# What is the scope of the [utility] tag?

It was pointed out to me that the description of the is ambiguous. It currently reads:

A tag for all questions involving a type of utility function.

With a wiki which is even worse:

STUB!!! See utility function.

Since I figured that I don't have enough knowledge about this topic, I wanted to poll someone else's opinion and expertise to help and clarify this tag's proper usage (or necessity, in case usage is too ambiguous).

• To people who know what a utility function is, the tag description looks fine. However, I've to agree the tag wiki is way too terse... – achille hui Dec 6 '17 at 11:32
• @achillehui: The problem is that some people don't know what a utility function is, and the excerpt should provide a quick guideline. For example, that these questions are often tagged under something like finance, or economics, or so on. And not under functional analysis, or whatever. – Asaf Karagila Dec 6 '17 at 11:34
• @AsafKaragila Results related to utility theory might occur in functional analysis, measure theory, and even -gasp- set theory. – Michael Greinecker Dec 6 '17 at 12:27
• @Michael: Sure. I was just tossing tags for sake of example... – Asaf Karagila Dec 6 '17 at 12:32
• @Michael: Not to mention, the Wikipedia links literally opens with "In economics, utility is a measure of preferences over some set of goods"... – Asaf Karagila Dec 6 '17 at 13:19
• (Admittedly, I'm not sure what the downvote signifies in this case. Is it against having a discussion on tags? Is it against having a discussion on this tag? Is it something else? Please, enlighten me!) – Asaf Karagila Dec 6 '17 at 14:43
• "What is the utility of [utility]?" :-) – quid Dec 6 '17 at 19:07
• @quid: Ah, crap. I can't believe I missed that one!!! – Asaf Karagila Dec 6 '17 at 19:21
• Surely, the usage of every other "utility" other than the function itself is off-topic here, but can we have it renamed as [utility-function] for clarity? – Andrew T. Dec 11 '17 at 4:52

A utility function is a numerical representation of an agents preferences. If $\succeq$ is a preference relation on a set of alternatives $X$, then the function $u: X\to\mathbb{R}$ is a utility representation of $\succeq$ if $x\succeq y$ holds if and only if $u(x)\ge u(y)$. In many cases, one might want the representation to be of a special form. For example, if $X$ is the set of probability distributions on a finite set $F=\{y_1,\ldots,y_n\}$ so that $x=(p_1,\ldots,p_n)$, then an expected utility representation of $\succeq$ is of the form $$u(x)=\sum_{i=1}^n p_iv(y_i)$$ for some function $v:F\to\mathbb{R}$.