Constructing a complicated formula

Linear, quadratic, module, parametric equations

Constructing a complicated formula

Postby Guest » Wed Mar 13, 2019 3:10 pm

Hi there,

I have been wrapping my head around this for a while now, am wondering how to put together a formula that would do this, solving for a given person's amount out of 100 they get. This is out of a game theory matrix:

Everyone at point A receives 53/(number at A)
Everyone at point B receives 34/(number at B)
Everyone at point C receives 13/(number at C)

If all people are at the same point (all at point B for example), they just get 100/(number of people). Here's where it gets kind of tricky:
B is the middle point, so if half the people are at A, and half are at C, then everyone at A gets 53/(number at A) + 34/2/(number at A). and then everyone at C gets 13/(everyone at C) + 34/2/(number at C).

So two examples:
3 people at A, 2 at B, 1 at C:
The three at A each get 17.67
The two at B each get 17
The one at C gets 13

3 people at B, 2 at C, none at A:
The three at B get (all of A which is 53 + all of B which is 34 = 87) / 3 = 29
The two at C get 6.5 each

Is this possible to do, to create an equation given a number "n" of people?
Guest
 

Re: Constructing a complicated formula

Postby HallsofIvy » Fri Mar 15, 2019 8:07 am

Unfortunately, you are not saying this very clearly! You say, to start, "a given person's amount out of 100" and then say
"Everyone at point A receives 53/(number at A)
Everyone at point B receives 34/(number at B)
Everyone at point C receives 13/(number at C)".
My first thought when I read that was that point A was labeled "53" and that was how many points you got. But "/" often indicates division and perhaps you meant 53 divided by the number of people at A. Finally I realized that "out of 100" meant that there were 100 people and that perhaps this is an example where there are 53 people at A so everyone there get 53 points, there are 34 people at B so everyone there gets 34 points, and there are 13 people at C so every one there gets 13 points.

Then you say "Here's where it gets kind of tricky:
B is the middle point, so if half the people are at A, and half are at C, then everyone at A gets 53/(number at A) + 34/2/(number at A). and then everyone at C gets 13/(everyone at C) + 34/2/(number at C)."
Wait, if half the people are at A and half are at C doesn't that mean threre are 50 people at each so everyone get 50 points? Or was I right before that, at A, we get "53 points divided by the number of people at A"? But what does "34/2/(number of people at A)" mean? Is that "34/2= 17" divided by 50 (the number of people at A)? This seems to contradict what you said, or at least what I thought you said, before.

Finally, you say:
"So two examples:
3 people at A, 2 at B, 1 at C:
The three at A each get 17.67
The two at B each get 17
The one at C gets 13"
So now you have dropped the total of 100 people?. "17.67", I suspect, is 17.6666.... or 17 and 2/3. That is 53/3 so the "53" is NOT "the number of people at A" but simply a number of points associated with A and that is divided by 3 since there are 3 people at A? The one person at C gets 13 points because 13 is the number of points associated with C? The number of points associated with B is 34 and 34 divided by 2 is 17. It looks like you are saying that if there are x people at A, y people at B, and C people at C, then the people at A get 53/x points, the people at B get 34/y, and the people at C get 13/z points.

"3 people at B, 2 at C, none at A:
The three at B get (all of A which is 53 + all of B which is 34 = 87) / 3 = 29
The two at C get 6.5 each"
Because there are NO people at A, its 53 points are distributed to the people at B? and that is divided by the number of people at A? And, because there at 2 people at C each gets 13/2= 6.5? Why are the points from B given only to A and not divided equally between B and C? Is it because A is "next to" B but not C (so the positions are [i]linear[/b] and not cyclic?)? If that's true then if there were 2 people at A, no people at B, and 3 people at C, would the people at A get (53+ 34)/2= 43.5 points? And the people at C get (34+ 13)/3= 14 and 2/3 points? Or would we distribute only half the points from B to A and half to C so that the people at A get (53+ 17)/2= 35 poits and the people at B get (17+ 13)/3= 10 points?

HallsofIvy
 
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