Pyramid Schemes I

Some more thoughts lifted from my ongoing work on my next book.

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The term “pyramid scheme” is sometimes used loosely as a synonym for “Ponzi scheme,” and their meanings are related, but they are in principle distinct.

A pyramid scheme is a business model in which payments are promised to one level of participants for the act in bringing in another level of participants. You, dear reader, have no doubt received the simplest form of a pyramid pitch as chain letters or their e-mailed equivalents. “Send me a dollar. Also, send out six copies of this email to friends of yours, You will get $6 as a return on your $1 investment.” Each of those six people will soon be in the same situation if you comply. It isn’t exactly a Ponzi scheme, although it shares the unsustainability thereof.

What’s the difference exactly? In a pyramid scheme, the originator can make a clean get-away. Once you’ve found your own six suckers, you’ve made your profit and the deal is done as far as you’re concerned. The issue of unsustainability will only bother those further down (though not too much further down, as we’ll see in a second).

In a ponzi scheme, the originator never gets away with the loot. He is always scrambling to raise a new round—and although he presumably skims some off for himself each time – he can only keep it going by returning most of it to the money shredder he has dressed up as a business, giving it out as ‘interest’ or ‘profits’ or ‘redemptions’ or whatever to the earlier ‘investors.’

The arithmetic of a pyramid scheme is a lot simpler than that for a ponzi deal: fewer variables.

The mathematics to grasp here is that of exponential increase. Assume person 0 starts the scheme and sends out letters to persons 1 – 6, and they comply with the message. Assume just 13 different links in the chain and no overlap as to the recipients of the different links. The pyramid looks like this:

LINK RECIPIENTS

6
36
216
1296
7776
46656
279936
1679616
10077696
60466176
362797056
2176782336
13060694016.

That last figure, one we could express with more economy as, 6¹³or just approximately as ‘more than 13 billion,’ represents a larger population than the planet earth. The number of live humans passed 7 billion in 2011 and was just a little above 7.1 billion last time I checked, in May 2013.

Relatedly, the population of the United States is about 315 million, so the recipients of the 11^th link in our chain will exceed that figure.

The practical lesson here is that if you receive a chain mail, or any sort of dressed-up invitation to participate in a pyramid, take it to authorities or, at the least, to a paper shredder. That is not a comment about your legal obligations. Assuming them away, it is a comment about probability. Since the population of the largest countries of the world, or the world itself, can’t support such a scheme for long, the odds are very good that anyone you know who would be susceptible to your appeal has gotten the same letter before you have, has already been tapped out and will receive your own request with something less than enthusiasm.

The Ponzi and pyramid sort of scheme can be combined. Madoff and his feeder funds indicate how this might be done. The culpability of the managers of the feeder funds is still a matter of controversy, but it seems fair to credit Madoff with the invention of the multi-level Ponzi scheme.

Pyramid schemes are illegal in many countries, though the legal theories under which they are prosecuted vary. In the U.S., one of their legal problems is that they fall afoul of a dilemma with securities regulators. If I have sent you the above note, have I offered you an investment contract, that is, a security, or have I not? Either the pyramid operators register participation in their operation as a “security” or they don’t.

If they do register the schemes as securities, they become subject to a variety of reporting requirements that no pyramid scheme wants to endure. Thus, they generally don’t’ register. Yet this puts them on legally untenable footing: pyramid schemes as such are securities, in the case imagined above we have an investment contract in which the buyer of the contract hopes for 400 percent return. Failure to register a security as such is a federal offense.

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