Posts from The Ultimate Question of Life, the Universe, and Everything

Moderators, please pin this in important!

So, here is the formulation of that very question.

The answer is very simple. Such polls should provide maximum info about HWers' tastes. To get maximum info, the number of answer options in the poll should be as large as possible. So, it's time to turn to combinatorics, namely the concept of combinations!

In combinatorics, a combination from n {\displaystyle n} by k {\displaystyle k} is a set of k {\displaystyle k} elements chosen from a given set containing n {\displaystyle n} distinct elements.

Well, that's not hard, it's not Newton's binomial... Oh wait, it actually is exactly that.

The number of combinations from n {\displaystyle n} by k {\displaystyle k} equals the binomial coefficient

This thing shows us how many different answers can be given in a poll where n is the number of items in the poll, and k is how many checkboxes at once the poll author has allowed us to tick.
It is precisely the number of combinations that we need to maximize so that the poll brings the greatest amount of information about forum members.
Generally speaking, it becomes quite obvious that for this, k needs to be chosen as something in between.

Pascal's triangle hints at this

Then the optimal number of how many answers one can choose seems like this:

Number of answer options in the poll = n
How many you can pick at once = k

n k
2 1
3 1
4 2
5 2
6 3
7 3
8 4
9 4
10 5
11 5
12 6
13 6
14 7
......

In other words, divide n in half and round either way. I chose rounding down because changing this number downward seems most reasonable (it's easier to choose).

Actually, when should one deviate from this rule in favor of smaller k? The answer is also obvious — if you believe that the number n is actually exaggerated.

A simple example: my Arknights poll contained 15 answer options, but two of them were guys. This means that guys entering the thread definitely won't choose those answer options. Well, girls entering the thread, on the contrary, will tend to choose the guys, while they are more indifferent to the girls. Based on this, the estimated value of n is 13, not 15. The estimated value of k in that case = 6.

Should I have then allowed choosing up to 6 answer options in the poll?

Well, perhaps still no. An additional consideration (though less clear-cut and mathematical) could be the estimated quality of the content. If you look at the girls in the poll and realize that yes, they're all just top-notch super-top-tier, then you should strictly follow the instruction and take k=n/2. Otherwise, you need to realize that some HWers won't want to pick so many answer options and will either deliberately choose fewer (ruining your statistics), or will suffer the agony of choice among several bad (for them) options. And our goal is not to torment anyone.

Based on this, when creating a poll, you need to subjectively determine an additional coefficient m, taking it within the range 0 < m <= 1.
In my Arknights poll, such a coefficient can be pulled out of thin air as 0.5 — and get exactly the choice of 3 out of 15.

That is, the final formula

k = n * m / 2

Note that if your m is too small, then either you're estimating it incorrectly, or there's something wrong with your content (why make a poll about insufficiently good girls?).

Thanks for your attention. Feel free to ask questions.

I think two is too much, and it should be divided by three, although I allow for rounding up. Otherwise, I agree.

Wouldn't that be a bit too much?

No.

(like a meme image with levels of brain development, which I'm too lazy to create)

Level 1: play gacha games about anime girls
Level 2: min-max in gacha games about anime girls
Level 3: min-max in polls about anime girls from gacha games

Dude, you started out so well and strictly, but then two "kuns" appeared from nowhere, and subjective weights came into play. For simplicity's sake, let's not mix heterogeneous objects.

First of all, I disagree with the goal of the research. We shouldn't provide information about the tastes of Heroes fans, but rather conduct an expert evaluation of the images by the Community.
Of course, we could set up an Olympic-style system with rounds, and that has already been done.

But our goal is still not to rank the objects, but simply to narrow down the selection. Moreover, I think that experts are also people, and they reach a certain point of saturation.

Of course, hysteresis loop immediately comes to mind – it’s like many gentle graphs.

I figured out empirically, and here's a nice formula:
y = round( log3(x) * 1.7 )

Attachment 64708

2	1
3	2
4	2
5	2
6	3
7	3
8	3
9	3
10	4
11	4
12	4
...	...
18	4
19	5
20	5
...	...
34	5
35	6

Interesting...
Well, it's impossible to avoid subjectivity here, because objectively, you just need to divide by two; the math doesn't lie. But without additional restrictions or weighting coefficients, it will be difficult for voters.
And why hysteresis, and where did the formula come from? It looks good, although I would use a less gradual logarithm (5 out of 34 seems a bit small to me; I would take 7).

Why hysteresis and where does the formula come from?

Hysteresis is simply an association with a graph that is quite proportional in the middle, but becomes more gradual at the edges.

In my opinion, that's how voting should be. Choosing 50 out of 100 options is pointless. And you can't keep dozens of images in your head. Seven out of twenty and seven out of fifty are almost the same. I think the only thing that matters is how much you can remember.

COMMANDER, INTERFERENCE, 504. DO NOT ... PANIC.