between an apple or a banana, I don’t have to ask you. I can just consult your utility function and see which ranks higher.
If you’re looking for a utility function that reproduces human behavior in all contexts, I’d say the empirical evidence is overwhelming that humans don’t have utility functions, bounded or otherwise.
If you’re looking for a utility function that merely reproduces human behavior approximately, how good does the approximation have to be in what circumstances? Does the utility function that someone “has” reproduce his behavior when the behavior is mediated by conscious philosophizing, or when it’s mediated by his gut? If conscious philosophizing, how much and what kind of conscious philosophizing? If gut, what framing of a given decision problem causes someone’s gut to make those decisions that are reproduced by the utility function that he “has”? (For example, if someone is more keen on paying some price to save 20 out of 100 lives than on paying the same price to allow 80 out of 100 people to die, does the utility function that he “has” say do it, or not?)
Practically, I agree, but I would maintain that people do have utility functions—it’s just that they are so complex that they are impossible to write down as a neat mathematical expression, just like it’s practically impossible to construct a function to accurately predict next week’s weather.
But if we define the utility function as the relation between (many!) input variables and the ultimate behavior chosen, certainly it exists. Just like that illusive function for predicting the weather.
How is rationality possible if people don’t have a utility function?
Might I suggest tabooing “utility function”? The phrase is used in this community at various levels of abstraction, and useful responses to your question depend on which level of abstraction you intend.
No, a utility function is a perfectly well-defined mathematical object. The question is what it means for a human to “have” such an object; so “have” is the word we should be tabooing.
Does Abraham Lincoln have a six-dimensional vector space? Does Spain have an abelian group? The question “do humans have a bounded utility function” is kind of like that.
“Does Abraham Lincoln have a personality?” would be somewhat analogous. (By somewhat I mean ‘more’.)
I’d personally phrase the answer more as ‘yes, but it’s actually 5-dimensional’ :)
A utility function can reproduce any combination of behavior.
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.