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One of this and one of that;
Don't you like my fancy hat?
When they looked at what they want,
I was found most elegant.

There's not much of me, you see;
But I'm quite meant to be.
In this social function you'll find:
I'm quite right every time.

Don't hang yourself upon my rhymes,
That will just waste all your time.
But try and find the banquet table:
The dish they're serving is quite fabled.

Hint:

The fancy hat is a red herring, I just wanted something elegant that rhymed.

Hint #2:

the hidden tag wasn't statistics, that's a little too ...specific.

Hint #3:

I guess technically there is a fancy hat, but you have to use your imagination.
(Yes, that is a valid hint)

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  • 2
    $\begingroup$ I am strongly against the usage of a hidden-tag tag. IMO, this is a meta tag and will eventually be removed from a question (if it's answered or not answered for a prolonged period). If you mean to hide tags, then please mention so in the body of the question, not in a new tag. $\endgroup$ – CodeNewbie Sep 16 '15 at 12:52
  • $\begingroup$ It was discussed in the meta boards, if you want to continue the discussion, that's the place to do it. $\endgroup$ – Kingrames Sep 16 '15 at 12:53
  • $\begingroup$ I agree with @CodeNewbie. This tag gives no clue at all, and any answer could be accepted. $\endgroup$ – ABcDexter Sep 16 '15 at 12:54
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    $\begingroup$ The answer to the meta discussion has also garnered more downvotes than upvotes, so I would think that this is something the community does not support. $\endgroup$ – CodeNewbie Sep 16 '15 at 12:56
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    $\begingroup$ Sounds like a one-to-one cocktail.. $\endgroup$ – Raystafarian Sep 16 '15 at 15:19
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I think the answer is

$\hat q$ (as far as I understand it, the estimate of the probability of failure in statistics)

One of this and one of that;

Refers to the practice of sampling in statistics -- take a small sample and base your estimate off of it.

Don't you like my fancy hat?

Refers to the circumflex (hat) on the letter q.

When they looked at what they want,
I was found most elegant.

This is the best (most elegant) way of estimating, given a small sample size.

There's not much of me, you see;

It's only a single letter.

But I'm quite meant to be.

Quite hints at the letter q.

In this social function you'll find:
I'm quite right every time.

Using $\hat q$ to derive an estimate is fairly accurate; another hint at the letter q.

Don't hang yourself upon my rhymes,
That will just waste all your time.

Don't take this poem too literally; instead look at all the q-words, and derive your answer that way.

But try and find the banquet table:

Banquet is another hint at the letter q.

The dish they're serving is quite fabled.

$\hat q$ is a well-known variable in statistics.

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  • $\begingroup$ From this, I wonder if it might be $\hat{p}$ instead. Generally you want success (p). $\endgroup$ – Aggie Kidd Sep 16 '15 at 15:52
  • $\begingroup$ @AggieKidd, feel free to submit your own answer, if you think that's the case. I picked $\hat q$ because I figured all the q-words were hints to the letter q. $\endgroup$ – GentlePurpleRain Sep 16 '15 at 15:54
  • $\begingroup$ Wow, this is really nice. I commend you on your efforts. I'll augment the riddle with some more clarification and some hints. $\endgroup$ – Kingrames Sep 16 '15 at 18:48
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π / PI / PIE

One of this and one of that; Don't you like my fancy hat?

π < Hat!

When they looked at what they want, I was found most elegant.

A Raspberry Pi is pretty elegant

There's not much of me, you see; But I'm quite meant to be.

A raspberry pi is small? Pi is a short word?

In this social function you'll find: I'm quite right every time.

π is a function?

Don't hang yourself upon my rhymes, That will just waste all your time.

Some of this is blah-blah filler stuff?

But try and find the banquet table: The dish they're serving is quite fabled.

Pie!

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  • $\begingroup$ How it this not the answer :) $\endgroup$ – redFur May 2 '18 at 19:20
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Totally ripping off/inspired by GentlePurpleRain's answer:

I think the answer is

$\hat p$ , the estimated probability of success in statistics.

One of this and one of that;

$\hat{p}$ is often used in binomial trials, which have either success or failure..

Don't you like my fancy hat?

Refers to the circumflex (hat) on the letter p, which signifies an estimate.

When they looked at what they want,
I was found most elegant.

Most people are interested in the probability of success p, but can't determine that exactly (at least frequentists). Thus, the hat makes it possible to estimate, and hats make things more elegant.

There's not much of me, you see;

It's only a single letter, and in many trials the probability for success may be small.

But I'm quite meant to be.

`The probability of something happening - meant to be - is p.

In this social function you'll find:
I'm quite right every time.

\hat{p} is the best estimator of the probability of success.

Don't hang yourself upon my rhymes,
That will just waste all your time.

Flipped upside down, a p may look like a noose hanging from something.

But try and find the banquet table:

p is often confusing in statistics because it is used to denote a lot of different things. Damn statisticians not having much imagination...

The dish they're serving is quite fabled.

p for p-values, probability, estimates of probability, etc...

All of this would lead me to guess that the "hidden tag" discussed in comments and in previous edits is:

Probability

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  • $\begingroup$ A lot of your findings are based on some solid logic, which is really nice. The thing you're looking for, however, is more than one letter. I wouldn't be so ambiguous as to say "there's not much of me" instead of "there's only one of me." $\endgroup$ – Kingrames Sep 16 '15 at 18:57
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My guess:

AI (Artificial Intelligence)

One of this and one of that; Don't you like my fancy hat?

One of this (I) and one of that (A) = AI

When they looked at what they want, I was found most elegant.

Humans want AI, and they are elegant.

There's not much of me, you see; But I'm quite meant to be.

There aren't many AIs so far, but they are inevitable in the near future.

In this social function you'll find: I'm quite right every time.

Some AIs can perform social functions / chatbots can reply with context to human users.

But try and find the banquet table: The dish they're serving is quite fabled.

AI has been written about for decades and so is 'fabled'.

Hint #3:

The A could be seen as a hat with some imagination.

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  • $\begingroup$ I'm not quite sure that they are right every time in social situations. Usually that's where they seem to go wrong. $\endgroup$ – Sensoray Apr 25 '18 at 15:27
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Are you...

a royal flush?

One of this and one of that; Don't you like my fancy hat?

a royal flush consists of 1 of each of the top cards in poker

When they looked at what they want, I was found most elegant.

a royal flush is all high numbers and contains all 3 of the royal cards (Jack, Queen, King)

There's not much of me, you see; But I'm quite meant to be.

In this social function you'll find: I'm quite right every time.

It's very rare to get a royal flush, but getting one will win you the game

Don't hang yourself upon my rhymes, That will just waste all your time. But try and find the banquet table: The dish they're serving is quite fabled.

Banquet tables could be used for playing poker. The dish could be referring to the rare hand or to winning the jackpot.

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0
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Are you

An Arrow

One of this and one of that;

It points at stuff.

Don't you like my fancy hat?

It has a cool umbrella-like hat when it is facing up.

When they looked at what they want,
I was found most elegant.

Maybe it is elegant when a arrow looks/points at what they want.

There's not much of me, you see;
But I'm quite meant to be.

It points to stuff?

In this social function you'll find:
I'm quite right every time.

You click the arrow to send a text and it usually sends.

Don't hang yourself upon my rhymes,
That will just waste all your time.
But try and find the banquet table:
The dish they're serving is quite fabled.

?, other than the "find" because an arrow can help you find your way?

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