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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).

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    $\begingroup$ 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... $\endgroup$
    – achille hui
    Dec 6, 2017 at 11:32
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    $\begingroup$ @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. $\endgroup$
    – Asaf Karagila Mod
    Dec 6, 2017 at 11:34
  • $\begingroup$ @AsafKaragila Results related to utility theory might occur in functional analysis, measure theory, and even -gasp- set theory. $\endgroup$
    – Michael Greinecker
    Dec 6, 2017 at 12:27
  • $\begingroup$ @Michael: Sure. I was just tossing tags for sake of example... $\endgroup$
    – Asaf Karagila Mod
    Dec 6, 2017 at 12:32
  • $\begingroup$ @Michael: Not to mention, the Wikipedia links literally opens with "In economics, utility is a measure of preferences over some set of goods"... $\endgroup$
    – Asaf Karagila Mod
    Dec 6, 2017 at 13:19
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    $\begingroup$ (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!) $\endgroup$
    – Asaf Karagila Mod
    Dec 6, 2017 at 14:43
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    $\begingroup$ "What is the utility of [utility]?" :-) $\endgroup$
    – quid Mod
    Dec 6, 2017 at 19:07
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    $\begingroup$ @quid: Ah, crap. I can't believe I missed that one!!! $\endgroup$
    – Asaf Karagila Mod
    Dec 6, 2017 at 19:21
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    $\begingroup$ 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? $\endgroup$
    – Andrew T.
    Dec 11, 2017 at 4:52

1 Answer 1

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I have edited the description and the tag-wiki. They are now:

For all questions involving utility function as used in economics and decision theory, including a study of their properties or how they can be used to represent preferences.

and

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 $v:F\to\mathbb{R}$.

respectively.

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