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

Moderators, please pin this in the important section!

So, here is the wording of that very question.

The answer is very simple. Such polls should provide maximum information about the tastes of HW players. To obtain maximum information, there must be a maximum number of answer options for the poll. This means it's time to turn to combinatorics, specifically the concept of combinations!

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

Well, this isn't hard, it's not like Newton's binomial... Oh wait, that's exactly what it is.

The number of combinations of n {\displaystyle n} taken k {\displaystyle k} is equal to the binomial coefficient

This little 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 the poll author allowed us to tick simultaneously.
It is precisely the number of combinations that we need to maximize so that the poll yields the greatest amount of information about the forum members.
Generally speaking, it becomes quite obvious that for this, k should be chosen as some kind of average.

Pascal's triangle hints at this

Then the optimal number of answers one can choose seems to be as follows:

Number of answer options in the poll = n
How many can be picked simultaneously = 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 in either direction. I chose rounding down because reducing this number seems more reasonable (it's easier to choose).

Specifically, 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 husbandos. This means that the husbandos visiting the thread certainly won't choose these options. On the other hand, the waifus visiting the thread will be inclined to choose husbandos, while they are more indifferent toward other waifus. Based on this, the estimated value of n is 13, not 15. The estimated value of k in this case = 6.

Should I have allowed up to 6 answer options in the poll in that case?

Well, perhaps still no. An additional consideration (though less clear and mathematical) could be the estimated quality of the content. If you look at the waifus in the poll and realize that yes, they are all absolutely top-tier, then you should strictly follow the instructions and take k=n/2. Otherwise, you must realize that some HW players won't want to pick so many options and will either intentionally choose fewer (ruining your statistics) or suffer the agony of choosing between several bad (for them) options. And our goal is not to torture anyone.

Based on this, when creating a poll, you should subjectively determine an additional coefficient m, taking it within the range 0 < m <= 1.
In my Arknights poll, such a coefficient could be arbitrarily taken as 0.5 — and that gives exactly a 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 are estimating it incorrectly, or there is something wrong with your content (why make a poll for insufficiently good waifus?).

Thank you for your attention. You may 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.