I’m not so sure of that, since most of the people that use “utility function” and “prior” can’t seem to agree on what they mean. They seem to be more terms of art; the art of showing off.
Huh? A utility function is a map from states/gambles/whatever to real numbers that respects preferences. A prior is a probability assigned without conditioning on evidence. Maybe some terms people use here are for showing off, but these two happen to be clear and useful.
A prior is a probability assigned without conditioning on evidence.
A prior is a probability distribution assigned prior to conditioning on some specific data. If I learn data1 today and data2 tomorrow, my overnight probability distribution is a posterior relative to data1 and a prior relative to data2.
The reason I nitpick this is because the priors we actually talk about here on LW condition on massive amounts of evidence.
More nitpicking: the data doesn’t really have to be “specified”—at least, it can be presented in the form of a black box with contents that are not yet known, or perhaps not yet even measured.
A utility function is a map from states/gambles/whatever to real numbers that respects preferences.
That’s not its only meaning. It’s not, for example the definition that a hedonist utilitarian would give (net pleasure-over-pain is not equivalent to preference; unless you’re giving preference a very broad interpretation, in which case you’ve just shifted the ambiguity back a level.)
I could go trawling through the literature to get you examples of non-preferentist usages of the words “utility function”, but if you’re willing to take my word for it, I can assure you that they’re pretty common (especially in happiness economics and pre-ordinalist economics, but also quite broadly apart from that). Indeed, it would be very strange if e.g. the hedonist account were a valid definition of utility, but no-one had thought to describe a mapping from states of the world into hedonist-utility as a utility function.
Guess I’ll take your word for it. Not sure I remember seeing that usage for “utility function” on LW, though.
ETA: It gets kind of confusing, because if I prefer that people are happy, their happiness becomes my utility, but in a way that doesn’t contradict utility functions as a description of preferences.
Not sure I remember seeing that usage for “utility function” on LW, though.
Many uses are ambiguous enough to encompass either definition. If you aren’t aware of the possible ambiguity then you’re unlikely to notice anything awry—at least up until the point where you run into someone who’s using a different default definition, and things start to get messy. (This has happened to me a couple of times.)
I’ve argued that utilitarians should probably employ surreal-valued utilitiy functions. However, that is hardly a major disagreement. It would be like the creationists arguing that evolution was a theory mired in controversy because of the “puctuated equilibrium” debate.
I’m not so sure of that, since most of the people that use “utility function” and “prior” can’t seem to agree on what they mean. They seem to be more terms of art; the art of showing off.
Huh? A utility function is a map from states/gambles/whatever to real numbers that respects preferences. A prior is a probability assigned without conditioning on evidence. Maybe some terms people use here are for showing off, but these two happen to be clear and useful.
A prior is a probability distribution assigned prior to conditioning on some specific data. If I learn data1 today and data2 tomorrow, my overnight probability distribution is a posterior relative to data1 and a prior relative to data2.
The reason I nitpick this is because the priors we actually talk about here on LW condition on massive amounts of evidence.
More nitpicking: the data doesn’t really have to be “specified”—at least, it can be presented in the form of a black box with contents that are not yet known, or perhaps not yet even measured.
That’s not its only meaning. It’s not, for example the definition that a hedonist utilitarian would give (net pleasure-over-pain is not equivalent to preference; unless you’re giving preference a very broad interpretation, in which case you’ve just shifted the ambiguity back a level.)
I’ve seen that called “utility” but never a “utility function”.
I could go trawling through the literature to get you examples of non-preferentist usages of the words “utility function”, but if you’re willing to take my word for it, I can assure you that they’re pretty common (especially in happiness economics and pre-ordinalist economics, but also quite broadly apart from that). Indeed, it would be very strange if e.g. the hedonist account were a valid definition of utility, but no-one had thought to describe a mapping from states of the world into hedonist-utility as a utility function.
Googling “experienced utility function” turns up a few examples, but there are many more.
Guess I’ll take your word for it. Not sure I remember seeing that usage for “utility function” on LW, though.
ETA: It gets kind of confusing, because if I prefer that people are happy, their happiness becomes my utility, but in a way that doesn’t contradict utility functions as a description of preferences.
Many uses are ambiguous enough to encompass either definition. If you aren’t aware of the possible ambiguity then you’re unlikely to notice anything awry—at least up until the point where you run into someone who’s using a different default definition, and things start to get messy. (This has happened to me a couple of times.)
I’ve argued that utilitarians should probably employ surreal-valued utilitiy functions. However, that is hardly a major disagreement. It would be like the creationists arguing that evolution was a theory mired in controversy because of the “puctuated equilibrium” debate.