John's Elephants and the Many Peanuts
Here it goes:
John is the owner of a hungry elephant.
John has 10 friends, and each one of his 10 friends has 10 friends.
Now, whenever one of John's 10 friends gets together with his own 10 friends (so that there are eleven of them) they each put 10 peanuts into the bowl. So that group collects 110 peanuts every week.
Each of John's friends gets together with their 10 friends each week, and they also collect 110 peanuts apiece. Thus, each week, 1100 peanuts is collected.
Then they start putting their peanuts in a warehouse to keep track.
One day, one of John's friends, Barry, says...why don't we extent this? Why don't each one of our friends get together with 10 of their friends once a week, like we, your ten friends, are already doing? Like a multi-level marketing scheme.
John replies, "that would be fine, but in order to make it worth your time, I think you should get a cut of the peanuts."
John would like to pay each one of his ten friends a certain amount of peanuts, based on how many groups they are overseeing.
He thinks, "what if I give each person 1,000 peanuts a week if they oversee 25 groups. After all, 25 groups are bringing 2,750 peanuts a week. Surely I can give them a thousand and have 1,750 left over for other purposes."
The problem is, if John makes this offer to everybody involved, there will inevitable be double dipping. In other words, if Barry gets to 100 groups, and one of his "subordinate" friends, Aaron, has 50 groups, then John would have to pay both Barry and Aaron, even though there is an overlap between Barry's 100 and Aaron's 50.
How can John "pay" his friends some peanuts, to make it worth their time, without eventually paying out more in peanuts than he is receiving for his elephant? How can he create a compensation system that is sustainable? And can the solution be reduced to a formula?