Introduction
The nature of this hierarchical network is based on the concept of Multi-Level Marketing strategy.
Example 1 - Unfair Situation
Ancestor receives 1 point for every descendant present in its network.
- Parent (3 points)
- Child A (2 points)
- Grandchild A
- Grandchild B
- Child A (2 points)
Parent will always receive more points than each of its descendant >:(
So what I have in mind is decreasing the point each descendant gives as the level increases.
Example 2.1 - Fairer Situation
Formula: 1/0.5^(level-1)
Parent is level 0, child is level 1, grandchild is level 2 and so on...
Each child gives 1 point and each grandchild gives 0.5 point.
- Parent (2 points)
- Child A (2 points)
- Grandchild A
- Grandchild B
- Child A (2 points)
Example 2.2
When Child A invites 1 more person.
- Parent (2.5 points)
- Child A (3 points)
- Grandchild A
- Grandchild B
- Grandchild C
- Child A (3 points)
This is fairer to Child A who had invited 3 person than Parent who had only invited 1 person, while still giving some cuts to the Parent.
Update 1 - 12/11/2012 11:16AM
In the event a ranking element is involved
From Example 1, the Parent only needs to invite just one person and its descendants will be doing all the "dirty work" for it. The Parent will always rank first no matter how hard/many its descendant invites. This is unfair to the descendants.
From Example 2, even though the Parent is always receiving cuts from its descendants, it is possible for the descendants to score and rank higher than the Parent. This is fairer to the descendants.
Requirements
Parent receives 1 point for every child that he/she has invited.
Ancestors(Parent, Grandparent, Great Grandparent...) receive reduced points for every descendants(Child, Grandchild, Great Grandchild...) present in their network.
Challenge: Any formula suggested must be able to prove that it indeed will guarantee fairness throughout the network.
Question: I'm looking for theory/study/statistical record to justify the reason why I use a certain formula instead of other formula (e.g 1/level). Is there any existing solution/formula that fulfills these requirements?
P.S. It does not have to be the formula given in Example 2, it was just an example.
Any help would be appreciated, thank you! :)