This is an open statistics question for anyone who can help. I'm trying to build a model/formula that allocates a % of x to each member of a group. The model should act as a welfare model where the % that is allocated to each member depends negatively on how much of the resources that member already has. Put differently if a group member already has a more than an equal share of the resource then the allocation should be smaller than an equal % allocation. Furthermore the degree by how much this is smaller depend on how far above the mean that member is. The idea is to produce a more equal distribution after the allocation than before the allocation. Does anyone know a model that can solve this problem?
This should be a comment but I dont have the points for it so here goes.
You could look at the empirical cumulative distribution function of the current resource distribution to get a sense of how "fair" or "unfair" the current resource allocation is. A straight, diagonal line means that the resource allocation is completely even, the less straight it is, the less even.
One solution to the problem could then be to allocate the inverse of said function to each member (if you want the distribution to become more "fair").
The Lorenz curve is essentially the same thing but coming from economics.