I have a situation where we are given a set of objects each with a numeric score stating it's importance. Let's call them Level 1 (or L1) objects.
There is another set of objects that are similarly scored/ranked. Let's call them L2 (for level 2). Each L2 object belongs to exactly one parent (i.e. L1 object). Thus we have a tree where the root is just an empty node (L0), so to speak, parents at L1, their children at L2 and so on.
The question is what is a "correct" way of scaling the scores of the children as per their parents so that the sum of scores at each level is 1?
Approach currently used:
- Normalize L1 so that scores are between 0 and 1 and add up to 1
- Normalize the children of each node in L1 so that sum of children = 1 and then multiply (scale) by the parent's score.
- Repeat for every level
This however has an anomaly in that if a particular parent has only one child, then the score of that child is equal to that of the parent - which makes the resulting prioritization skewed. It seems the less children that a parent has the higher the child scores and conversely if there are more children each child gets a smaller score.
Is there a more "correct" way of handling hierarchical scaling/prioritization or do we just accept this as an anomaly of mathematics and 'ignore' outliers?
UPDATE: Clarification on what is meant by 'score is influenced by parent' - It implies that although the child levels can be scored/prioritized independent of their parents (i.e. by comparing with each other perhaps) the final score should be 'scaled by' (read influenced by) that of their parent.
- Parent A $(5)$
- child x $(2)$
- child y $(3)$
- child z $(6)$
- Parent B $(8)$
- child p $(6)$
- child q $(4)$
- child r $(3)$
- child s $(5)$
- ...and so on**
(The numbers in parenthesis are the scores of that item)
So all parents could be scored/prioritized independently and so their children and children's children (not shown). The scoring scheme needs to be such so as to prioritize these items in a mathematically correct manner. A simple scheme would be to multiply the score of each child by that of the parent (similar to solution shown above)
Context: This is a prioritization scheme for ordering groups and must also lend itself for ordering the children within the subgroups and so on. Items at a particular level i.e. all parents or all children in the above example are 'comparable' i.e. a comparing A and s make no sense but x and s does.