I have to distribute a number, x, to a certain number of people, n. I know that I want to distribute the maximum, a, to the top person, and the minimum, b, to the lowest person.
My question is, what is a function given x, n, a, and b, that will evenly distribute n values between a and b between the x people.
For example: if I have 10,000 dollars, I want to give 1000 to the top earner and 200 to the bottom. How much do I give to each person in between so that the remaining 8,800 dollars are distributed proportional to the rank of the person?
What do you mean by evenly distribute?
In order of ratings, you give y more for each person
b, b + y, b + 2y, b + 3y, ... b + (n - 1)y?
Then x = nb + n(n - 1)y/2 = nb + n(a - b)/2.
So you can find y but x becomes fixed.
The problem is over determined.
So bottom gets b, top gets a and there is x - a - b
left for everybody else who gets (x - a - b)/(n - 2)?