Matrix Donations

I just read a description on Wikipedia about matrix schemes – you know, where you get promised an iPod if you get other people to join? I was thinking that the basic motivator for people to join such a scheme, namely greed, could really be exploited for better purposes – such as raising donations for a good cause.

A simplified and less inflationary version of a matrix scheme could be described this way:

  1. Every participant pays N currency units into a pool, and gets appended to a reward list.
  2. Every time the number of participants is a multiple of X, the first participant on the reward list is paid a reward of M currency units, and subsequently removed from the list. The remaining participants consequently move up one place on the list.
  3. Continue at #1

So why would people join such a scheme?

  • If M is sufficiently larger than N, the return of investment may prompt your greed.
  • Your chance of winning is fairly good, and can be improved by your actively finding participants – provided enough people participate after you. If you assume that an infinite number of people participate, you can be certain of your reward. As that’s not likely to happen, let’s try to view this from a different angle: the earlier you participate, the higher the chance that you’ll win. The reverse is also true, the later you participate, the higher the chance that you’ll lose1.
  • If N is sufficiently small, you’ll likely not miss the amount much if you lose2.

To summarize: you’re more likely to win than in a lottery, and if you don’t win, you know it’s for a good cause.

  1. Either way, the chances of you winning are likely higher and more easily calculated than when you play the lottery, for example []
  2. Interestingly enough, the same reasoning applies for regular donations – give an amount that doesn’t hurt you []