This comes in two forms: one where you are free to reorder the owning set, and one where you are not.

If you are free to reorder the owning set, for any distribution of the commodity, you can find some fraction n for which the top n of the set has 1-n of the commodity. If every individual has the same amount, then n and n-1 are both 50%. The extremity of n can be used as a measure of the imbalance of the distribution. Note that in this version, n can always be chosen not to exceed 50% since if 60% of the people have 40% of the money that implies that the other 40% have 60% of the money...

The case where you are not free to reorder the owning set essentially describes the behavior of any nondecreasing function f such that f(0) = 0, f(1) = 1, and f(x)<1 for all x on the region (0,1). These functions can describe the amount of partial progress in a process that takes finite time. Look how much of the end goal you have accomplished after doing a fraction n of the work required to achieve that goal.

If filing your nails to perfection takes 1 minute each, how close to perfection do you get if you file each for 10 seconds? If building a hut takes a week, how much shelter do you get out of the first day's work?

So long as your progress is always positive, there will only be one point for which f(n) = 1-n, so you can construct a n/1-n rule from it. If the greater part of the benefit is upfront, then n will be low and 1-n high (probably the case with the nails, as you will have smoothed them out); if the greater part of the benefit comes only after most of the work, you can get n high and 1-n low (probably the case with the hut - a framework won't be all that useful for sleeping under).

In both cases, n cannot be 0 or 1. In the first case, that would imply that a) everyone has nothing, and b) no one (0% of the population) has everything (100% of the commodity), which is an unfortunate situation.

In the second case, n = 0 would imply that you don't need to do anything to achieve everything, and n = 1 would imply that even if you do everything you don't get anything done.

The common 20%-80% form is simply a common degree of imbalance.

I find it amusing that we have 2 "--mancer" at this node... death and dreams...